The Geneva Accords of 1954

The Geneva Accords of 1954 The Geneva Accords of 1954 were an attempt to end eight years of fighting between France and Vietnam. They did that, but they also set the stage for the American phase of fighting in Southeast Asia. Background Vietnamese nationalist and communist revolutionary Ho Chi Minh expected that the end of World War II on September 2, 1945, would also be the end of colonialism and imperialism in Vietnam. Japan had occupied Vietnam since 1941; France had officially colonized the country since 1887. Because of Hos communist leanings, however, the United States, which had become the leader of the western world after World War II, did not want to see him and his followers, the Vietminh, take over the country. Instead, it approved Frances return to the region. In short, France could wage a proxy war for the U.S. against communism in Southeast Asia. The Vietminh waged an insurgency against France which culminated in the siege of the French base in northern Vietnam at Dienbienphu. A peace conference in Geneva, Switzerland, sought to extricate France from Vietnam and leave the country with a government suitable to Vietnam, Communist China (a Vietminh sponsor), the Soviet Union, and Western governments. Geneva Conference On May 8, 1954, representatives of Democratic Republic of Vietnam (communist Vietminh), France, China, the Soviet Union, Laos, Cambodia, the State of Vietnam (democratic, as recognized by the U.S.), and the United States met in Geneva to work out an agreement. Not only did they seek to extricate France, but they also sought an agreement that would unify Vietnam and stabilize Laos and Cambodia (which had also been part of French Indochina) in the absence of France. The United States committed to its foreign policy of containment of communism and determined not to let any part of Indochina go communist and thereby put the domino theory in play, entered the negotiations with doubt. It also did not want to be a signatory to an agreement with the communist nations. Personal tensions were also rife. U.S. Secretary of State John Foster Dulles reportedly refused to shake the hand of Chinese Foreign Minister Chou En-Lai. Main Elements Of the Agreement By July 20, the contentious meeting had agreed to the following: Vietnam would be divided in half along the 17th Parallel (in the thin neck of the country).The Vietminh would control the northern section, the State of Vietnam would control the south.General elections would occur in both north and south on July 20, 1956, to decide which Vietnam would govern the whole country. The agreement meant the Vietminh, who occupied significant territory south of the 17th Parallel, would have to withdraw to the north. Nevertheless, they believed that the 1956 elections would give them control of all Vietnam. A Real Agreement? Any use of the term agreement with respect to the Geneva Accords must be done loosely. The U.S. and the State of Vietnam never signed it; they simply acknowledged that an agreement had been made between other nations. The U.S. doubted that, without United Nations supervision, any election in Vietnam would be democratic. From the outset, it had not the intention of letting Ngo Dinh Diem, president in the south, call the elections. The Geneva Accords got France out of Vietnam, certainly. However they did nothing to prevent an escalation of discord between free and communist spheres, and they only hastened American involvement in the country.

Analysing Changes Needed To Reduce Domestic Violence Social Work Essays

Analysing Changes Needed To Reduce Domestic Violence Social Work Essays Analysing Changes Needed To Reduce Domestic Violence Social Work Essay Analysing Changes Needed To Reduce Domestic Violence Social Work Essay The purpose of this assignment is to foreground the job of domestic force in the London Borough of Barking and Dagenham. Domestic force is any incident of endangering behavior, force or maltreatment ( psychological, physical, sexual, fiscal or emotional ) between spouses or household members, irrespective of gender or gender ( Hester and Westmarland, 2005 ) . Harmonizing to the British Crime Survey ( 2009 ) there were 293,000 incidents of domestic force in 2008/2009 in the UK. ( Cited by The National Health Service { NHS } , 2009 ) . As domestic force is likely to be under-reported, the true figure for incidents of domestic force is likely much higher. Although both work forces and adult females can be affected, 77 % of those who experience domestic force are adult females. Domestic force is increasing each twelvemonth and alterations need to be addressed shortly in the borough of Barking and Dagenham. This assignment will place why alterations are needed to cut down victims of domestic force in the borough of Barking and Dagenham. The borough has one of the highest rates of domestic force across London with 4,506 incidents reported to the Police in 2009/10. Tackling and cut downing domestic force is one of the cardinal precedences for the Community Safety Partnership and the Council. Domestic force histories for 22 % of notifiable offenses in Barking and Dagenham, and hence poses a serious concern for a alteration ( Barking and Dagenham Domestic Violence Forum, 2009a ) In Barking and Dagenham intoxicant abuse besides impacts on domestic force figures and it is of import that the borough set up schemes that will turn to the injury caused by intoxicant to both culprits and