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2 years ago

5

The volume of a cone is 141.3 cubic inches. The height of the cone is 15 inches. What is the radius of the cone, rounded to the

nearest inch? Use π = 3.14. (5 points)

1 answer:

kkurt [141]2 years ago

8 0

Answer:

3

Step-by-step explanation:

V=πr²h/3 = π3²·15/3 = 141.37167

-hope it helps

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A sequence is a function whose domain is the set of __numbers.

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we know that A has 60% of salt, so if way we had "x" amount of ounces of A solution the amount in it will be 60% of "x", or namely (60/100)*x = 0.6x.

Likewise for solution B if we had "y" ounces of it, the amount of salt in it will be (75/100) * y or 0.75y, thus

$\begin{array}{lcccl} &\stackrel{solution}{quantity}&\stackrel{\textit{\% of }}{amount}&\stackrel{\textit{oz of }}{amount}\\ \cline{2-4}&\\ A&x&0.60&0.6x\\ B&y&0.75&0.75y\\ \cline{2-4}&\\ mixture&60&0.65&39 \end{array}~\hfill \begin{cases} x+y=60\\ 0.6x+0.75y=39 \end{cases} \\\\\\ \stackrel{\textit{since we know that}}{x+y=60}\implies y = 60 - x~\hfill \stackrel{\textit{substituting on the 2nd equation}}{0.6x+0.75(60-x)=39}$

$0.6x+45-0.75x=39\implies -0.15x+45=39\implies -0.15x=-6 \\\\\\ x = \cfrac{-6}{-0.15}\implies \boxed{x = 40} \\\\\\ \stackrel{\textit{we know that}}{y = 60 - x}\implies y = 60-40\implies \boxed{y = 20}$

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2 years ago

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The value of x is 2/5.

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3 years ago

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The population of a certain country in 1996 was 286 million people. In addition, the population of the country was growing at a

Fudgin [204]

Answer:

A) In 2004 the population will reach 306 million.

B) In 2033 the population will reach 386 million.

Step-by-step explanation:

Given : The population of a certain country in 1996 was 286 million people. In addition, the population of the country was growing at a rate of 0.8% per year. Assuming that this growth rate continues, the model $P(t) = 286(1.008 )^{t-1996}$ represents the population P (in millions of people) in year t.

To find : According to this model, when will the population of the country reach A. 306 million? B. 386 million?

Solution :

The model represent the population is $P(t) = 286(1.008 )^{t-1996}$

Where, P represents the population in million.

t represents the time.

A) When population P=306 million.

$306 = 286(1.008 )^{t-1996}$

$\frac{306}{286}=(1.008 )^{t-1996}$

$1.0699=(1.008 )^{t-1996}$

Taking log both side,

$\log(1.0699)=\log((1.008 )^{t-1996})$

$\log(1.0699)=(t-1996)\log(1.008)$

$\frac{\log(1.0699)}{\log(1.008)}=(t-1996)$

$8.479=t-1996$

$t=8.479+1996$

$t=2004.47$

$t\approx2004$

Therefore, In 2004 the population will reach 306 million.

B) When population P=386 million.

$386 = 286(1.008 )^{t-1996}$

$\frac{386}{286}=(1.008 )^{t-1996}$

$1.3496=(1.008 )^{t-1996}$

Taking log both side,

$\log(1.3496)=\log((1.008 )^{t-1996})$

$\log(1.3496)=(t-1996)\log(1.008)$

$\frac{\log(1.3496)}{\log(1.008)}=(t-1996)$

$37.625=t-1996$

$t=37.625+1996$

$t=2033.625$

$t\approx2033$

Therefore, In 2033 the population will reach 386 million.

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