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Ilya [14]
1 year ago
8

A spherical balloon is inflated with gas at the rate of 500 cubic centimeters per minute. How fast is the radius of the balloon

increasing at the instant the radius is 70 centimeters
Mathematics
1 answer:
zmey [24]1 year ago
4 0

Using implicit differentiation, it is found that the radius is increasing at a rate of 0.0081 cm per minute.

<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}

Applying implicit differentiation, the rate of change is given by:

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

In this problem, we have that:

\frac{dV}{dt} = 500, r = 70

Hence the rate of change of the radius is given as follows:

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

19600\pi\frac{dr}{dt} = 500

\frac{dr}{dt} = \frac{500}{19600\pi}

\frac{dr}{dt} = 0.0081

The radius is increasing at a rate of 0.0081 cm per minute.

More can be learned about implicit differentiation at brainly.com/question/25608353

#SPJ1

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Please help with this question.
andrew11 [14]

Answer:

p3+13=37

We move all terms to the left:

p3+13-(37)=0

We add all the numbers together, and all the variables

p^3-24=0

7 0
3 years ago
U(8, 9) and V(2, 5) are the endpoints of a line segment. What is the midpoint M of that line segment?
Crazy boy [7]

Answer:

(5, 7 )

Step-by-step explanation:

Given 2 points (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is

[ 0.5(x₁ + x₂ ), 0.5(y₁ + y₂ ) ]

here (x₁, y₁ ) = U(8, 9) and (x₂, y₂ ) = V(2, 5), thus

midpoint = [0.5(8 + 2), 0.5(9 + 5) ] = [0.5(10), 0.5(14) ] = (5, 7 )

6 0
3 years ago
John is five years older than his sister. The product of their present ages is 150.
photoshop1234 [79]
Took 3 of us in grade 10 but johns present age is 77.5 and his sister is 72.5
5 0
3 years ago
6000 increased by 145%
Lisa [10]
Your question would be clearer if written as "What is 145% of 6000?"

1.45(6000) = 8700
8 0
3 years ago
Anonymous 3 years ago
amm1812
Two angles are said to be complementary, if the sum of the measures of the to angles is equal to 90 degrees.

Thus, given that HFG is complementary to ACB, them mHFG + mACB = 90 degrees.

From the figure, given that the line from point F meats line CE at point P, then HFG = CFP.
But mCFE = 90 degrees and mCFE = mCFP + mPFE
Also PFE = DFH

Thus, mCFE = mCFP + mPFE = mHFG + mDFH = 90 degrees

Recall that mHFG + mACB = 90 degrees

Thus, mHFG + mACB = mHFG + mDFH

Therefore, mACB = mDFH.
5 0
3 years ago
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