3,6
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Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume
Answer: cos(Θ) = (√15) / 4
Explanation:
The question states:
1) sin(Θ) = 1/4
2) 0 < Θ < π / 2
3) find cos(Θ)
This is how you solve it.
1) Use the fundamental identity (in this part I use α instead of Θ, just for facility of wirting the symbols, but they mean the same for the case).

2) From which you can find:

3) Replace sin(α) with 1/4
=>

=>

4) Given that the angle is in the first quadrant, you know that cosine is positive and the final answer is:
cos(Θ) =

.
And that is the answer.

the denominator cannot be zero, because the division by zero is not defined, therefore:
![\begin{gathered} x^2-9=0 \\ \text{Solving for x:} \\ x^2=9 \\ \sqrt[]{x^2}=\sqrt[]{9} \\ x=\pm3 \end{gathered}](https://tex.z-dn.net/?f=%5Cbegin%7Bgathered%7D%20x%5E2-9%3D0%20%5C%5C%20%5Ctext%7BSolving%20for%20x%3A%7D%20%5C%5C%20x%5E2%3D9%20%5C%5C%20%5Csqrt%5B%5D%7Bx%5E2%7D%3D%5Csqrt%5B%5D%7B9%7D%20%5C%5C%20x%3D%5Cpm3%20%5Cend%7Bgathered%7D)
Therefore the domain of (f o g)(x) is: