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love history [14]
3 years ago
5

the pie factory sells an apple pie with a diameter of 16 in. for $10.99. What's the approximate cost per square inch of surface

area of the pie? Use 3.14 for π
Mathematics
1 answer:
AURORKA [14]3 years ago
5 0
I'm going to assume the crust covered by the dosenot matter because the total surface area cannot be found without the depth of the pie.

So the surface are is the area of the top of the pie, the top of the pie is circular and is equal to 2\pir²

The diameter is the sum of 2 radii, hence r=8

D=12
  = 2r =12
r=8

With the raduis the area can be found
A= 2\pir²
A=2\pi8² 
A=2(64)\pi
A=128\pi

If the pie cost 10.99, the cost per inch can be found by dividing the area by cost

cost/inch =128 \pi/10.99
cost/inch =11.64\pi
               = 11.64(3.14)
               = 36.57

The pie costs 36 cents per square inch
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3 years ago
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A scuba diving company currently charges $100per dive. On average, there are 30 customers per day. The company performed a study
Semenov [28]

A. Total Revenue (R) is equal to price per dive (P) multiplied by number of customers (C). We can write R=PC.

Per price increase is $20. So four price increase is $20*4=$80. Hence, price per dive is 100+80=$180.

Also per price increase, 2 customers are reduced from 30. For 4 price increases, 4*2=8 customers are reduced. Hence, total customers is 30-8=22.

So Total Revenue is:

R=180*22=3960


B. Each price increase is 20. So x price increase is 20x. Hence, new price per dive would be equal to the sum of 100 and 20x.

Also per price increase, customers decrease by 2. So per x price increases, the customer decrease is 2x. Hence, new number of customers is the difference of 30 and 2x.

Therefor we can write the quadratic equation for total revenue as the new price times the new number of customers.

R=(100+2x)(30-2x)=-40x^{2}+400x+3000


C. We are looking for the point (x) at which the equation modeled in part (B) gives a maximum value of revenue (y). That x value is given as x=-\frac{b}{2a}, where a is the coefficient of x^{2} and b is the coefficient of x. So we have,

x=-\frac{b}{2a}=- \frac{400}{(2)(-40)}=5

That means, the greatest revenue is achieved after 5 price increases. Each price increase was 20, so 5 price increase would be 5*20=100. So the price that gives the greatest revenue is 100+100=200.

ANSWERS:

A. $3960

B. R=-40x^{2}+400x+3000

C. $200

4 0
3 years ago
Calculate the distance between each given pair of points. Round your answer to the nearest tenth, if necessary.
Ksju [112]
The answer is 5 

Here are the steps:

First off, we will be using the distance formula of 
d=\sqrt{(x_ {2}- x_{2}) ^{2}+( y_{2}- y_{1})^2     }

So we have the ordered pairs of (3,1) and (6,5)

Once you plug them into the formula it should look like this: 
d= \sqrt{(6-3)^2+(5-1)^2}

Now we do the math inside the parenthesis and end up with:
d=\sqrt{3^2+4^2}

Then you multiply by the power and simplify to get:
d=\sqrt{25}

And the \sqrt{25}=5

So your answer is 5
8 0
3 years ago
I need help with all 8!
a_sh-v [17]
1) D
2)
3) B
4 ) F
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I'm not sure about questions 4 and 7, but they may be correct.

I couldn't because I couldn't see the 2nd question
3 0
3 years ago
7 + 2y = 8x 3x - 2y = 0 Solve the system of equations by substitution. (70/3, 140/9) (7/5, 21/10) no solution coincident
Wittaler [7]
So we have the system of equations:
7+2y=8x equation (1)
3x-2y=0 equation (2)

To use substitution, we are going to solve for one variable in one of our equations, and then we are going to replace that value in the other equation:
Solving for x in equation (2):
3x-2y=0
3x=2y
x= \frac{2}{3}y equation (3)

Replacing equation (3) in equation (1):
7+2y=8x
7+2y=8( \frac{2}{3} y)
7+2y= \frac{16}{3} y
7= \frac{10}{3} y
y= \frac{7}{ \frac{10}{3} }
y= \frac{21}{10} equation (4)

Replacing equation (4) in equation (3):
x= \frac{2}{3}y
x=( \frac{2}{3} )( \frac{21}{10} )
x= \frac{7}{5}

We can conclude that the solution of our system of equations is <span>(7/5, 21/10)</span>
5 0
3 years ago
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