<p>Back to square one: visual approach (my favorite).</p>
<p>M is the midpoint of PS.</p>
<p>Connect P and T, T and M.</p>
<p>The square consists of four congruent triangles.
PQTS - of three of them.</p>
<p>Area(PQTS) = 3/4 Area(PQRS) = 3/4 (3) = 9/4
- just as Tsenguun said.</p>
<p>Thnx tsengunn, dchow, baphomet and gcf101. Im sorry for my little outburst b4 but I was kinda high and wasnt thinkin straight... yea..um.. and now I feel a little chagrined ( since I'm back to my old self now)</p>
<p>Dchow I did that Q u asked me:</p>
<p>the wheel travels 33/15 yards in ! revolution, which is the circumference.
(22/7)xDiameter= 33/15
Diameter= 7/10</p>
<p>This is a Q that I picked up from another thread but I dint get the explanation.</p>
<p>There are 3 roads from Plattsville to Ocean Heights and 4 roads from Ocean Heights to Bay Cove. If Martina drives from Plattsville to Bay Cove and back, and passes through Ocean Heights in both directions, and does not travel any road twice, how many different routes for the trip are possible?</p>
<p>( no more outbursts, promise)</p>
<p>I just died trying to figure out Humna's... I got 18 but that's probably very wrong</p>
<p>Rosalita rode her bike to the repair shop and rode the bus home by the same route. Excluding the time she spent at the shop, she spent a total of 1 hour traveling from her home to the shop and back again. If she rode her bicycle at an average speed of 5 miles per hour, and the bus traveled at an average speed of 20 miles per hour, then for how many miles did she ride her bicycle?
(A) 2
(B) 4
(C) 5
(D) 8
(E) 10</p>
<p>ah i think it's actually 36 (humna)!</p>
<p>For Humna, I guess it's 72.
You know, during the first drive, there are 3 possible roads from A to B, 4 roads from B to C (let's simplify it using A, B, C). Then it's gonna be 3<em>4=12, just in the first half.
It says the car will go back, but dont think of as going back. think of it as going forward. then from C to B 3 roads and B to A 2 roads, since the car cannot go the same road. so the answer is 12</em>3*2=72</p>
<p>For Ducktape, let's substitute x as the total of time of riding bicycle, and y as the time of riding the bus. so x + y = 1;
Since she used the same road, the length of the distance is same. So we can write an equation like this.
S = 20mph * y (1)
S = 5mph * x (2)
x + y = 1 (3)
From (1) and (2), we can get the correlation between x and y, which is x = 4y and use it in (3) to find out that y was 0.2 hour and x was 0.8 hours.
I tried to make a long and clear description. But on the test, this kind of problems should be solved in 30 sec or sth.</p>
<p>Humna's roads problem: Yes, there are 72 possibilities. There are 12 ways to go to Bay Cove (3 x 4), and if you draw a diagram, you can figure out that there are only 6 ways to go back without going on the same road. 12 x 6 = 72. Now I have to say I had to spend a bit of time on it, and my explanation made it seem easy.</p>
<p>Ducktape: The answer is (B) 4. Tsenguun, you never gave the answer!</p>
<p>Explanation. </p>
<p>Okay, let's call the number of miles from Rosita's house to the bike shop "m."
