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3 years ago

8

Last year, at the Great American Pie Festival, over 16,000 slices of pie was eaten. If each piece of pie is 1/8 of and entire pi

e, how many pies were eaten at the festival?

1 answer:

egoroff_w [7]3 years ago

4 0

16,000 slices/8 slices per pie=2,000 pies.

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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:

<u>Optimizing With Derivatives </u>

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

I need a answer to this problem asap please help

Georgia [21]

First factor (x square -36), the answer will be (x+6)(x-6).

Second, cancel the x .

6x/ (x+6)(x-6)

4x/(6)(-6)

4x/-36

4 0

4 years ago

Tricia got a 6% raise on her weekly salary. The raise was $30 per week. What was her original weekly salary in dollars per week?

serious [3.7K]

Answer: Original salary = $500

Step-by-step explanation: Tricia got a 6% raise on her weekly salary. The

raise was $30 per week.

Let x be the original salary

x times the raise percentage = raise amount

6%= 6/100=0.06, raise amount = 30

Now we solve for x

Divide by 0.06 on both sides

Original salary = $500

6 0

3 years ago

The sum of two numbers is 8and the sum of their squares is 34. What is the smaller number?

gladu [14]

Answer:

3

Step-by-step explanation:

3 squared is 9. 5 squared is 25. 25 + 9 = 34. 5 + 3 = 8. So the smaller number is 3.

4 0

4 years ago

Read 2 more answers

Ana will spin the spinner. What is the probability that Ana's spin will land on yellow? If there are 2 Red Sections, 3 Blue Sect

Dvinal [7]

Answer:

The probability is 1/3

Step-by-step explanation:

Here, we are interested in calculating the probability that the spinner will land on the yellow section.

Firstly, we need to calculate the total number of sections. That would be = 2 + 3 + 4 + 3 = 12 sections

Now, the probability that the spinner will land on the yellow section = number of yellow sections/total number of sections

There are four yellow sections

Thus, the probability of the spinner falling on a yellow section = 4/12 = 1/3

3 0

3 years ago