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vovikov84 [41]
3 years ago
9

Show that the maximum rate of change, with respect to radius, of the volume of a deflating balloon is four times the sphere's in

itial great circle circumference
Mathematics
1 answer:
dmitriy555 [2]3 years ago
7 0

Step-by-step explanation:

Let's say R is the initial radius of the sphere, and r is the radius at time t.

The volume of the sphere at time t is:

V = 4/3 π r³

Taking derivative with respect to radius:

dV/dr = 4π r²

This is a maximum when r is a maximum, which is when r = R.

(dV/dr)max = 4π R²

This is 4 times the sphere's initial great circle area, but not the great circle circumference.  The problem statement contains an error.

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a state charges an 8.5% sales tax and a 10% excise tax on gasoline. he purchased $25 of gasoline before tax. How should he find
Mama L [17]

Answer:

The total money spend on total tax of purchase is $4.625

Step-by-step explanation:

Given as :

The percentage of sales tax applied on gasoline purchase = 8.5%

The percentage of excise tax applied on gasoline purchase = 10%

The price of gasoline before tax = $25

Let The total money on total tax of purchase = $x

Now, Total percentage of tax = sales tax percentage + excise tax percentage

i.e  Total percentage of tax = 8.5% + 10%

Or,  Total percentage of tax = 18.5%

<u>Again</u>

total money on total tax of purchase = $25 of total total tax percentage

Or, x = $25 × 18.5%

Or, x = $25 × \dfrac{18.5}{100}

Or, x = $25 × 0.185

∴  x = $4.625

So,The total money on total tax of purchase = x = $4.625

Hence,The total money spend on total tax of purchase is $4.625 Answer

4 0
2 years ago
How to solve 9x 4 2/5 in words
Natalija [7]

Answer:

39.6

Thirty nine point six

Step-by-step explanation:

9 x 4 2/5

9 x 22/5

198/5 = 39.6

Thirty nine point six

3 0
3 years ago
What is the value of x
zzz [600]

Answer:

x = 5

Step-by-step explanation:

Δ EAB and Δ EDC are similar by the AA postulate , so the ratio of corresponding sides are in proportion , that is

\frac{AB}{DC} = \frac{EA}{ED} , substitute values

\frac{10}{4} = \frac{2x+10}{x+3} ( cross- multiply )

10(x + 3) = 4(2x + 10 ) ← distribute parenthesis on both sides

10x + 30 = 8x + 40 ( subtract 8x from both sides )

2x + 30 = 40 ( subtract 30 from both sides )

2x = 10 ( divide both sides by 2 )

x = 5

8 0
2 years ago
1. An AP Statistics class starts a project to estimate the average number of hours a student at their high school sleeps per nig
Aleks [24]

Answer:

(C) Sample: the 120 students surveyed. Population: the 1200 students at the high school. Parameter of interest: the average number of hours a student at this high school sleeps per night.

Step-by-step explanation:

The correct answer is (C). The sample is a subset of the population, and the parameter is a characteristic of the population of interest.

6 0
3 years ago
An art teacher makes a batch of purple paint by mixing 3/4 cup red paint with 3/4 cup of blue paint. If she mikes 13 batches, ho
Pepsi [2]
She will have 19.5 cups of purple paint.
I couldn’t write the explanation of how you get the answer, but look your question up on Brainly and it’ll give you your explanation.

Hope this helped! :)
5 0
2 years ago
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