Air is being pumped into a spherical balloon at the rate of 7 cm3/sec. What
is the rate of change of the radius at the in stant the volume equals 36π cm3
? The volume of
the sphere of radius r is (4 over PI )r power of 3

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]V=\frac{4}{3} \pi r^3\\\frac{dV}{dt} =\frac{4}{3} ~\pi \times ~3r^2\frac{dr}{dt} \\\frac{dV}{dt} =4\pi r^2\frac{dr}{dt} \\7=4\pi r^2\frac{dr}{dt} \\\frac{dr}{dt} =\frac{7}{4\pi r^2} \\when~V=36 \pi cm^3\\36\pi =\frac{4}{3} \pi r^3\\r^3=\frac{36\pi \times 3}{4\pi } =27=3^3\\r=3~cm\\\frac{dr}{dt} =\frac{7}{4\pi \tmes 3^2} \\\frac{dr}{dt} =\frac{7}{36 \pi } cm/sec[/tex]


Related Questions

(2a+15ab)-(7a+6b-10ab)

Answers

Answer:

Step-by-step explanation:

-5a - 6b + 25ab

add like terms

identify whether the given mathematical sentences below is true or false, then write your reason. If false , write the correct answer.​

Answers

Answer:

Step-by-step explanation:

first winter event question: wort 50 points and best explenation wins brainliest

whats 50 x 23 = ? Explain your awenser

Answers

Answer:

1150

Step-by-step explanation:

50x 23=150 +100=1150

Which expression is equivalent to squareroot 100?
A10
B10^2
C50
D50^2

Answers

The answer is A. The square root of 100 is ten because ten times ten is 100.

Answer:

10^2=100

because all u would do is put down 10 two times and then u just multiply those 2 numbers

Step-by-step explanation:

How many solutions does this system have?

y = 2/3x + 3

2x - 3y = -9


A. one solution

B. two solutions

C. no solutions

D. infinitely many solutions

Answers

Answer:

the answer is A .

Step-by-step explanation:

-2x+y=3 ----> 2x - y = -3

6x=9-3y

6x + 3y = 9

divide by 3 ,

2x + y = 3

Since the slopes are different, they will intersect.

So ONE solution.

Using the slope formula, find the slope of the line through the points (0,0) and (4,8).
Use pencil and paper. Explain how you can use mental math to find the slope of the line. (please show how to do on pencil and paper)

Answers

Answer:

[tex]m = 2[/tex]

Step-by-step explanation:

Using mental math to find the slope of the line:

If you think about the formula, then you set up the points in your head, you will notice that the first point is on top of the second point. And that way makes it easy to simplify. All you would need to do is subtract down in your head: For example:

(0, 0)

(4, 8)

As you can see, the first point is on top of the other, and that way you can just subtract from bottom to top. If you do it that way, it is set up (Remember, you would do this all in your head)

pls help i need help with this been working fo a bit

Answers

[tex]\\ \sf\Rrightarrow \dfrac{6}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}(y+x)[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{6}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}x+\dfrac{5}{7}y[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{6}{7}x+\dfrac{5}{7}x-\dfrac{2}{5}y+\dfrac{5}{7}y[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{11}{7}x+\dfrac{-14+25}{35}y[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{11}{7}x+\dfrac{11}{35}y[/tex]

Done!

[tex] \boxed{\huge \bf \: Question:—}[/tex]

[tex] \sf \longmapsto \: \dfrac{6}{7} x - \dfrac{2}{5} y + \dfrac{5}{7} (y + x)[/tex]

[tex]\boxed{\huge\bf \: Solution:—}[/tex]

[tex] \boxed{\bf \: Distribute:—}[/tex]

[tex]\sf \longmapsto \: \dfrac{6}{7} x - \dfrac{2}{5} y + \dfrac{5}{7} y + \dfrac{5}{7} \: x[/tex]

[tex]\sf \longmapsto \dfrac{6}{7} x + \dfrac{ - 2}{5} y + \dfrac{5}{7} y \: + \dfrac{5}{7} x[/tex]

[tex] \boxed{\bf \: Combining \: Like \: Terms:—}[/tex]

[tex]\sf \longmapsto\dfrac{6}{7} x + \dfrac{ - 2}{5} y + \dfrac{5}{7} y \: + \dfrac{5}{7} x[/tex]

[tex]\sf \longmapsto \bigg(\dfrac{6}{7} x + \dfrac{5}{7} x \bigg) \: + \bigg( \dfrac{ - 2}{5} y + \dfrac{5}{7} \: y \bigg)[/tex]

[tex]\sf \longmapsto \: \dfrac{11}{7} x \: + \dfrac{11}{35} y[/tex]

[tex]\boxed{\bf \: Answer:—}[/tex]

[tex] \boxed{\bf \: \dfrac{11}{7} x \: + \dfrac{11}{35} y}[/tex]

(-4x^3-x^2+3)-(x^3-2x^2-7x+2)

Answers

[tex](-4x^3-x^2+3)-(x^3-2x^2-7x+2)\\\\=-4x^3 -x^2 +3 - x^3 + 2x^2 + 7x -2 \\\\= -5x^3 +x^2 +7x +1 \\\\=-5x^3 -5x^2 +6x^2 +6x+ x+1\\\\=-5x^2(x+1) +6x(x+1) + (x+1)\\\\=(x+1)(-5x^2 +6x +1)\\\\=-(x+1)(5x^2 -6x -1)[/tex]

6. (5 points) Graph using two intercepts; show your work in finding the intercepts. 6x - 3y = 18
х

Answers

Answer:

Divide both sides by 18. The new coefficients will be the reciprocals of the intercepts:

[tex]6x-3y=18 \rightarrow \frac6{18}x - \frac3{18}y = 1 \rightarrow \frac x3-\frac y6 =1[/tex] The two intercepts are then 3 and -6.

(I know, dividing by 3 both sides of the equations would have made the whole process way easier).

Alternatively, plug x = 0 to find the y intercept and y=0 to find the x intercept. Either way the graph will look something like the one I'm sketching on paint.

Enrique bought a football and a puzzle at a store.



He paid $15.35 for the football.
He paid a total of $24.02 for the football and the puzzle.

​How much did Enrique pay for the puzzle, in dollars and cents?

Answers

Answer:

8 dollars and 67 cents...8.67

Step-by-step explanation:

5 dollar bill

3 one dollar bills

2 quarters

1 dime

1 nickel

2 pennies

solve 557+3 using number disks

Answers

557+3=560 cuz 57+3 = 60 and 60+500= 560

I need help with this badly. It's geometry and angles.

Answers

Answer:

∠ C = 118°

Step-by-step explanation:

DE = DF , then Δ DEF is isosceles with base angles congruent , then

∠ DEF = ∠ DFE = [tex]\frac{180-56}{2}[/tex] = [tex]\frac{124}{2}[/tex] = 62°

∠ DFE and ∠ DFB are adjacent angles on a straight line and sum to 180° , so

∠ DFB = 180° - 62° = 118°

BCDF is a parallelogram ( opposite sides are parallel )

The opposite angles of a parallelogram are congruent , then

∠ C = ∠ DFB = 118°

Ok done. Thank to me :>

please help i have a few minutes left!!
A. {a, c, g, j, k, r}
B. {C, g)
C. {a}
D. {a, c, g, j, q, k, r}

Answers

Answer:

Short

"Option A is the answer"

At the movie theatre, child admission is $5.50 and adult admission is $8.90. On Friday four times as many adults tickets as child tickets were sold, for a total sales of $986.40. How many child tickets were sold that day?

Answers

Answer:

You can use grouping, quantity and value to solve this question.

Child admission = $5.50

Adult admission = $8.90

Friday sales (Quantity):

Child = x

Adult = 4x

Total sales = 5x

Friday sales (Value):

Child = $5.50

Adult = 4 × $8.90

         = $35.60

Total sales = $986.40

1 group = $5.50 + $35.60

            = $41.10

Number of groups = $986.40 ÷ $41.10

                               = 24

The number of child tickets sold is 24.

The sum of a number times 7 and 15 is at least -19

Answers

Answer:

x(7+15) [tex]\leq[/tex] -19

Step-by-step explanation:

allison made a playlist that included 9/12 country songs. what are two equivalent fractions that represent the part of the play list that is country songs. explain why your fractions are correct?

Answers

Answer:

3/4,18/24

Step-by-step explanation:

You can mutiply the numerator and denominator by the same number or divide it by the same number as long as it is a whole number. Ex. (9/3) over (12/3)=3/4. Or (9x2)/(12x2)=18/24

Solve for x.

5(x−4)2=4x+14


x = 9

x = 8

x=−6

x=−16

Answers

Answer:

9 is the answer.

Step-by-step explanation:

5(x − 4)2 = 4x + 14

=> 10x - 40 = 4x + 14

=> 6x = 54

=> x = 9

Therefore, 9 is the answer.

Hoped this helped.

The value of the x after solving the equation 5 (x - 4) 2 = 4x + 14 is x = 9.

What are Linear Equations?

Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.

Given linear equation,

5 (x - 4) 2 = 4x + 14

5 × 2 (x - 4) = 4x + 14

10 (x - 4) = 4x + 14

By distributive property, p (q + r) = p q + p r

10x - (10 × 4) = 4x + 14

10x - 40 = 4x + 14

10x - 4x = 14 + 40

6x = 54

x = 54 / 6

x = 9

Hence the value of x is 9.

To learn more about Linear Equations, click on the link given below :

https://brainly.com/question/11897796

#SPJ2

Judith bought a rowboat priced at 671.65.shipping anf handling cost and additional 20% of the prices What was the total cost of the rowboat,including shipping and handilng?

