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3 years ago

Which transformation of x?

Mathematics

1 answer:

Nady [450]3 years ago

3 0

Its C! Hope this helps and can you mark me as brainliest :))

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A spherical balloon currently has a radius of 19cm. If the radius is still growing at a rate of 5cm or minute, at what rate is a

miv72 [106K]

Answer:

22670.8 cm³/min

Step-by-step explanation:

Given:

Radius of the balloon at a certain time (r) = 19 cm

Rate of growth of radius is, $\frac{dr}{dt}=5\ cm/min$

The rate at which the air is pumped in the balloon can be calculated by finding the rate of increase in the volume of the balloon.

So, first we find the volume of the sphere in terms of 'r'. As the balloon is spherical in shape, the volume of the balloon is equal to the volume of a sphere. Therefore,

Volume of balloon is given as:

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

Now, rate of increase of volume is obtained by differentiating both sides of the equation with respect to time 't'.

Differentiating both sides with respect to time 't', we get:

$\frac{dV}{dt}=\frac{d}{dt}(\frac{4}{3}\pi r^3)\\\\\frac{dV}{dt}=\frac{4\pi}{3}(3r^2)(\frac{dr}{dt})\\\\\frac{dV}{dt}=4\pi r^2(\frac{dr}{dt})$

Now, plug in 19 cm for 'r', 5 cm per minute for $\frac{dr}{dt}$ and solve for $\frac{dV}{dt}$ . This gives,

$\frac{dV}{dt}=4\pi (19 cm)^2(5\ cm/min)\\\\\frac{dV}{dt}=4\times 3.14\times 361\times 5\ cm^3/min\\\\\frac{dV}{dt}=22670.8\ cm^3/min$

Therefore, the rate at which the air is being pumped into the balloon is 22670.8 cm³/min.

4 0

3 years ago

Select the simplification that accurately explains the following statement.

Mariana [72]

Answer

Explanation

9⁽¹/²⁾² = (9⁽¹/²⁾)²

= 9¹/² × 9¹/² (Since the base are the same, we can add the power.)

= 9⁽¹/² ⁺¹/²⁾

= 9 ¹

= 9

The correct simplification is D.

8 0

3 years ago

Find three consecutive odd integers such that the sum of the largest and twice the smallest is 25. If x represents the smallest

Murrr4er [49]

1. x
2. x + 2
3. x + 4

x + 4 + 2x = 25. Second option is the answer.

Combine like terms
3x + 4 = 25
Subtract 4 from both sides
3x = 21
Divide both sides by 3
x = 7

5 0

3 years ago

What is the exact area of a circle whose radius is 9 yd? Enter your answer in the box. Express your answer in terms of

atroni [7]

Answer:

$81\pi$

Step-by-step explanation:

Area = pi*r^2

Area = pi*9^2

Area = $81\pi$

6 0

2 years ago

Read 2 more answers

hey the question is, " The length of a rectangle is twice its width. The perimeter of the rectangle is 126 feet."

Tema [17]

Answer:

42 = l

21 = w

Step-by-step explanation:

{l = 2w

{126 = 2w + 2l

126 = 2w + 2[2w]

126 = 2w + 4w

126 = 6w

21 = w [Plug this back into both equations to get the length of 42]; 42 = l

I am joyous to assist you anytime.

4 0

3 years ago

Which transformation of x?​

Which transformation of x?