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3 years ago

A. A frog is climbing out of a well that is 8 feet deep. The frog can climb 4 feet per

Mathematics

1 answer:

Fiesta28 [93]3 years ago

4 0

Answer:

A: 5 hrs. B: 14 hrs. and 40 min.

Step-by-step explanation:

too long to explain.

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How to find three consecutive odd numbers whose product is 2145?

balu736 [363]

Hello :
2145 = 11×13×3×5 ( prime factorisation product)
2145 = 11×13×15
the three consecutive odd numbers whose product is 2145 are : 11 , 13 ,15

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3 years ago

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Viktor [21]

Answer:

False

Step-by-step explanation

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3 years ago

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If nine is X percent of 45, what is X percent of 5

antoniya [11.8K]

Answer:

x percent of 5 is 1

Step-by-step explanation:

Nine is x percent of 45

x = 20

20 % of 5 = 1

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4 years ago

Analyze the diagram below and complete the instructions that follow.

Damm [24]

D. Angel 6 because vertical is just asking what angle is on the other side of angle 3

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3 years ago

A metal cylinder can with an open top and closed bottom is to have volume 4 cubic feet. Approximate the dimensions that require

Aleksandr-060686 [28]

Answer:

$r\approx 1.084\ feet$

$h\approx 1.084\ feet$

$\displaystyle A=11.07\ ft^2$

Step-by-step explanation:

Optimizing With Derivatives

The procedure to optimize a function (find its maximum or minimum) consists in :

Produce a function which depends on only one variable
Compute the first derivative and set it equal to 0
Find the values for the variable, called critical points
Compute the second derivative
Evaluate the second derivative in the critical points. If it results positive, the critical point is a minimum, if it's negative, the critical point is a maximum

We know a cylinder has a volume of 4 $ft^3$ . The volume of a cylinder is given by

$\displaystyle V=\pi r^2h$

Equating it to 4

$\displaystyle \pi r^2h=4$

Let's solve for h

$\displaystyle h=\frac{4}{\pi r^2}$

A cylinder with an open-top has only one circle as the shape of the lid and has a lateral area computed as a rectangle of height h and base equal to the length of a circle. Thus, the total area of the material to make the cylinder is

$\displaystyle A=\pi r^2+2\pi rh$

Replacing the formula of h

$\displaystyle A=\pi r^2+2\pi r \left (\frac{4}{\pi r^2}\right )$

Simplifying

$\displaystyle A=\pi r^2+\frac{8}{r}$

We have the function of the area in terms of one variable. Now we compute the first derivative and equal it to zero

$\displaystyle A'=2\pi r-\frac{8}{r^2}=0$

Rearranging

$\displaystyle 2\pi r=\frac{8}{r^2}$

Solving for r

$\displaystyle r^3=\frac{4}{\pi }$

$\displaystyle r=\sqrt[3]{\frac{4}{\pi }}\approx 1.084\ feet$

Computing h

$\displaystyle h=\frac{4}{\pi \ r^2}\approx 1.084\ feet$

We can see the height and the radius are of the same size. We check if the critical point is a maximum or a minimum by computing the second derivative

$\displaystyle A''=2\pi+\frac{16}{r^3}$

We can see it will be always positive regardless of the value of r (assumed positive too), so the critical point is a minimum.

The minimum area is

$\displaystyle A=\pi(1.084)^2+\frac{8}{1.084}$

$\boxed{ A=11.07\ ft^2}$

8 0

3 years ago