victims of domestic force. Domestic force demands to be addressed because it can hold an tremendous consequence on people A ; acirc ; ˆâ„ ¢s mental wellness. It is now good accepted that maltreatment ( both in childhood and in big life ) is frequently one of the chief factor in the development of depression, anxiousness and other mental wellness upsets, and may take to kip perturbations, self-harm, self-destruction and attempted self-destruction, eating upsets and substance abuse ( Golding J 1999, Humphreys et al 2003 ) . Children who live with domestic force are at increased hazard of behavioral jobs and emotional injury, and mental wellness troubles in big life. There should be different attacks in this borough in order to forestall farther exploitation of domestic force. These attacks should affect multi-agency coaction and information-sharing between the constabulary, instruction and wellness attention professionals and societal services. The London Borough of Barking and Dagenham has a Multi Agency Risk Assessment Conference ( MARAC ) which meets on a monthly footing. It addresses the demands of high hazard victims and it besides measures the domestic force repetition exploitation rate. Current public presentation in 2009/2010 is 24 % against an one-year mark of 28 % . This shows that there is much to be done in order to make the one-year mark. ( Barking and Dagenham Domestic Violence Forum, 2009b ) Domestic force affects all societal groups, including rich and hapless, heterosexual, bisexual, transsexual or homosexual people and even kids. Hegarty and Taft ( 2001 ) suggested that adult females will unwrap information about maltreatment more readily if wellness professionals inquire them to. It is of import, hence, that wellness professionals create a private environment where it is safe to speak about force. Work force are besides abused by female spouses. However, domestic force against males is non ever acknowledged ( Lewis and Sarantakos, 2001 ) and small is known about the Numberss of work forces who are abused or treated violently by their spouses. Many of the effects of maltreatment are the same for work forces as for adult females. They are likely to experience profoundly ashamed, frightened, see a loss of self-worth and assurance, feel isolated, guilty and confused about the state of affairs ( Leonard, 2003 ) . The function of wellness professionals A ; acirc ; ˆâ„ ¢ proactive intercession in the early designation of domestic force instances is important for victims and their kids. A survey found that 80 % of adult females in a violent relationship had sought aid from the wellness service at least one time Department of Health ( DH, 2000 ) . Similarly one of the most of import demands of victims flying force is entree to safe, procure lasting lodging, and the function of lodging professionals can help in the initial phases of designation of the issue. Awareness of domestic force through public instruction demands to be raised. Research shows that in the first case, most domestic force victims turn to households and friends for support ( Humphreys, 2000 ) . Increasing the consciousness of domestic force amongst the general populace is hence an of import portion of increasing support for victims. Public information demands to be readily available in different linguistic communications, and be culturally relevant to black and cultural minority communities within the borough of Barking and Dagenham. In order to efficaciously raise consciousness amongst cardinal professionals, domestic force and good pattern preparation must be compulsory. Such preparation must, nevertheless, be supported by the development of clear policies and processs within organisations that set clear criterions of pattern and answerability. Healthcare professionals are the first-line response for many people who experience domestic force ( Du Plat-Jones, 2006 ) . Therefore consciousness should be raised about the issue in pattern and there should be in-depth preparation for wellness professionals with in the borough. Staffs require appropriate preparation and supervising to increase consciousness and cognition of how to recognize and cover with domestic force. Prosecuting with kids and immature people at the earliest chance is important to forestall future domestic force. It is besides of import to supply those populating with domestic force of which kids form the largest group with information and support to better their safety and seek aid. Equally good as safeguarding and advancing the safety of kids, schools need to include domestic force in their course of study scheduling. Domestic force is a cardinal issue in the borough of Barking and Dagenham and in UK as a whole, because it affects the wellness and public assistance of work forces, adult females and kids. It is non restricted to any one group in society. It is of import to educate the populace about the rhythm of force and the serious and durable consequence this has on kids and besides to admit that domestic force against work forces is an increasing wellness issue. All wellness professionals should go actively involved in interrupting the silence environing force, so that they can supply an appropriate and effectual service. There is much work underway to turn to this issue with in the borough in footings of victims and culprits. Whilst good advancement is being made within the borough of barking and Dagenham, there is still important work to be done.

