Math Midterm Help

[FazeD]

Ok, my math midterm assignment is coming up and I could really use some help because I am horrible at math now. If anyone wants to do any of these questions and show full solutions, it would be greatly appreciated. Oh the ^ just mean that the number following it is an exponent as I cant do superscript. Any variable for x is lowercase, multiplication is capital. Any number in brackets in the line of the question [Ex. 1 Evaluate: (4)] is the number of marks the question is out off.

1.) Evaluate: (4)
3^(-4) + 3^(-2)
3^(-4) - 3^(-1)

2.) in 30hrs, a sample of plutonium-243 decays to 1/64 of its original amount. Determine the half-life of this sample.(3)

3.) Simplify:(4)
2x-1 + 2x + 1
2x^(2) + 3x +1 3x(2) + 4x +1
4.) A stone is thrown into the air from a bridge over a river. The stone falls into the river. The height of the stone, h, in meters, above the river, t seconds after the stone is thrown is given by h=-5t^(2) + 10t + 7. Determine the maximum height of the stone above the river, and when it reaches this maximum height.(5)

5.) Is it possible for a rectangle with a perimeter of 46cm to have an area of 120cm^(2)? If so, find the dimensions of the rectangle.(5)

6.) The approximate temperature, T, in degrees Celsius, of rocks beneath the surface of the Earth can be found by multiplying their depth,d, in km, by 35 and adding 20 to this product.
a.) Write a function T(d) that expresses the temperature of some rocks in therms of their depth.(1)

b.) Find the inverse of this function.(3)

c.) What does this inverse represent?(1)

[Jimdalf]

The answer to five is like... one side is 8, the other 15. But I got that through trial and improvement so thats useless. Drat. The rest of it can bugger off, I haven't done that kind of maths in a decade.

[Irish Kin]

1)
3^(-4) + 3^(-2) = 0.0003 + 0.03 = 0.0303 = 0.1008991 repeating
3^(-4) - 3^(-1)____0.0003 + 0.3____0.3003

3) Can't tell whats where

Everything else I can't help you with because it's been at least a year on it. But that first one should be right. I'll probably never forget how to do those kinds of problems.

[Snoman]

Well here are the answers that I got, I don't have a scanner so I'm working on a way of getting the solutions up (I hate typing math work).

1.) 10/-26 = -0.385

2.) t(1/2) = 5 hours

3.) (10x^2 + 3x) / (6x^3 + 11x^2 + 6x + 1)

4.) t=1 ; h=12

5.) Jimdalf was right, the only possible dimensions are 8 and 15.

6a.) T = 35d + 20

b.) d = (T-20)/35

c.) The inverse represents depth as a function of temperature.

I'm not 100% sure if that's what 6b/c was asking for. And Irish Kin did #1 wrong. 3^(-4) = 1/(34) = 0.01234. He was thinking of 3X10^(-4) = 0.0003. I'll try to see if I can maybe take a couple pictures of my work to post it.

Edit: Ok, I don't have a scanner so I improvised:
ImageShack - Hosting :: sspx0111yg4.jpg
ImageShack - Hosting :: sspx0112oo8.jpg
ImageShack - Hosting :: sspx0113fv9.jpg
ImageShack - Hosting :: sspx0114mi6.jpg

[OME6A]

I'm pretty impressed. I never had to do stuff like this in school, and boy am I glad because 10 yrs later and I've never had to use it.

Good luck.

[SkandaL]

Originally Posted by OME6A

I'm pretty impressed. I never had to do stuff like this in school, and boy am I glad because 10 yrs later and I've never had to use it.

Good luck.

LMAO, thats funny as hell. I always knew we wouldn't use half the things we get taught in school.

[FazeD]

Thanks Sno, got a 95% on my midterm assignment thanks to you, the other parts that I did I made stupid mistakes.