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
1 answer:
Answer:
The rate rate of change of radius is 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
Differentiate the above formula with respect to time.
Substitute the respective values in the above formula,
The rate rate of change of radius is inches per second when the diameter is 12 inches.
When d=16
Thus, the radius is changing more rapidly when the diameter is 12 inches.
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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)=
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