Sequences on ACT Math Strategy Guide and Review

Sequences on ACT Math Strategy Guide and Review SAT / ACT Prep Online Guides and Tips Sequences are patterns of numbers that follow a particular set of rules. Whether new term in the sequence is found by an arithmetic constant or found by a ratio, each new number is found by a certain rule- the same rule- each time. There are several different ways to find the answers to the typical sequence questions- †What is the first term of the sequence?†, â€Å"What is the last term?†, â€Å"What is the sum of all the terms?†- and each has its benefits and drawbacks. We will go through each method, and the pros and cons of each, to help you find the right balance between memorization, longhand work, and time strategies. This will be your complete guide to ACT sequence problems- the various types of sequences there are, the typical sequence questions you’ll see on the ACT, and the best ways to solve these types of problems for your particular ACT test taking strategies. Before We Begin Take note that sequence problems are rare on the ACT, never appearing more than once per test. In fact, sequence questions do not even appear on every ACT, but instead show up approximately once every second or third test. What does this mean for you? Because you may not see a sequence at all when you go to take your test, make sure you prioritize your ACT math study time accordingly and save this guide for later studying. Only once you feel you have a solid handle on the more common types of math topics on the test- triangles (comng soon!), integers, ratios, angles, and slopes- should you turn your attention to the less common ACT math topics like sequences. Now let's talk definitions. What Are Sequences? For the purposes of the ACT, you will deal with two different types of sequences- arithmetic and geometric. An arithmetic sequence is a sequence in which each term is found by adding or subtracting the same value. The difference between each term- found by subtracting any two pairs of neighboring terms- is called $d$, the common difference. -5, -1, 3, 7, 11, 15†¦ is an arithmetic sequence with a common difference of 4. We can find the $d$ by subtracting any two pairs of numbers in the sequence- it doesn’t matter which pair we choose, so long as the numbers are next to one another. $-1 - -5 = 4$ $3 - -1 = 4$ $7 - 3 = 4$ And so on. 12.75, 9.5, 6.25, 3, -0.25... is an arithmetic sequence in which the common difference is -3.25. We can find this $d$ by again subtracting pairs of numbers in the sequence. $9.5 - 12.75 = -3.25$ $6.25 - 9.5 = -3.25$ And so on. A geometric sequence is a sequence of numbers in which each successive term is found by multiplying or dividing by the same amount each time. The difference between each term- found by dividing any neighboring pair of terms- is called $r$, the common ratio. 212, -106, 53, -26.5, 13.25†¦ is a geometric sequence in which the common ratio is $-{1/2}$. We can find the $r$ by dividing any pair of numbers in the sequence, so long as they are next to one another. ${-106}/212 = -{1/2}$ $53/{-106} = -{1/2}$ ${-26.5}/53 = -{1/2}$ And so on. Though sequence formulas are useful, they are not strictly necessary. Let's look at why. Sequence Formulas Because sequences are so regular, there are a few formulas we can use to find various pieces of them, such as the first term, the nth term, or the sum of all our terms. Do take note that there are pros and cons for memorizing formulas. Pros- formulas are a quick way to find your answers, without having to write out the full sequence by hand or spend your limited test-taking time tallying your numbers. Cons- it can be easy to remember a formula incorrectly, which would lead you to a wrong answer. It also is an expense of brainpower to memorize formulas that you may or may not even need come test day. If you are someone who prefers to use and memorize formulas, definitely go ahead and learn these! But if are not, then you are still in luck; most (though not all) ACT sequence problems can be solved longhand. So if you have the patience- and the time to spare- then don’t worry about memorizing formulas. That all being said, let’s take a look at our formulas so that those of you who want to memorize them can do so and so that those of you who don’t can still understand how they work. Arithmetic Sequence Formulas $$a_n = a_1 + (n - 1)d$$ $$\Sum \terms = (n/2)(a_1 + a_n)$$ These are our two important arithmetic sequence formulas and we will go through how each one works and when to use them. Terms Formula $a_n = a_1 + (n - 1)d$ If you need to find any individual piece of your arithmetic sequence, you can use this formula. First, let us