Questions

[papergangsta]

P = {p,l,u,s}
Q= {m,i,n,u,s}
R= {t,i,m,e,s}
How many elements are in ( P union Q) interjection (P union R)
I keep getting five.

Find the instantaneous rate of change of the reciprocal of a number with respect to the number when the number is 4.

The are a of a right isosceles triangle is 12.5cm^2. Its perimeter is:

A box contains circular poker chips that are congruent in shape but not color. There are red, blue, and white chips. Drew randomly draws out a chip. He gets 5 points if it is a blue chip, 1 point if it is a white chip, and he loses 3 points if it is a red chip. The probability of drawing out a red one is 25%, a blue one is 60%, and a white one is 15%. What is his mathematical expectation on any one draw?

[stupidityismygam]

[papergangsta]

Thanks. I have a few more.

Numbers 9, 17, 20 (could you give me a brief description of each of those please), 44, 47, 49, 51, and 60.

[AuSmith]

What are the problems?? What test?

[papergangsta]

Stupid me. Sorry.

Last year's UIL C.

Question numbers 9, 17, and 60 (I don't know how to put those questions on here.)

20. The type of graph of the polar equation r= a cos (nθ) is called a:
The answer is rose, but I have no clue what roses, limacons, lemniscates, cardiods, or Archimedian spirals are. Could you give me a brief description of each?

44. Manuel Awff gets his first week's allowance of $15.00. He will get 50 cents more each week. If he saves his entire allowance for 1 year, how much money will he have?
Answer: $1443.00

47. Let sin(2x)= -cos(x), where -π < x < π. The sum of the solutions is:
Answer: -π

49. Find C if the remainder when 5x^3 - 3x^2 +x + C is divided by x+2 is -50.
Answer: 4

51. Harry Upp ran the first stage of the race at an average speed of 6 mph, the second stage at an average speed of 5 mph, and the final stage at an average speed of 4 mph. What was his average speed for all three stages if each stage was the same distance? (nearest hundreth)
Answer: 4.86 mph

[AuSmith]

9. If you divide both sides by 3, you see that x must be a multiple of 3. Similarly, divide both sides by 5 to see that y is a multiple of 5. Moreover, if x is a multiple of 3, there is an integer y that solves the equation (and vice versa). That quickly brings your solutions down to [unparseable or potentially dangerous latex formula].

17. I don't think it's too bad if you just compute A, B, and C... So, 34/7 is 4 with a remainder 6/7 (which gives you A=4). Next, 1/(6/7)=1 with a remainder of 1/6 (meaning B=1). And finally, 1/(1/6)=5+1 (giving C=5).

[unparseable or potentially dangerous latex formula]

60. I think direction is assumed to mean the angle going counterclockwise from the positive x-axis...
Do you know how to add vectors? Head to foot?

[papergangsta]

I do not know how to add vectors.

[AuSmith]

http://www.physchem.co.za/Vectors/Addit ... allelogram

[papergangsta]

Okay, I think I got it. I'm not sure if I did it correctly or I just stumbled upon it.

First: I found the x and y components of both vectors and added them.
X component: 15.66
Y component: 13.99

Then I did the tanθ = Y/X which got me 41. 78
Is this correct?

[AuSmith]

Yea, that's how you do it. Here's why. If V is a vector with magnitude [unparseable or potentially dangerous latex formula] and direction [unparseable or potentially dangerous latex formula] respectively, you can write it as the vector sum of its [unparseable or potentially dangerous latex formula] component and its [unparseable or potentially dangerous latex formula] component...

[unparseable or potentially dangerous latex formula]

So, when you break up both vectors, [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula], into [unparseable or potentially dangerous latex formula] and [unparseable or potentially dangerous latex formula] components, [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula], [unparseable or potentially dangerous latex formula], and [unparseable or potentially dangerous latex formula], then you can rearrange them

[unparseable or potentially dangerous latex formula]

I will get to your other questions later if no one else does.

[Shawn007]

44. It is a summation sort of problem.
Solution A: The summation of 15+.5*(x-1) as x goes from 1 to 52= 1443.00
Solution B:
Week 1 pay: $15.00
Week 51 pay: $40.50
Total pay times: 52
((15+40.50)/2)*(52)= 1443.00

49. By the remainder theorm, which works when dividing by a linear quantity ex. (X-a). Remainder=f(a).
So 5*(-2)^3-3*(-2)^2-2+C=-50
-40-12-2+c=-50
-54+c=-50
c=4

[Shawn007]

51. Average rate= Total distance/Total time
Lets say each leg was a mile.
Time for leg A= 1/6
Time for leg B= 1/5
Time for leg C= 1/4
Total distance= 1*3=3
Total Time= 1/6+1/5+1/4= approxiatmely .6166
Average rate= 3/.6166= 4.86 MPH

On the other two, I don't really know the "correct" way to do them, but I do have how I would do them. I would like someone to respond though, for my education.
20. Graph it and look?
47. Since I have an 89 I would use solve() and add the solutions in range.

[AuSmith]

20. This is called an Archimedean Spiral. You can google the others if you want.

47. If you recall the trig identity [unparseable or potentially dangerous latex formula], this reduces to

[unparseable or potentially dangerous latex formula]

Of course, there won't be any solutions for [unparseable or potentially dangerous latex formula]. Then, [unparseable or potentially dangerous latex formula] always forms supplemental pairs, so you're going to get [unparseable or potentially dangerous latex formula] even if the [unparseable or potentially dangerous latex formula] changes to any negative constant greater than [unparseable or potentially dangerous latex formula].