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FaultyClockwork

I need Math help guyz

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So my Math exam is Thursday and Friday and I'm having issues with some of the practice problems. Here's some I need done and explained:

1) Find the value of x: e^x + 1 = 4.

2) What is the period of the function y = 5 sin 3x?

  1. 5
  2. 2(pi)/5
  3. 3
  4. 2(pi)/3

3) If Jamar can run at 3/5 of a mile in 2 minutes 30 seconds, what is his rate in miles per minute?

  1. 4/5
  2. 6/25
  3. 3 and 1/10
  4. 4 and 1/6

4) A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides?

  1. 1
  2. 2
  3. 3
  4. 4

5) An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at t = 4, what is the value of k?

  1. 128
  2. 64
  3. 8
  4. 4

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It's been a long time... I'll give it a whirl, though.

1) Find the value of x: e^x + 1 = 4.

log(e)^x = log(4)

X log(e)= log (4)

X = log (4)/log (x)

make both sides a logarithm. Then bring down the X. Collect both logs to one side. When you have a log subtract a log it's treated as division.

3) If Jamar can run at 3/5 of a mile in 2 minutes 30 seconds, what is his rate in miles per minute?

  1. 4/5
  2. 6/25
  3. 3 and 1/10
  4. 4 and 1/6

6/25

He can run .6 miles in 2 minutes 30 seconds. .6/1 = 2.5/x and cross multiply it out.

4) A box contains one 2-inch rod, one 3-inch rod, one 4-inch rod, and one 5-inch rod. What is the maximum number of different triangles that can be made using these rods as sides?

  1. 1
  2. 2
  3. 3
  4. 4

4.

The possible combinations with fundamental counting are:

1x1x2 = 2

1x1x1 = 1

1x1x1 = 1

543

542

532

432

Your hypotenuse must ALWAYS be the 5 or 4 inch bar. After that you need one smaller bar followed again by another smaller bar. So if your hypotenuse is the 5 inch bar, the next bar must be four or three as. The last bar must always be three or two.

Wish I could remember how the rest work.

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2) What is the period of the function y = 5 sin 3x?

  1. 5
  2. 2(pi)/5
  3. 3
  4. 2(pi)/3

The period of a function is, well, the length traveled until the function repeats itself.

The period of y = sinx is 360 degrees, or 2pi. However, since the equation here is 5sin3x, the length of x necessary for one full period is cut in third. The period of y = 5sin3x is 120 degrees, or 2pi/3, which would be choice D.

Simply remember the period of the basic functions, then divide that by any multipliers you have in the function. Or, you can just graph the function out and look at it.

Periods of basic functions:

sinx: 360 degrees

secx: 360 degrees

cosx: 360 degrees

cscx: 360 degrees

tanx: 180 degrees

cotx: 180 degrees

I can't remember the non-calculus way to do #5, and I'm sure you don't know calculus yet.

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5) An archer shoots an arrow into the air such that its height at any time, t, is given by the function h(t) = -16t^2 + kt + 3. If the maximum height of the arrow occurs at t = 4, what is the value of k?

  1. 128
  2. 64
  3. 8
  4. 4

Since the equation given is a parabolic formula and it is a concave down parabola, the maximum height of the arrow occurs at the vertex of the parabola (if it is concave up, the minimum height occurs at the vertex instead). Use y = ax^2 + bx + c and what's known about the vertex to find k...

y = -16x^2 + kx + 3

a = -16

b = k

c = 3

The x coordinate of a vertex is -b/2a. It's given to us that it is also 4, so set -b/2a = 4 and use that to solve for b (which is also k).

(-k)/(2)(-16) = 4

(-k)/(-32) = 4

k = 4(32) = 128

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