Mathematics, 21.12.2020 05:10, texas101st78

The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the instant when the volume of the sphere is 77 cubic centimeters, what is the rate of change of the radius? The volume of a sphere can be found with the equation V=\frac{4}{3}\pi r^3.V= 3
4

πr
3
. Round your answer to three decimal places.

Answers: 1

Show answers

Answers

answered: AQUI

$\frac{dr}{dt} = -1.325 \ cm/s$

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Calculus

Derivatives

Basic Power Rule:

f(x) = cxⁿ f’(x) = c·nxⁿ⁻¹

Taking Derivatives with respect to time

Step-by-step explanation:

Step 1: Define

Given:

$V = \frac{4}{3} \pi r^3$

$\frac{dV}{dt} = -116 \ cm^3/s$

$V = 77 \ cm^3$

Step 2: Solve for r

Substitute: $77 = \frac{4}{3} \pi r^3$ Isolate r term: $\frac{77}{\frac{4}{3} \pi} = r^3$ Isolate r: $\sqrt[3]{\frac{77}{\frac{4}{3} \pi}} = r$ Evaluate: 2.63917 = r

Rewrite: $r = 2.63917 \ cm$

Step 3: Differentiate

Differentiate the Volume Formula with respect to time t.

Define: $V = \frac{4}{3} \pi r^3$ Differentiate [Basic Power Rule]: $\frac{dV}{dt} = \frac{4}{3} \pi \cdot 3 \cdot r^{3-1} \cdot \frac{dr}{dt}$ Simplify: $\frac{dV}{dt} = 4 \pi r^2 \cdot \frac{dr}{dt}$

Step 4: Find radius rate

Substitute in variables: $-116 \ cm^3/sec = 4 \pi (2.63917 \ cm)^2 \cdot \frac{dr}{dt}$ Isolate dr/dt rate: $\frac{-116 \ cm^3/s}{4 \pi (2.63917 \ cm)^2} = \frac{dr}{dt}$ Evaluate: $-1.3253 \ cm/s = \frac{dr}{dt}$ Rewrite: $\frac{dr}{dt} = -1.3253 \ cm/s$ Round: $\frac{dr}{dt} = -1.325 \ cm/s$

Our radius is decreasing at a rate of -1.325 cm per second.

answered: Guest

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1 1

1 2

1 3

1 4

2 1

2 2

2 3

2 4 = not 1, and 4

3 1

3 2

3 3

3 4 = not 1, and 4

only 2 outcomes have passed the given condition.

step-by-step explanation:

answered: Guest

add 8+12 to get a simplified answer of 12r-20

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 12:30, Jasten

Timed*** there are 8 rows and 8 columns, or 64 squares on a chessboard. suppose you place 1 penny on row 1 column a, 2 pennies on row 1 column b, 4 pennies on row 1 column c, and so on … how many pennies are on each square? a = b = c = d = e = f = g = h =

Answers: 1

continue

Mathematics, 21.06.2019 18:00, purplefish53

Jose predicted that he would sell 48 umbrellas. he actually sold 72 umbrellas. what are the values of a and b in the table below? round to the nearest tenth if necessary

Answers: 2

continue

Mathematics, 21.06.2019 22:00, amandajennings01

22. catie is starting a babysitting business. she spent $26 to make signs to advertise. she charges an initial fee of $5 and then $3 for each hour of service. write and solve an inequality to find the number of hours she will have to babysit to make a profit. interpret the solution.!

Answers: 1

continue

Mathematics, 21.06.2019 22:30, DatBoiCedd

Convert (-3,0) to polar form. a. (3,0’) b. (-3,180’) c. (3,180’) d. (3,360’)

Answers: 1

continue

Do you know the correct answer?

The volume of a sphere is decreasing at a constant rate of 116 cubic centimeters per second. At the...