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enot [183]
2 years ago
14

The function f(x) = xπ−−√ gives the diameter, in inches, of a proposed spherical sculpture with a surface area of x square inche

s. The artist making the sculpture wants to know how the diameter changes if the surface area is increased. What is the average rate of change for the function as the surface area changes from 12.6 in.2 to 28.3 in.2? Round your answer to the nearest hundredth of an inch.
Mathematics
1 answer:
natka813 [3]2 years ago
3 0

Answer:

The average rate of change of f(x) = 3.14 inches⁻¹

The change in f(x) = 49.32 in

Step-by-step explanation:

The surface area of the spherical sculpture = x and its diameter f(x) = πx.

The average rate of change of f(x) as x changes is df(x)/dx = π = 3.14

Now the change in diameter Δf(x) = df(x) = (df(x)/dx)dx = πdx  

dx = Δx = 28.3 in² - 12.6 in² = 15.7 in²

df(x) = π × 15.7 = 49.32 in

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1 year ago
Your school wants to take out an ad in the paper congratulating the basketball team on a successful​ season, as shown to the rig
Serga [27]

Answer:

1.4in

Step-by-step explanation:

Length of Photo = 4in

Width of Photo = 3in

Unknown:

Value of X = ?

Solution:

Follow these steps:

  Area of a rectangle  = l x w

Since the photo is a rectangle; area of photo:

  Area of photo  = 4in x 3in = 12in²

For the area of the ad;

   Length of ad  = 4 + x

   Width of ad = 3 + x

Given that,

                  the area of the photo  = \frac{1}{2} area of ad

                           12in²  = \frac{1}{2} area of ad

                   Area of ad  = 24in²

Area of the ad;

             (4 + x) (3 + x)  = 24

               12 + 4x + 3x + x² = 24

                12 + 7x + x²  = 24

                       x² + 7x = 24 - 12

                       x² + 7x = 12

                     x² + 7x - 12  = 0

            Using the almighty formula where

     a  = 1, b = 7 and c = -12

          x  = \frac{-b (+/-) \sqrt{b^{2} } - 4ac}{2a}

     

          x = \frac{-7 + \sqrt[]{-7^{2} - 4x1x-12 } }{2x1}   or \frac{-7 - \sqrt[]{-7^{2} - 4x1x-12 } }{2x1}

          x  = 1.4  or  -8.4

therefore the answer is 1.4in

x is 1.4in

4 0
1 year ago
Wendy opens a bank account with money she has saved. After this initial deposit, Wendy then deposits the same amount of money ea
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If the table is:


x | y

------

1 | 76

------

2 | 92

---------

3 | 108

-----------

4 | 124



-------------------------------------------------------------------------------------------------------------------


Find the change inbetween each amount per week


92 - 76 = 16

108 - 92 = 16


etc.


This means that her initial deposit should be subtracting 16 from her first deposit.


76 is the amount first deposited


76 - 16 = 60


A) $60 should be your answer


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8 0
2 years ago
Read 2 more answers
There are 9 students in a service club. The club is making gift baskets for children in a hospital. Each club member donated 4 c
VladimirAG [237]

Answer:

Step-by-step explanation:

Let x represent the number of toys that each club member donated.

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If each club member donated 4 children's books for the baskets, it means that the total number of books donated by the club members would be

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If each club member also donated an equal number of toys. It means that the total number of toys donated by the club members would be

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A total of 63 items were collected for the baskets. Therefore, the linear equation that you can use to find how many toys each club member donated would be

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nadya68 [22]

Answer:

The answer would be A. 55.

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For the 3/8 you would divide and get .375 then you would multiply that by 200 which would give you 75 yellow tags. Then you would add 75 and 70 and get 145. Then subtract 145 from 200 to get 55. Therefore there would be 55 red tags.

5 0
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