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balu736 [363]
3 years ago
7

At the circus, a clown is shot from a cannon. This situation can be modeled by the function: h = – 16t2 + 45t + 15, where 'h' is

height in feet and 't' is time in seconds. What is the maximum height of the clown?
A. 45 Feet
B. 109. 4 Feet
C. 72.3 Feet
D. 87.3 Feet
Mathematics
1 answer:
weeeeeb [17]3 years ago
4 0

Answer:

The maximum height is 46.64 feet.

Step-by-step explanation:

If we take the derivative of h whit respect to t and equal this to zero we would find the value of t which corresponds to the maximum h.

So, we have the function h(t):

h(t)=-16t^{2} + 45t + 15

Taking the derivative, we have:

\frac{dh(t)}{dt}=-32t + 45=0

Now, we solve it for t:

t=\frac{45}{32}=1.4\: s

Finally, we put this value of t into the original equation.

h(t)=-16(1.4)^{2} + 45(1.4) + 15

h_{max}=46.64\: ft      

Therefore, the maximum height is 46.64 feet. All the given options are wrong, the one that comes closest is option A.

I hope it helps you!          

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