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Roman55 [17]
3 years ago
15

Find the volume of the square pyramid showing. round to the nearest 10th if necessary

Mathematics
1 answer:
solong [7]3 years ago
5 0
The volume of a square pyramid is (1/3)(area of base)(height of pyramid).

Here the area of the base is (10 ft)^2 = 100 ft^2.

13 ft is the height of one of the triangular sides, but not the height of the pyramid.  To find the latter, draw another triangle whose upper vertex is connected to the middle of one of the four equal sides of the base by a diagonal of length 13 ft.  That "middle" is 5 units straight down from the upper vertex.  Thus, you have a triangle with known hypotenuse (13 ft) and known opposite side 5 feet (half of 10 ft).  What is the height of the pyramid?  
To find this, use the Pyth. Thm.:  (5 ft)^2 + y^2 = (13 ft)^2.  y = 12 ft.

Then the vol. of the pyramid is (1/3)(area of base)(height of pyramid) =
(1/3)(100 ft^2)(12 ft) = 400 ft^3 (answer)
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Crank

Option D: $f(x)=-2(x+2)(x-4)$ is the function

Explanation:

Let the general form of quadratic equation be $y=a x^{2}+b x+c$

The function passes through the intercepts (-2,0) and $(4,0)$ and also passes though the point $(-1,10)$

Substituting the points (-2,0), $(4,0)$ and $(-1,10)$ in the equation $y=a x^{2}+b x+c$, we get,

4a -2b+c=0  -----------(1)

16a +4b+c=0 ----------(2)

a-b+c=10    -----------(3)

Subtracting (1) and (2), we get,

\ \ 4a -2b+c=0\\ 16a +4b+c=0\\\---------\\ \  \ -12a-6b=0  -----------(4)

Subtracting (2) and (3), we get,

16a +4b+c=0\\\ \ a \ \ - \ \ b \ +c=10\\---------\\15a+5b=-10  ------------(5)

Multiplying equation (4) by 5 and equation (5) by 4, to cancel the term b when adding, we get,

-60a-30b=0\\\ 90a+30b=-60\\--------\\30a=-60\\\ \ a=-2

Thus, the value of a is a=-2

Substituting a=-2 in equation (4), we get,

$\begin{aligned}-12 a+6 b &=0 \\-12(-2)-6 b &=0 \\ 24-6 b &=0 \\ 24 &=6 b \\ 4 &=b \end{aligned}$

Thus, the value of b is b=4

Now, substituting the value of a and b in equation (1), we have,

$\begin{aligned} 4 a-2 b+c &=0 \\ 4(-2)-2(4)+c &=0 \\-8-8+c &=0 \\ c &=16 \end{aligned}$

Thus, the value of c is c=16

Now, substituting the value of a,b and c in the general formula $y=a x^{2}+b x+c$, we get,

y=-2x^{2} +4x+16

Taking out the common term as -2 we get,

y=-2(x^{2} -2x-8)

Factoring , we get,

$y=-2(x+2)(x-4)$

Thus, the function is $f(x)=-2(x+2)(x-4)$

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