the volume of a prism which has an altitude of 10 units and has a right triangle base with a hypotenuse of 13 units and a leg of
12 units is
1 answer:
Check the picture below.
since we know the hypotenuse and one of the legs of the triangular base, we can use the pythagorean theorem to get the missing leg, namely the base of the triangle, as you see in the picture. Thus we end up with a triangle whose base is 5 and height is 12.
now, the volume of the prims, is just the area of its triangular base, times the length, namely 10.
![\bf \textit{volume of the triangular prism}\\\\ V=\stackrel{length}{(10)}\stackrel{base's~area}{\left[ \cfrac{1}{2}(5)(12) \right]}](https://tex.z-dn.net/?f=%5Cbf%20%5Ctextit%7Bvolume%20of%20the%20triangular%20prism%7D%5C%5C%5C%5C%0AV%3D%5Cstackrel%7Blength%7D%7B%2810%29%7D%5Cstackrel%7Bbase%27s~area%7D%7B%5Cleft%5B%20%5Ccfrac%7B1%7D%7B2%7D%285%29%2812%29%20%5Cright%5D%7D)
since we know the hypotenuse and one of the legs of the triangular base, we can use the pythagorean theorem to get the missing leg, namely the base of the triangle, as you see in the picture. Thus we end up with a triangle whose base is 5 and height is 12.
now, the volume of the prims, is just the area of its triangular base, times the length, namely 10.
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Answer:
The maximum amount of profit is 32
Step-by-step explanation:
Given
Required
Determine the maximum profit
This is calculated by calculating the maximum of the function.
A quadratic function is of the form
and its maximum is:
So:
We have that
<em>Hence, the maximum amount of profit is 32</em>