talk about why it works and then we can look at some problems in action. $a_1$ is the first term in our sequence. Though the sequence can go on infinitely, we will always have a starting point at our first term. $a_n$ represents any missing term we want to isolate. For instance, this could be the 4th term, the 58th, or the 202nd. Why does this formula work? Well let’s say we wanted to find the 2nd term in the sequence. We find each new term by adding our common difference, or $d$, so the second term would be: $a_2 = a_1 + d$ And we would then find the 3rd term in the sequence by adding another $d$ to our existing $a_2$. So our 3rd term would be: $a_3 = (a_1 + d) + d$ Or, in other words: $a_3 = a_1 + 2d$ And the 4th term of the sequence, found by adding another $d$ to our existing third term, would continue this pattern: $a_4 = (a_1 + 2d) + d$ Or $a_4 = a_1 + 3d$ So, as you can see, each term in the sequence is found by adding the first term to $d$, multiplied by $n - 1$. (The 3rd term is $2d$, the 4th term is $3d$, etc.) So now that we know why the formula works, let’s look at it in action. What is the difference between each term in an arithmetic sequence, if the first term of the sequence is -6 and the 12th term is 126? 3 4 6 10 12 Now, there are two ways to solve this problem- using the formula, or finding the difference and dividing by the number of terms between each number. Let’s look at both methods. Method 1: Arithmetic Sequence Formula If we use our formula for arithmetic sequences, we can find our $d$. So let us simply plug in our numbers for $a_1$ and $a_n$. $a_n = a_1 + (n - 1)d$ $126 = -6 + (12 - 1)d$ $126 = -6 + 11d$ $132 = 11d$ $d = 12$ Our final answer is E, 12. Method 2: finding difference and dividing Because the difference between each term is regular, we can find that difference by finding the difference between our terms and then dividing by the number of terms in between them. Note: be very careful when you do this! Though we are trying to find the 12th term, there are NOT 12 terms between the first term and the 12th- there are actually 11. Why? Let’s look at a smaller scale sequence of 3 terms. 4, __, 8 If you wanted to find the difference between these terms, you would again find the difference between 4 and 8 and divide by the number of terms separating them. You can see that there are 3 total terms, but 2 terms separating 4 and 8. 1st: 4 to __ 2nd: __ to 8 When given $n$ terms, there will always be $n - 1$ terms between the first number and the last. So, if we turn back to our problem, now we know that our first term is -6 and our 12th is 126. That is a difference of: $126 - -6$ $126 + 6$ $132$ And we must divide this number by the number of terms between them, which in this case is 11. $132/11$ $12$ Again, the difference between each number is E, 12. As you can see, the second method is just another way of using the formula without actually having to memorize the formula. How you solve these types of questions completely depends on how you like to work and your own personal ACT math strategies. Sum Formula $\Sum \terms = (n/2)(a_1 + a_n)$ This formula tells us the sum of the terms in an arithmetic sequence, from the first term ($a_1$) to the nth term ($a_n$). Basically, we are multiplying the number of terms, $n$, by the average of the first term and the nth term. Why does this work? Well let’s look at an arithmetic sequence in action: 4, 7, 10, 13, 16, 19 This is an arithmetic sequence with a common difference, $d$, of 3. A neat trick you can do with any arithmetic sequence is to take the sum of the pairs of terms, starting from the outsides in. Each pair will have the same exact sum. So you can see that the sum of the sequence is $23 * 3 = 69$. In other words, we are taking the sum of our first term and our nth term (in this case, 19 is our 6th term) and multiplying it by half of $n$ (in this case $6/2 = 3$). Another way to think of it is to take the average of our first and nth terms- ${4 + 19}/2 = 11.5$ and then multiply that value by the number of terms in the sequence- $11.5 * 6 = 69$. Either way, you are using the same basic formula, so it just depends on how you like to think of it. Whether you prefer $(n/2)(a_1 + a_n)$ or $n({a_1 + a_n}/2)$ is completely up to you. Now let’s look at the formula in action. Andrea is selling boxes of cookies door-to-door. On her first day, she sells 12 boxes of cookies, and she intends to sell 5 more boxes per day than on the day previous. If she meets her goal and sells boxes of cookies for a total of 10 days, how many boxes total did she sell? 314 345 415 474 505 As with almost all sequence questions on the ACT, we have the choice to use our formulas or