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klemol [59]
3 years ago
11

The volume of a spherical hot air balloon v(r) = 4/3 πr^3 changes as its radius changes. the radius is a function of time given

by r(t) = 3t. find the average rate of change of the volume with respect to t as t changes from t = 1 to t = 4.
Mathematics
1 answer:
Nataliya [291]3 years ago
3 0
<span>At t = 1: The radius is 3(1) = 3 The volume is 4/3 π(3)^3 = 113 At t = 4: The radius is 3(4) = 12 The volume is 4/3 π(12)^3 = 7238 We can find the change in the volume: The change in volume is 7238 - 113 = 7125 The change in volume occurred during a time of 3 seconds. To find the average rate of change in the volume, we need to divide the change in the volume by the time. average rate of change = 7125 / 3 = 2375 The average rate of the change in the volume is 2375 (The units should be (m^3/s) or (ft^3/s) or (cm^3/s) etc...)</span>
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The ratio of boys to girls in a class is 5:4. There are 36 students in the class. How many students are girls?
maksim [4K]

Answer:

16 girls

Step-by-step explanation:

If the ratio Is b:g, then we can assume the majoraty are boys.

If we look at the factors for these numbers, it goes like this: 5, 10, 15, 20, 25 for 4, we get 4, 8, 12, 16, 20, 24. If you look at the fourth factor, 20, and 16, then you can see that they add up to 36.

5 0
3 years ago
Y+7=y–3 how many solutions does this equation have?
Anettt [7]

Answer:

No value

Step-by-step explanation:

Y has zero solutions

7 0
4 years ago
The perimeter of the picture frame is 38 inches. The width of the frame is 7 inches, what is the length?
o-na [289]

Answer:

12 inches

Step-by-step explanation:

So you know that the perimeter of a picture frame (a rectangle) is 2 widths plus 2 lengths.

Let x= lengths and w= widths

From the question we already know that w=7, so we can set up an equation that says:

2x + 2w = 38

2x + 2(7) = 38

2x+14 = 38

2x +14 -14 = 38-14

2x = 24

2x/2 = 24/2

x= 12

Since x= lengths =12

the length of the frame is 12 inches.

7 0
4 years ago
The volume of a cylinder is 1225π cm. The height of the cylinder is 25 cm. What is the radius of the​ cylinder?
monitta

Answer:

Volume of cylinder = pi r^2 h

1225 pi = pi×r^2×25

r^2= 1225/25=49

so, r= 7 cm

7 0
3 years ago
Marilyn uses a credit card with a 19.9% APR compounded monthly to pay for car repairs totaling $991.38. She can pay $410 per mon
Leokris [45]
Marilyn's finance charge at the end of the first month will be
  $991.38 × 0.199/12 = $16.44
The balance subject to the next month's finance charge will be
  $991.38 +16.44 -410.00 = $597.82

The finance charge at the end of the second month will be
  $597.82 × 0.199/12 = $9.91
The balance remaining after the second payment will be
  $597.82 +9.91 -410.00 = $197.73

The finance charge applied at the end of the third month is
  $197.73 × .199/12 = $3.28
so Marilyn can make one final payment of
  $197.73 +3.28 = $201.01
to pay off the balance.

In all, Marilyn has paid 2×$410.00 +201.01 = 
  $1021.01 . . . . . . . . corresponds to the first choice

_____
In real life, Marilyn's credit card may not accrue any finance charge until after the first statement on which the charge appears. Thus the total cost of the purchase may be only $1004.02. The attached spreadsheet shows the beginning balance and the finance charges for each month for the two different scenarios.

8 0
3 years ago
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