By bike, Rosita goes 5 miles per hour. If Rosita went 20 miles by bike, it would take her 4 hours. So you can see that it takes Rosita m/5 hours to get to the shop by bike.</p>
<p>Okay, by bus now, which goes 20 miles per hour. It takes Rosita m/20 hours to get home by bus.</p>
<p>We also know that it took her a total of 1 hour.</p>
<p>The time it took to go to the repair shop + the time it took to go home = 1 hour.</p>
<p>Using m,</p>
<p>m/5 + m/20 = 1 hour. </p>
<p>(Note: keep in mind that we're not just dividing by 5, we're dividing by 5 miles/hour. So m/5 would not be in units of distance but in units of time.)</p>
<p>Now we use the least common multiple: 4m/20 + 1m/20 = 1.</p>
<p>5m/20 = 1
5m = 20
m=4.</p>
<p>The distance from Rosita's house to the repair shop is 4 miles. That means that Rosita rode on her bike a total of 4 miles, which is B.</p>
<p>For rate problems, you may want to use a chart to organize your data. Later on, when you get more practice, you will be so used to doing these problems that you don't even need a chart anymore.</p>
<pre><code> speed x time = distance
mph hours miles
</code></pre>
<ol>
<li>Biking: Speed: 5 Time = m/5 Distance = m<br></li>
<li>Bussing: Speed: 20 Time = m/20 Distance = m
TOTAL: Time = 1</li>
</ol>
<p>m/5 + m/20 = 1.</p>
<p>Solving for m we get m = 4.</p>
<p>Now I have a problem for you, Ducktape. Yeah you!</p>
<p>"Peter can walk a mile in 10 minutes. He can travel a mile on his bicycle in 2 minutes. How far away is his uncle's house if Peter can walk there and bicycle back in 1 hour exactly?" No Choices!</p>
<p>-from Gruber's Complete Preparation for the New SAT</p>
<p>My advice: Make a chart with the columns being speed, time, and distance.
Rows are for walking and bicycling.
Complete the chart and find a variable, then solve! </p>
<p>Tell me what you get! Have fun!</p>
<p>for ducktape's problem, here's my fast, in-your-head approach to the problem. It won't solve all rate problems, just ones extremely similar to this one (like dchow's)</p>
<p>the average speed is total distance traveled divided by total time, or twice the distance we're trying to find.
the bus is 4x faster than the bike, meaning it took four times as long to cover the distance on a bike.</p>
<p>average speed is the average of both speeds weighted by time.
therefore average speed is
(4<em>5 + 1</em>20)/5 = 40/5 = 8</p>
<p>half of 8 is 4, the answer is B.</p>
<p>there. no variables to keep track of, just brute logic. However, until you're really comfortable with rate problems, I wouldn't try time saving tricks.</p>
<p>Also, Humna, just to give a longer explanation for why it's 72:</p>
<p>Going there there are 12 ways. (for each of the three ways, there are 4 choices after Ocean Heights)...(3x4)</p>
<p>Getting back there will always be 6 ways (there's only three roads to choose from from BC to OH, then only 2 from OH to P)</p>
<p>then the problem repeats. There are 12 ways to get there, and then six choices for each of the 12 on the way back. 12*6=72</p>
<p>Thnx to all those who answered the Q!!!
I totally get it now and boy do I feel dumb</p>
<p>um do u need to show ure work on the SAT? cuz i just figured out the answer to the problem in less than 10 seconds. All u need to see is </p>
<p>3.00 = reg, 4.50 = prem, 4.00 = mixed. So u see that the price of the mixed is closer to the prem meaning more prem was used. 4.50 - 3.00 = 1.50. Now 4.00 is leaning towards 4.50. So more Prem was used. 4.00 = 30/3
30/3 = 10. IF u dont get it, well im a bad teacher. Its just how my mind works. Soz but i got that answer.</p>
<p>can someone explain this to me...blue book #18 p.313 "For all positive values of x, the function f is defined by f(x)= x^3-x^-2. Which best approximates of f(x) for values of x greater than 1000?
a.x^3
b.x^4
c.x^5
d.x^6
e. x^9
answer is x^3...why?</p>
<p>p.338-339 10.
f(x)=(x+1)^3/4
What are all values of x for which f(x) is real numbers?
the answer is b. x greater than or equal to -1</p>
<p>why is that so?</p>
<p>if x is an integer and 2<x<7...how many different triangles can you make with side lengths 2,7,x?