do the problem longhand. Let’s try both ways. Method 1: formulas We know that our formula for arithmetic sequence sums is: $\Sum = (n/2)(a_1 + a_n)$ In order to plug in our necessary numbers, we must find the value of our $a_n$. Once again, we can do this via our first formula, or we can find it by hand. As we are already using formulas, let us use our first formula. $a_n = a_1 + (n - 1)d$ We are told that the first term in our sequence is 12. We also know that she sells cookies for 10 days and that, each day, she sells 5 more boxes of cookies. This means we have all our pieces to complete this formula. $a_n = 12 + (10 - 1)5$ $a_10 = 12 + (9)5$ $a_10 = 12 + 45$ $a_10 = 57$ Now that we have our value for $a_n$ (in this case $a_10$), we can complete our sum formula. $(n/2)(a_1 + a_n)$ $(10/2)(12 + 57)$ $5(69)$ $345$ Our final answer is B, 345. Method 2: longhand Alternatively, we can solve this problem by doing it longhand. It will take a little longer, but this way also carries less risk of mis-remembering a formula. The decision is, as always, completely up to you on how you choose to solve these kinds of questions. First, let us write out our sequence, beginning with 12 and adding 5 to each subsequence number, until we find our nth (10th) term. 12, 17, 22, 27, 32, 37, 42, 47, 52, 57 Now, we can either add them up all by hand- $12 + 17 + 22 + 27 + 32 + 37 + 42 + 47 + 52 + 57 = 345$ Or we can use our arithmetic sequence sum trick and divide the sequence into pairs. We can see that there are 5 pairs of 69, so $5 * 69 = 345$. Again, our final answer is B, 345. Whoo! Only one more formula to go! Geometric Sequence Formulas $$a_n = a_1( r^{n - 1})$$ (Note: there is a formula to find the sum of a geometric sequence, but you will never be asked to find this on the ACT, and so it is not included in this guide.) This formula, as with the first arithmetic sequence formula, will help you find any number of missing pieces in your sequence. Given two pieces of information about your sequence ($a_n$ $a_1$, $a_1$ $r$, or $a_n$ $r$), you can find the third. And, as always with sequences, you have the choice of whether to solve your problem longhand or with a formula. What is the first term in a geometric sequence if each number is found by multiplying the previous term by -3 and the 8th term is 4,374? -0.222 0.667 -2 6 -18 Method 1: formula If you’re one for memorizing formulas, we can simply plug in our values into our equation in place of $a_n$, $n$, and $r$ in order to solve for $a_1$. $a_n = a_1( r^{n - 1})$ $4374 = a_1(-3^{8 - 1})$ $4374 = a_1(-3^7)$ $4374 = a_1(-2187)$ $-2 = a_1$ So our first term in the sequence is -2. Our final answer is C, -2. Method 2: longhand Alternatively, as always, we can take a little longer and solve them problem by hand. First, set out our number of terms in order to keep track of them, with our 8th term, 4374, last. ___, ___, ___, ___, ___, ___, ___, 4374 Now, let’s divide each number by -3 down the sequence until we reach the beginning. ___, ___, ___, ___, ___, ___, -1458, 4374 ___, ___, ___, ___, ___, 486, -1458, 4374 And, if we keep going thusly, we will eventually get: -2, 6, -18, 54, -162, 486, -1458, 4374 Which means that we can see that our first term is -2. Again, our final answer is C, -2. As with all sequence solving methods, there are benefits and drawbacks to solving the question in each way. If you choose to use formulas, make very sure you can remember them exactly. And if you solve the questions by hand, be very careful to find the exact number of terms in the sequence. The ACT will always provide bait answers for anyone who is one or two terms off the nth term- in this problem, if you had accidentally assigned 4374 as the 7th term or the 9th term, you would have chosen answer B or D. Once you find the strategy that works best for you, the pieces will all fall into place. Typical ACT Sequences Questions Because all sequence questions on the ACT can be solved (if sometimes arduously) without the use or knowledge of sequence formulas, the test-makers will only ever ask you for a limited number of terms or the sum of a small number of terms (usually less than 12). As we saw above, you may be asked to find the 1st term in a sequence, the nth term, the difference between your terms (whether a common difference, $d$, or a common ratio, $r$), or the sum of your terms in arithmetic sequences only. You also may be asked to find an unusual twist on a sequence question that combines your knowledge of sequences. For example: What is the sum of the first 5 terms of an arithmetic sequence in which the 6th term is 14 and the 11th term is 22? 