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Vinvika [58]
4 years ago
13

The parent function of the function g(x) = (x-h)2 + k is f(x) = (x)2. The vertex of function g(x) is located at (9,-8) what are

the values of h and k
Mathematics
1 answer:
Furkat [3]4 years ago
7 0
(h, k) is the vertex, (9, -8).
h = 9
k = -8
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92.61<br> x 50.49<br> How to do this decimal multiplication
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92.61 • 50.49= 4675.8789

answer = 4675.8789


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4 years ago
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Suppose that the population​ P(t) of a country satisfies the differential equation dP/dt = kP (600 - P) with k constant. Its pop
jeka94

Answer:

The country's population for the year 2030 is 368.8 million.

Step-by-step explanation:

The differential equation is:

\frac{dP}{dt}=kP(600 - P)\\\frac{dP}{P(600 - P)} =kdt

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\int\limits {\frac{1}{P(600-P)} } \, dP =k\int\limits {1} \, dt \\(\frac{1}{600} )[(\int\limits {\frac{1}{P} } \, dP) - (\int\limits {\frac{}{600-P} } \, dP)]=k\int\limits {1} \, dt\\\ln P-\ln (600-P)=600kt+C\\\ln (\frac{P}{600-P} )=600kt+C\\\frac{P}{600-P} = Ce^{600kt}

At <em>t</em> = 0 the value of <em>P</em> is 300 million.

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\frac{P}{600-P} = Ce^{600kt}\\\frac{300}{600-300}=Ce^{600\times0\times k}\\\frac{1}{300} =C\times1\\C=\frac{1}{300}

It is provided that the population growth rate is 1 million per year.

Then for the year 1961, the population is: P (1) = 301

Then \frac{dP}{dt}=1.

Determine <em>k</em> as follows:

\frac{dP}{dt}=kP(600 - P)\\1=k\times300(600-300)\\k=\frac{1}{90000}

For the year 2030, P (2030) = P (70).

Determine the value of P (70) as follows:

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Thus, the country's population for the year 2030 is 368.8 million.

3 0
3 years ago
The volume of a right circular cone varies jointly as the altitude and the square of the radius of the base. If the volume of th
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Answer:13.5 inches

Step-by-step explanation:

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Putting the value of V,h,r,

we get,

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Now we have volume = 77 cu and radius of the base =7/3, so putting the values we get,

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Find the area of this triangle. Round to<br> the nearest tenth.l
trasher [3.6K]

Answer:

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Step-by-step explanation:

<em>Hey there!</em>

Well to find area we'll use the following formula.

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Plug in the given info,

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<em>Hope this helps :)</em>

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3 years ago
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