Evaluate each expression.
3) 19C3
A) 969
C) 5,814
B) 484
D) 1,130

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Ответ:

natalie2sheffield

13.11.2022

Mathematics

31.64 feet

Step-by-step explanation:

The height is given by the equation:

$h(x) = -32x^2/45^2 + x +210 = -\frac{32}{45^2}x^2 + x +210$

where x is the horizontal distance of the projectile from the face of the cliff.

If the height is maximum, then its derivative must be h'(x)=0. Remembering that the derivative of x^n is $nx^{n-1}$ , we have:

$h'(x) = (-\frac{32}{45^2}x^2 + x +210)' = (-\frac{32}{45^2}x^2)' + (x)' +(210)'=-2\frac{32}{45^2}x+1$

And we want h'(x)=0, so:

$-2\frac{32}{45^2}x+1=0$

This will give us the horizontal distance from the face of the cliff when the height of the projectile is at its maximum. We then do:

$2\frac{32}{45^2}x=1$

$x=\frac{1}{2}\frac{45^2}{32}=31.64$

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Evaluate each expression. 3) 19C3 A) 969 C) 5,814 B) 484 D) 1,130