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3 years ago

5

Suppose that one worker can produce 15 cookies, two workers can produce 35 cookies together, and three workers can produce 60 co

okies together. what is the marginal product of the 3rd worker?

1 answer:

Ksenya-84 [330]3 years ago

7 0

Suppose that one worker can produce 15 cookies, two workers can produce 35 cookies together, and three workers can produce 60 cookies together. What is the marginal product of the 3rd worker? Select one: a. 20 cookies b. 25 cookies c. 60 cookies d. 35 cookies

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A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. Find the dimensions of a norman

Yanka [14]

Answer:

$W\approx 8.72$ and $L\approx 15.57$ .

Step-by-step explanation:

Please find the attachment.

We have been given that a norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular. The total perimeter is 38 feet.

The perimeter of the window will be equal to three sides of rectangle plus half the perimeter of circle. We can represent our given information in an equation as:

$2L+W+\frac{1}{2}(2\pi r)=38$

We can see that diameter of semicircle is W. We know that diameter is twice the radius, so we will get:

$2L+W+\frac{1}{2}(2r\pi)=38$

$2L+W+\frac{\pi}{2}W=38$

Let us find area of window equation as:

$\text{Area}=W\cdot L+\frac{1}{2}(\pi r^2)$

$\text{Area}=W\cdot L+\frac{1}{2}(\pi (\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W}{2})^2)$

$\text{Area}=W\cdot L+\frac{\pi}{2}(\frac{W^2}{4})$

$\text{Area}=W\cdot L+\frac{\pi}{8}W^2$

Now, we will solve for L is terms W from perimeter equation as:

$L=38-(W+\frac{\pi }{2}W)$

Substitute this value in area equation:

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

Since we need the area of window to maximize, so we need to optimize area equation.

$A=W\cdot (38-W-\frac{\pi }{2}W)+\frac{\pi}{8}W^2$

$A=38W-W^2-\frac{\pi }{2}W^2+\frac{\pi}{8}W^2$

Let us find derivative of area equation as:

$A'=38-2W-\frac{2\pi }{2}W+\frac{2\pi}{8}W$

$A'=38-2W-\pi W+\frac{\pi}{4}W$

$A'=38-2W-\frac{4\pi W}{4}+\frac{\pi}{4}W$

$A'=38-2W-\frac{3\pi W}{4}$

To find maxima, we will equate first derivative equal to 0 as:

$38-2W-\frac{3\pi W}{4}=0$

$-2W-\frac{3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}=-38$

$\frac{-8W-3\pi W}{4}*4=-38*4$

$-8W-3\pi W=-152$

$8W+3\pi W=152$

$W(8+3\pi)=152$

$W=\frac{152}{8+3\pi}$

$W=8.723210$

$W\approx 8.72$

Upon substituting $W=8.723210$ in equation $L=38-(W+\frac{\pi }{2}W)$ , we will get:

$L=38-(8.723210+\frac{\pi }{2}8.723210)$

$L=38-(8.723210+\frac{8.723210\pi }{2})$

$L=38-(8.723210+\frac{27.40477245}{2})$

$L=38-(8.723210+13.70238622)$

$L=38-(22.42559622)$

$L=15.57440378$

$L\approx 15.57$

Therefore, the dimensions of the window that will maximize the area would be $W\approx 8.72$ and $L\approx 15.57$ .

8 0

3 years ago

Which of the following is more than 0.35 but less than 0.41

Hoochie [10]

Its B because 3/10ths is a little bit more than 0.35, but way less than 0.41

6 0

3 years ago

Read 2 more answers

Which equation represents the relationship shown in the graph below?

fomenos

I believe the answer is B
:)

3 0

3 years ago

Find the distance between the two points rounding to the nearest tenth (if necessary). (2,−3) and (0,−8)

saveliy_v [14]

Answer:

square root of 29

Step-by-step explanation:

use the distance formula and then plug the numbers in, i got the sqrt(29) after i did that

6 0

3 years ago

Javier bought a microwave for $105.The cost was 30% off the original price.what was the price of the microwave before the sale

tatuchka [14]

Answer:

$ 150

Step-by-step explanation:

Given:

Cost price of a microwave = $105

Discount % = 30

Question asked:

what was the price of the microwave before sale = ?

Solution:

Let the price of the microwave before sale = $x$

Price before sale - 30 % discount = cost price of microwave (by Javier)

$x - 30\% of x = 105$

$x - \frac{30x}{100} = 105$

$\frac{70x}{100} = 105\\$

Multiplying both side by 100

$70x = 105 \times 100$

$70x = 10500$

Dividing both side by 70

$x = \frac{10500}{70} \\x = 150$

x = price of the microwave before sale = $ 150

Thus, price of the microwave before the sale = $150

6 0

3 years ago