2.2 6.0 12.4 32.6 46.0 Again, let us look at both formulaic and longhand methods for how to solve a problem like this. Method 1: formulas In order to find our common difference, we can use our main arithmetic sequence formula. But this time, instead of beginning with the actual $a_1$, we are beginning with our 6th term, as this is what we are given. Essentially, we are designating our 6th term as our 1st term and our 11th term as our 6th term and then plugging these values into our formula. $a_n = a_1 + (n - 1)d$ $22 = 14 + (6 - 1)d$ $22 = 14 + 5d$ $8 = 5d$ $1.6 = d$ Now, we can find our actual 1st term by using the $d$ we just found and our 11th term value of 22. $a_n = a_1 + (n - 1)d$ $22 = a_1 + (11 - 1)1.6$ $22 = a_1 + (10)1.6$ $22 = a_1 + 16$ $6 = a_1$ The 1st term of our sequence is 6. Now, we need to find the 5th term of our sequence in order to use our arithmetic sequence sum formula to find the sum of the first 5 terms. $a_n = a_1 + (n - 1)d$ $a_5 = 6 + (5 - 1)1.6$ $a_5 = 6 + (4)1.6$ $a_5 = 6 + 6.4$ $a_5 = 12.4$ And finally, we can find the sum of our first 5 terms by using our sum formula and plugging in the values we found. $(n/2)(a_1 + a_n)$ $5/2(6 + 12.4)$ $2.5(18.4)$ $46$ Our final answer is E, 46. As you can see, this problem still took a significant amount of time using our formulas because there were so many moving pieces. Let us look at this problem were we to solve it longhand instead. Method 2: longhand First, let us find our common difference by finding the difference between our 6th term and our 11th term and dividing by how many terms are in between them, which in this case is 5. (Why 5? There is one term between the 6th and 7th terms, another between the 7th and 8th, another between the 8th and 9th, another between the 9th and 10th, and the last between the 10th and 11th terms. This makes a total of 5 terms.) This gives us: $22 - 14 = 8$ $8/5 = 1.6$ Now, let us simply find all the numbers in our sequence by working backwards and subtracting 1.6 from each term. ___, ___, ___, ___, ___, 14, ___, ___, ___, ___, 22 ___, ___, ___, ___, ___, 14, ___, ___, ___, 20.4, 22 ___, ___, ___, ___, ___, 14, ___, ___, 18.8, 20.4, 22 And so on, until all the spaces are filled. 6, 7.6, 9.2, 10.8, 12.4, 14, 15. 6, 17.2, 18.8, 20.4, 22 Now, simply add up the first 5 terms. $6 + 7.6 + 9.2 + 10.8 + 12.4$ $46$ Our final answer is E, 46. Again, you always have the choice to use formulas or longhand to solve these questions and how you prioritize your time (and/or how careful you are with your calculations) will ultimately decide which method you use. You've seen the typical ACT sequence questions, so let's talk strategies. Tips For Solving Sequence Questions Sequence questions can be somewhat tricky and arduous to slog through, so keep in mind these ACT math tips on sequences as you go through your studies: 1: Decide before test day whether or not you will use the sequence formulas Before you go through the effort of committing your formulas to memory, think about the kind of test-taker you are. If you are someone who lives and breathes formulas, then go ahead and memorize them now. Most sequence questions (though, as we saw above, not all of them) will go much faster once you have the formulas down straight. If, however, you would rather dedicate your time and brainpower to other math topics or to the method of performing sequence questions longhand, then don’t worry about your formulas! Don’t even bother to try to remember them- just decide here and now not to use them and forget about the formulas entirely. Unless you can be sure to remember them correctly, a formula will hinder more than help you when it comes time to take your ACT, so make the decision now to either memorize them or forget about them. 2: Write your values down and keep your work organized Though many calculators can perform long strings of calculations, sequence questions by definition involve many different values and terms. Small errors in your work can cause a cascade effect. One mistyped digit in your calculator can throw off your work completely, and you won’t know where the error happened if you do not keep track of your values. Always remember to write down your values and label them in order to prevent a misstep somewhere down the line. 3: Keep careful track of your timing No matter how you solve a sequence question, these types of problems will generally take you more time than other math questions on the ACT. For this reason, most all sequence questions are located in the last third of the ACT math section, which means the test-makers think of sequences as a â€Å"high difficulty† level problem. Time is your most valuable asset on the ACT, so always make sure you are using yours wisely. If you can answer two other math questions in the time it takes you to answer one sequence question, then maximize your point gain by focusing on the other two questions. Always remember that each question on the ACT math section is worth the same amount of points, so prioritize quantity and don’t let your time run out trying to solve one problem. If you feel that you can answer a sequence problem quickly, go ahead! But if you feel it will take up too much time, move on and come back to it later. Ready to put your knowledge to the test? Test Your Knowledge Now let’s test your sequence knowledge with real ACT math problems. 