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aliya0001 [1]
3 years ago
8

A spherical balloon is being inflated at a rate of 3 cubic inches per second. Determine the change in the rate of the radius.How

fast is the radius of the balloon changing at the instant the balloon’s diameter is 12 inches? Is the radius changing more rapidly when d=12 or when d=16 ? Why?
Mathematics
1 answer:
Novay_Z [31]3 years ago
5 0

Answer:

The rate rate of change of radius is \frac{1}{48\pi} inches per second when the diameter is 12 inches.

The radius is changing more rapidly when the diameter is 12 inches.

Step-by-step explanation:

Consider the provided information.

A spherical balloon is being inflated at a rate of 3 cubic inches per second.

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

Differentiate the above formula with respect to time.

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

Substitute the respective values in the above formula,

3=4\pi 6^2\frac{dr}{dt}

\frac{1}{48\pi}=\frac{dr}{dt}

The rate rate of change of radius is \frac{1}{48\pi} inches per second when the diameter is 12 inches.

When d=16

3=4\pi 8^2\frac{dr}{dt}

\frac{3}{256\pi}=\frac{dr}{dt}

Thus, the radius is changing more rapidly when the diameter is 12 inches.

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The probability distribution for the rate of return on an investment is
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Answer:

a)0.7

b) 10.03

c)  0.0801

Step-by-step explanation:

Rate of return   Probability

9.5                           0.1

9.8                           0.2

10                             0.3

10.2                          0.3

10.6                          0.1

a.

P(Rate of return is at least 10%)=P(R=10)+P(R=10.2)+P(R=10.6)

P(Rate of return is at least 10%)=0.3+0.3+0.1

P(Rate of return is at least 10%)=0.7

b)

Expected rate of return=E(x)=sum(x*p(x))

Rate of return(x)   Probability(p(x))    x*p(x)

9.5                           0.1                       0.95

9.8                           0.2                      1.96

10                             0.3                        3

10.2                          0.3                        3.06

10.6                          0.1                       1.06

Expected rate of return=E(x)=sum(x*p(x))

Expected rate of return=0.95+1.96+3+3.06+1.06=10.03

c)

variance of the rate of return=V(x)=sum(x^2p(x))-[sum(x*p(x))]^2

Rate of return(x)   Probability(p(x))    x*p(x)    x²*p(x)

9.5                           0.1                       0.95       9.025

9.8                           0.2                      1.96         19.208

10                             0.3                       3             30

10.2                          0.3                       3.06        31.212

10.6                          0.1                       1.06         11.236

sum[x²*p(x)]=9.025+19.208+30+31.212+11.236=100.681

variance of the rate of return=V(x)=sum(x²*p(x))-[sum(x*p(x))]²

variance of the rate of return=V(x)=100.681-(10.03)²

variance of the rate of return=V(x)=100.681-100.6009

variance of the rate of return=V(x)=0.0801

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<span>245/7</span>

2. <span>Calculate 700 ÷ 245, which is 2 with a remainder of 210.
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3. <span>Bring down 0, so that 2100 is large enough to be divided by 245.
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<span><span>0.0285</span><span>245|7.</span><span>4.90</span><span>2.100</span><span>1.960</span><span>1400</span><span>1225</span><span>175</span></span>

7. <span>Therefore, 7 divided by 245 approximately equals 0.0285
</span><span><span>7÷245≈0.0285</span></span>

8. <span>Simplify
</span><span><span><span>0.0285  <------------- Answer :) </span></span>
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