Answers

Answer:

805.98

Step-by-step explanation:

671.65x.20=134.33

134.33+671.65=805.98

The line passes through point Q, located at (-1, 2), and point R, located at (1, -2). Which two points determine a line parallel to line Q R ?

Answers

Answer:

i need a picture to see sorry

Find the value of x.
950°
1280°
60°

Answers

Answer:

x=77

Step-by-step explanation:

128+95+60+x=360

283+x=360

x=77

An electronic company refurbishes game systems The table shows the profit made for the number of game systems sold. How much profit will be made for 35 game systems?

Answers

Answer: Give me the table and ill answer..

Step-by-step explanation:

I don’t understand this question can you please help me ?.

Answers

Answer:

Girl: YES = 12 ; NO = 38

Boy: YES = 29 ; NO = 21

Total: YES = 41 ; NO = 59

Step-by-step explanation:

hope this helps! :D

have a miraculous day!! <3

Girl yes=12;no=38 boy yes=29 no=59 and Yes=41 and no =59

A runner ran 1 4/5 miles on Monday and 6 3/10 on Tuesday. How many times her Monday's distance was her Tuesday's distance? Please help me I need an answer that makes sense

Answers

He ran more than enough that’s all extra talk

At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f (n) represents the total cost of shoe rental and n games, what is the recursive equation for f (n)?

f (n) = 2.75 + 4.75 + f (n − 1), f (0) = 2.75
f (n) = 4.75 + f (n − 1), f (0) = 2.75
f (n) = 2.75 + 4.75n, n > 0
f (n) = (2.75 + 4.75)n, n > 0

Answers

The recursive equation for f(n) will be:

f(n) = 2.75 + 4.75n, n > 0

The cost of the shoe rental = $2.75

The cost of 1 game = $2.75

The cost if n games = 4.75n

The total cost of shoe rental and n games = Cost of the shoe rental + cost of n games

Let the total cost of shoe rental and n games be f(n)

f(n) = 2.75 + 4.75n

Since at least 1 game will be played,

the recursive equation for f(n) will be:

f(n) = 2.75 + 4.75n, n > 0

Learn more on recursive functions here: https://brainly.com/question/11316313

A unique source of water pollution contributing to water quality problems in the Ganges River is: A. raw sewage. B. disease-causing organisms. C. zebra mussels. D. PCBs. E. ash from human cremations.

Answers

Is this a multiple choice answer? If not, the answer is E. Ash from human cremations

Two cards are drawn from a well-shuffled deck of 52 playing cards. Let X denote the number of aces drawn. Find P(X = 1).

Answers

Answer:

0.14479638

Step-by-step explanation:

Because 2 cards out of 52 are drawn without replacement, hypergeometric probability distribution should be used. Hence,

Combination of drawing 1 ace of 4 total aces C(4,1)

Combination of drawing 1 non-ace of 48 total non aces C(48,1)

Combination of drawing 2 cards of total 52 cards C(52.2)

C(4,1) = 4, C(48,1) = 48, C(52,2) = 1326

4*48/1326 = 0.14479638

y=sech(tan‐¹x) find the derivative ​

Answers

Recall that

d/dx sech(x) = - sech(x) tanh(x)

d/dx tan⁻¹(x) = 1/(1 + x²)

Then by the chain rule,

dy/dx = - sech(x) tanh(x) / (1 + x²)

What is the perimeter of the triangle?

Answers

Answer:

34

Step-by-step explanation:

12 on two of the sides and 10 on bottom

There is a problem with the question since it is supposed to say how much length does each box in the graph consider. But assuming that each box length is 1 unit...

The pythagorean formula states a^2 + b^2 equals c^2 .... Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)

So, lets just divide the blue triangle in half, symmetrically so that we can get a 90 degree angle. "a" is height of the half triangle and "b" is base of the half triangle so we have to find "c" (the hypotenuse) Now that we already can count and find the value of a is 12 unit and b is 5 unit.

So, 12^2 + 5^2 equals c^2 ... now if we solve the formula, the value of "c" comes 13 (it also comes -13 but negative number can not be counted in the diagram)

The triangle is a isoceles triangle which means both the sides of "c" are equal so... one side is 13 then the other side is also 13. and we already know the base is 10 units. So just add them up-   13+13+11 comes 37 units. (Its kinda complicated and i am bad at making someone understand so just learn the pythagorean theorum...)

SO THE FINAL ANSWER IS 37 UNITS. i am not sure so let me know if am correct. And if i m wrong... pls forgive me T-T

I need help please I'll give you 25 points​

Answers

Answer:

t = 11/21

Step-by-step explanation:

Hope this helps!!

Help me pls thank you so much

Answers

Answer: the second one

Step-by-step explanation:

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