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mr Goodwill [35]
3 years ago
14

While chasing its prey, a cheetah is running slowly and then increases its speed by 50.6 miles per hour to reach a top speed of

70 miles per hour. What is the cheetah's initial speed? And what is the answer in miles per hour
Mathematics
1 answer:
shusha [124]3 years ago
3 0

Answer:

The Cheetah's initial speed is 19.4 miles per hour

Step-by-step explanation:

Since the Cheetah is initially running and then gradually increases its speed by 50.6 miles per hour to reach a top speed of 70 miles per hour, let the Cheetah's initial speed be u.

Also, let the increase in the Cheetah's speed be Δu and let v be the Cheetah's final speed.

Now, the final speed, v = initial speed, u + change in speed, Δu

So, v = u + Δu

So, the Cheetah's initial speed is u = v - Δu

Now, v = 70 mi/h and Δu = 50.6 mi/h

Substituting v and Δu into the equation, we have

u = v - Δu

u = 70 mi/h - 50.6 mi/h

u = 19.4 mi/h

So, the Cheetah's initial speed is 19.4 miles per hour

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Step-by-step explanation:

First we have to understand the problem, we have a box of unknown dimensions (base b, depth d and height h), and we want to optimize the used material in the box. We know the volume V we want, how we want to optimize the card used in the box we need to minimize the Area A of the box.

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The hessian matrix is defined as,

H=\left[\begin{array}{ccc}\frac{\partial^2 A}{\partial d^2} &\frac{\partial^2 A}{\partial d \partial h}\\\frac{\partial^2 A}{\partial h \partial d}&\frac{\partial^2 A}{\partial p^2}\end{array}\right]

we know that,

\frac{\partial^2 A}{\partial d^2}=\frac{\partial}{\partial d}(-\frac{400}{d^2}+2h )=\frac{800}{d^3}

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H=\left[\begin{array}{ccc}4&2\\2&4\end{array}\right]

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