1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
andrew11 [14]
3 years ago
5

A beach ball is inflated so its diameter increases from 12 inches to 12.5 inches. Given that the formula for the volume of a sph

ere is V=4/3π,r^3 the change in the volume of the beach ball using differentials is approximately.
a. 367π cubic inches.
b. 727π cubic inches.
c. 1447π cubic inches.
d. 288.7π cubic inches.
Mathematics
1 answer:
Oxana [17]3 years ago
5 0

Answer:

V = 36π cubic inches.

Step-by-step explanation:

Given that:

The volume of the sphere is V = \dfrac{4}{3} \pi r^3

If the diameter is represented by P.

Then P = 2r

and r = P/2

∴

V = \dfrac{4}{3} \pi ( \dfrac{P}{2})^3

By differentiating both sides;

dV = \dfrac{4}{3} \pi \times 3 ( \dfrac{P}{2})^2 \times \dfrac{1}{2} \times dP

dV  = \dfrac{1}{2} \pi P^2 \ dP

where;

P = 12

dP = 12.5 - 12

dP = 0.5

Then;

\dfrac{1}{2} \pi ( 12)^2 \times 0.5

= 36π

Thus, the volume is V = 36π cubic inches.

You might be interested in
The rock hard company is going to transport truckloads of stones to a highway project. It will cost $4200 to rent trucks, and it
Darya [45]

Answer:

c =4200+275s

Step-by-step explanation:

C is the total cost

4200 is how much to rent the trucks

275 is the price for each ton

s is how many tons of stone in being transported

4 0
4 years ago
Decide whether a triangle with side lengths of sqr5, 5, and 5.5 is right, acute, or obtuse.
LUCKY_DIMON [66]
It is acute isosceles triangle
4 0
3 years ago
On a hot Saturday morning while people are working​ inside, the air conditioner keeps the temperature inside the building at 24
Helen [10]

Answer:

30.06 degree Celsius at 4:00 PM.

Step-by-step explanation:

We have been given that on a hot Saturday morning while people are working​ inside, the air conditioner keeps the temperature inside the building at 24 degrees C. At noon the air conditioner is turned​ off, and the people go home. The temperature outside is a constant 35 degrees C for the rest of the afternoon. The time constant for the building is 5 ​hr. We are asked to find the temperature inside the building at 4:00 PM.

We will use Newton's law of cooling to solve our given problem.

T(t)=M_0+(T_0-M_0)e^{-kt}, where

T(t) = Temperature after t hours.

M_0 = Temperature of surrounding environment,

k = Time constant.

\frac{1}{k}=5\Rightarrow k=\frac{1}{5}

Upon substituting our given values in Newton's cooling law, we will get:

T(t)=35+(24-35)e^{-\frac{t}{5}}

T(t)=35-11e^{-\frac{t}{5}}

To find the temperature at 4:00 pm, we will substitute t=4 in our formula as:

T(4)=35-11e^{-\frac{4}{5}}

T(4)=35-\frac{11}{e^{\frac{4}{5}}}

T(4)=35-\frac{11}{2.2255409284924674}

T(4)=35-4.9426186052894379601

T(4)=30.05738139471

T(4)\approx 30.06

Therefore, the temperature inside building would be approximately 30.06 degree Celsius at 4:00 PM.

5 0
3 years ago
MATH QUESTION HELP. Hhhhnh
maksim [4K]

Answer:

y

Step-by-step explanation:

that easy just isolate the variables

3 0
2 years ago
Plzz what the answer I’m stuck
castortr0y [4]

Answer:

the answer to your question is 576 square feet

Step-by-step explanation:

Step 1: 96 ÷ 4 = 24

Step 2: 24×24 =576

5 0
3 years ago
Other questions:
  • A stoplight has the following cycle: green for 1 minute, yellow for 3 seconds, and red for 1 minute 40 seconds. If you arrive at
    10·2 answers
  • Can someone please help me with this ?
    5·1 answer
  • 1 Find the value of x in the triangle shown below.​
    7·1 answer
  • Convert 300 Kelvin to Celsius. Write your answer using decimals.
    8·1 answer
  • What does 4 feet equal
    6·1 answer
  • Need help with this question please!
    6·1 answer
  • Solve for x.<br><br> x<br> 18<br> = 10<br><br> A) 8 <br> B) 28 <br> C) 162 <br> D) 180
    9·2 answers
  • Please help me, its due today!!!
    6·1 answer
  • Which graph represents y=x^3-4
    8·1 answer
  • Benjamin works at a printing company. He is making T-shirts for a high school volleyball team. The press he runs can imprint 3 T
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!