1. What is the first term in the arithmetic sequence if terms 6 through 9 are shown below? ...196, 210, 224, 238 7 14 98 126 140 2. What is the sum of the first 8 terms in the arithmetic sequence that begins: 7, 10.5, 14,... 143.5 154 162.5 168 176.5 3. Answers: D, B, E Answer Explanations: 1. As always, we can solve this problem with formulas or via longhand. For the sake of brevity, we will only use one method per problem here. In this case, let us solve our problem via longhand. We are told this is an arithmetic sequence, so we can find our common difference by subtracting neighboring terms. Let us take a pair and subtract to find our $d$. $238 - 224 = 14$ $d = 14$ We know our common difference is 14, and 196 is our 6th term. Let us work backwards to find our 1st term. ___, ___, ___, ___, ___, 196, 210, 224, 238 ___, ___, ___, ___, 182, 196, 210, 224, 238 ___, ___, ___, 168, 182, 196, 210, 224, 238 And so on, until we reach our first term. 126, 140, 154, 168, 182, 196, 210, 224, 238 As long as we kept our work organized, we will find the first term in our sequence. In this case, it is 126. Our final answer is D, 126. 2. Again, we have many options for solving our problem. In this case, we can use a combination of longhand and formula (in addition to the standard options of using either method alone). First, we must find our common difference between our terms by subtracting any neighboring pair. $14 - 10.5 = 3.5$ $d = 3.5$ Now that we have found our $d$, let us finish our sequence until the 8th term by continuing to add 3.5 to each successive term. 7, 10.5, 14, 17.5, 21, 24.5, 28, 31.5 And finally, we can plug in our values into our sum formula to find the sum of all our terms. $(n/2)(a_1 + a_n)$ $(8/2)(7 + 31.5)$ $(4)(38.5)$ $154$ The sum of the first 8 terms in the sequence is 154. Our final answer is B, 154. 3. Again, we can use multiple methods to solve our problem. In this case, let us use our formula for geometric sequences. First, we need to find our common ratio between terms, so let us divide any pair of neighboring terms to find our $r$. ${-27}/9 = -3$ $r = -3$ Now we can plug in our values into our formula. $a_n = a_1( r^{n - 1})$ $a_7 = 1(-3^{7 - 1})$ $a_7 = 1(-3^6)$ $a_7 = 1(-729)$ $a_7 = 729$ The 7th term of our sequence is 729. Our final answer is E, 729. You did it, you genius you! The Take Aways Sequence questions often take a little time and effort to get through, but they are usually made complicated by their number of terms and values rather than being actually difficult to solve. Just remember to keep all your work organized and decide before test-day whether you want to spend your study efforts memorizing, or if you would prefer to work out your sequence problems by hand. As long as you keep your values straight (and don’t get tricked by bait answers!), you will be able to grind through these problems without fail, using either method. What’s Next? Phew! You have officially mastered ACT sequence questions. So...now what? Well you're in luck because there are a lot more ACT math topics and guides to check out! Want to brush up on your ratios? How about your trigonometry? Coordinate geometry and slopes? No matter what ACT topic you want to master, we've got you covered. Feel like you're running out of time on ACT math? Check out our guide to help you beat the clock. Want to know the score you should aim for? Start by looking at how the scoring works and what that means for you. Looking to get a perfect score? Our guide to getting a 36 on ACT math (written by a perfect-scorer) will help you get to where you want to be! Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. Check out our 5-day free trial:

The interactional view theory Essay Example | Topics and Well Written Essays - 750 words

