Answer:
284.3
Step-by-step explanation:
Trapezoid Formula:
A=a+b/2*h
plug in the numbers
Check the picture below.
as you can see, the graph of the volume function comes from below goes up up up, reaches a U-turn then goes down down, U-turns again then back up to infinity.
the maximum is reached at the close up you see in the picture on the right-side.
Why we don't use a higher value from the graph since it's going to infinity?
well, "x" is constrained by the lengths of the box, specifically by the length of the smaller side, namely 5 - 2x, so whatever "x" is, it can't never zero out the smaller side, and that'd happen when x = 2.5, how so? well 5 - 2(2.5) = 0, so "x" whatever value is may be, must be less than 2.5, but more than 0, and within those constraints the maximum you see in the picture is obtained.
It could be B but I want to say D because it relates more to the question.
Note: a² - b² = (a-b)(a+b)
9x² - 16y² = (3x)² - (4y)² = (3x - 4y)(3x + 4y)
Hat means y + z = 180.
<span>y is thrice than z means y = 3 * z. </span>
<span>replace y with 3 * z in the equation of y + z = 180 to get 3 * z + z = 180. </span>
<span>combine like terms to get 4 * z = 180. </span>
<span>solve for z to get z = 180 / 4 = 45 degrees. </span>
<span>since y = 3 * z, then y = 3 * 45 = 135 degrees. </span>
y = 135
<span>z = 45 </span>
y + z = 180 becomes 135 + 45 = 180
<span>y = 3 * z = 135 = 3 *45 </span>
<span>solution is confirmed to be good.</span>