i chose 4...but the answer is one? Is it because you can only choose one # and they did not ask for the #combinations?</p>
<p>akati: </p>
<p>Question 1: Okay, well, x^-2 is the same thing as 1/ (x^2).</p>
<p>So the function is the same as y = x^3 - 1/(x^2)</p>
<p>Write that out on a piece of scratch paper. </p>
<p>Now, let's say x gets super huge. Then x^2 gets super huge, and 1/(x^2) gets super small, really close to zero. The bigger x gets, the closer to 0 that 1/(x^2) will be, so x^3 - x^-2 will get closer and closer to x^3.</p>
<p>Next: When you do a number to the 3/4 power, that number can't be negative. This is because a negative number ^ 3/4 is the same as (negative#) to the 1/4 power, and that cubed.</p>
<p>x^(3/4) = (x^ [1/4])^3.</p>
<p>You can't take the 1/4 power of a negative number. Just imagine doing it the other way around, how can you take something to the fourth power and make it be negative? It's impossible!</p>
<p>Going back, (x+1) cannot be negative. That means that x must be greater than or equal to -1.</p>
<p>Next question:</p>
<p>First, the basics. Can you have a triangle with sides 2,3, and 1000?</p>
<p>No. </p>
<p>Why?</p>
<p>Right, because the two tiny edges can't form a triangle when the other side is too big.</p>
<p>Now, can you form a triangle with sides of 2, 5, and 7?</p>
<p>No.</p>
<p>Why?</p>
<p>Because your triangle would end up being a straight line, because the long side would be long enough that the two small sides would have to line up in order to connect, and then you wouldn't have a triangle.</p>
<p>So if 2<x<7, there are only 4 potential possibilities for x: 3,4,5, and 6.</p>
<p>Can you make a triangle with sides 2,3, and 7?</p>
<p>No, because the sides of 2 and 3 would be too tiny to connect to both sides of the 7. </p>
<p>The only value that works is 6.</p>
<p>That's why the answer is one.</p>
<p>Akati, I think that people can't get better at things without sufficient practice. So, I have a question for YOU.</p>
<p>If x is an integer, how many different triangles can you make with side lengths 3, 8, x? Hint: Be Careful.</p>
<p>If you have any questions, please ask. This stuff is not easy to explain, especially the first question.</p>
<p>either i am plain dumb are the explanations were too bland...</p>
<p>why does x^3 best approximates of f(x) for values of x greater than 1000...why don't the other choices work as well...?</p>
<p>"Going back, (x+1) cannot be negative. That means that x must be greater than or equal to -1."
I think you mean you cannot take the root of negative #...power 3/4= square root 4 to ^3....IS zero is a real number?... </p>
<p>could you explain the triangle differently because i kind of get the explanation but it seems like logic guess and check...is there a equation or theorem?</p>
<p>akati:</p>
<p>x^3 - 1/x^2</p>
<p>As x gets really huge,</p>
<p>1/x^2 approaches zero.</p>
<p>x^3 - 1/x^2 = x^3 - 0 = x^3.</p>
<p>Yes, zero is a real number! So it a million, -1/2, and pi. And yes, you can't take the 1/4 power of a negative number. Only positive and zero work. But you CAN take a negative number and do it to the 1/3 power. For instance, (-8)^(1/3) = -2, because -2 x -2 x -2 = -8. But it doesn't work if you multiply a negative number by itself an even number of times, because that will get you a positive number. That's why you can't do (-81)^(1/4).</p>
<p>No, there's no equation or theorem. Well, you can say this: When you have a triangle, whenver you add up two smaller sides, they have to be greater than the other side. So a 3,4,5 triangle works because 3+4>5, but 3,4,8 won't.</p>
<p>i understand this :"x^3 - 1/x^2</p>
<p>As x gets really huge,</p>
<p>1/x^2 approaches zero.</p>
<p>x^3 - 1/x^2 = x^3 - 0 = x^3."</p>
<p>but don't the other examples work?...</p>
<p>They were asking which best approximates the function f(x)= x^3-x^-2, right? Think about it. When x=1000, f(x) = 1000^3 - some small value, which is negligible. If we use x^3 as our approximation, we get 1000^3 as our approximation, but if we use x^4 to approximate f(x), when x=1000, the "approximation" is 1000^4, which is about 1000 times more than the actual value of f(x) when x=1000. Just use real numbers, and you'll see why.</p>