The interactional view theory - Essay Example The interaction view theory was developed by Paul Watzlwick, a scholar in family studies who developed detailed therapies concerning miscommunication in family units. The main aim behind the theory development was to study the interaction of family units and occurrence of miscommunication problems within the family that may arise in different situations. Basically, there are five main concepts under interaction view theory that Watzlwick developed in studying miscommunication within families. The concepts are that as a family it is impossible not to communicate, and that communication is determined by the relationships between members of a group. Moreover, the theory postulates that relationships are developed through punctuation and that any communication has to be either digital or analogic. The last concept of the theory is that communication may either be complementary or symmetrical (Griffin 186-191). No one brings about the meaning and concepts of the interaction view theory better than the characters in the in the film stuck in love. In this film, parents have apparently split after the wife is caught cheating on the husband. Their two kids in the meanwhile live with their father while their mother has found a new husband with whom they live together. On one occasion, the daughter eventually finds her mom kissing her new husband notwithstanding she had not divorced with her dad. As a result, the daughter becomes furious with her mom and even refuses to speak to her. On the other hand, the daughter is still furious with her dad in that her father had refused to let her mother go through a divorce and had no plans of getting back together with her. Nevertheless, after the family members took time to reconsider their actions away from their controlling emotions, they come back to their senses and the family shows signs of improvement. Finally, the family is back

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Ethics and Professionalism in Medicine-Journal Essay

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Case Study Counselor Recommendation Example | Topics and Well Written Essays - 750 words

Counselor Recommendation - Case Study Example According to their comments, I predict future conflicts and misunderstanding among them and the parents will find a hard time to make the children live together amicably. The positive thing that is evident in the new family is that every family member is optimistic that everything will go well and the family will be strong. They all have accepted to give it a chance and see whether the new family overcomes the future challenges and difficulties (Knox & Schacht, 2013). The things that the family will need to improve on include; playing ones role and averting conflicts. They should not be worried on the challenges that will come, but find credible ways of solving the tribulations that might arise. In utilizing the lessons learnt from the case study, terminal course objectives and threaded discussions in the family, it is significant to note that innumerable couples prefer cohabitation to marriage. This is because of the economic and emotional trauma from the preceding divorce, which af fects them mentally. It is established that parents given custody of the children by the family court are the ones involved in remarriage (Knox & Schacht, 2013). These parents always lack moral support and face economical impenetrability; hence, they always look for someone or a place to comfort. In this case, the family has to understand and accept the common argument that states that a stepparent will never be as good as a real parent. Hence, the Rose and Jason have to understand that in stepfamilies, the issues of biological parent will always be somewhere in the picture. For this reason, the parents have to teach the kids to accept the change and learn to be corrected and accept them as... In utilizing the lessons learnt from the case study, terminal course objectives and threaded discussions in the family, it is significant to note that innumerable couples prefer cohabitation to marriage. This is because of the economic and emotional trauma from the preceding divorce, which affects them mentally. It is established that parents given custody of the children by the family court are the ones involved in remarriage. These parents always lack moral support and face economical impenetrability; hence, they always look for someone or a place to comfort. In this case, the family has to understand and accept the common argument that states that a stepparent will never be as good as a real parent. Hence, the Rose and Jason have to understand that in stepfamilies, the issues of biological parent will always be somewhere in the picture. For this reason, the parents have to teach the kids to accept the change and learn to be corrected and accept them as parents. They have to accept correction by their stepparent and listen to his/her advice before making any judgments.