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Ugo [173]
3 years ago
10

Look at the attached questions! Please answer both properly with explanation!!!

Mathematics
1 answer:
Alex777 [14]3 years ago
8 0

Answer:

Step-by-step explanation:A car takes 4 hours to reach a destination travelling at the speed of 63 km/h.

Speed = distance / time

Distance = speed × time

Distance it took the car, travelling for 4 hours to a destination at a speed of 63 kilometers per hour would be

4 × 63 = 252 kilometers.

if the car travels at a different speed of 56 kilometers per hour and the distance remains 252 kilometers, the time it takes will be

Time = distance / speed

= 252/56 = 4.5 hours

The time varies inversely with the speed. The more the speed, the lesser the time and the lesser the speed, the more the time.

Let speed = s and let time = t

s varies inversely with t

Introducing constant of inverse variation k, it becomes

s = k/t

When s = 56, t = 4.5

56 = k/4.5

k = 4.5 × 56 =252

This is the distance

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The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute. At the instant when the volume of
Inessa05 [86]

Using implicit differentiation, it is found that the rate of change of the surface area of the sphere -2201.293 square centimeters per second.

<h3>What is the volume of a sphere?</h3>
  • The volume of a sphere, of radius r, is given by:

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

<h3>What is the surface area of a sphere?</h3>
  • The surface area of a sphere, of radius r, is given by:

S = 4\pi r^2

<h3>What is the rate of change?</h3>

Applying <em>implicit differentiation</em>, the rate of change of both the volume and the surface area can be found, as follows:

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

\frac{dS}{dt} = 8\pi r\frac{dr}{dt}

Volume of 3131 cubic centimeters, hence:

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

\frac{4\pi r^3}{3} = 3131

4\pi r^3 = 3(3131)

r = \sqrt[3]{\frac{3(3131)}{4\pi}}

r = 9.0754

The volume of a sphere is decreasing at a constant rate of 9988 cubic centimeters per minute, hence:

\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}

-9988 = 4\pi (9.0754)^2\frac{dr}{dt}

\frac{dr}{dt} = -\frac{9988}{4\pi (9.0754)^2}

\frac{dr}{dt} = -9.651

Then, the <u>rate of change of the surface area</u> of the sphere is given by:

\frac{dS}{dt} = 8\pi (9.0754)(-9.651) = -2201.293

The rate of change of the surface area of the sphere -2201.293 square centimeters per second.

To learn more about implicit differentiation, you can take a look at brainly.com/question/25608353

4 0
3 years ago
Which function describes the arithmetic sequence shown?
Irina-Kira [14]

Answer:

D)

because thats the only answer that would make sence.

6 0
3 years ago
Divide this please urgent!
Sergeeva-Olga [200]

Answer:

3y² / x⁴z⁶

Step-by-step explanation:

12xy³z⁶ / 4x⁵yz¹² = 12/4 * x/x⁵ * y³/y * z⁶/z¹²

                           = 3 * 1/x⁴ * y² * 1/z⁶

                           = 3y² / x⁴z⁶

3 0
3 years ago
Read 2 more answers
How.can you get 103,727,495 to an espanded form
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<span>103,727,495

100,000,000 + 3,000,000 + 700,000 + 200,000 + 7,000 + 400 + 90 + 5
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4. a. In a survey of mobile and telephone, it was found that 200 people had telephone, 25
Kay [80]

Answer:

Socratic app

Step-by-step explanation:

it will help you

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