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Gre4nikov [31]
3 years ago
7

The equation of a circle is (x - 3)^2 + (y - 1)^2 = 64. Find the equation of the circle after it is shifted 2 units to the right

and 4 units up. * 2 points
Mathematics
1 answer:
torisob [31]3 years ago
8 0

Answer:

(x-5)²+(y-5)²=64.

Step-by-step explanation:

When it comes to shifting, we simply need to change the vertex of the equation. Remember that the formula for a circle is:

(x-h)²+(y-k)²=r²---- (h,k) being the vertex.

In this case, h=3 and k=1. We are also shifting 2 units to the right, meaning we need to subtract 2 from the 'h' value. A shift of 4 units up means we have to subtract 4 from the 'k' value.

Our new equation is:

(x-5)²+(y-5)²=64.

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3 years ago
The population, P(t), of China, in billions, can be approximated by1 P(t)=1.394(1.006)t, where t is the number of years since th
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Answer:

At the start of 2014, the population was growing at 8.34 million people per year.

At the start of 2015, the population was growing at 8.39 million people per year.

Step-by-step explanation:

To find how fast was the population growing at the start of 2014 and at the start of 2015 we need to take the derivative of the function with respect to t.

The derivative shows by how much the function (the population, in this case) is changing when the variable you're deriving with respect to (time) increases one unit (one year).

We know that the population, P(t), of China, in billions, can be approximated by P(t)=1.394(1.006)^t

To find the derivative you need to:

\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=\\\\\mathrm{Take\:the\:constant\:out}:\quad \left(a\cdot f\right)'=a\cdot f\:'\\\\1.394\frac{d}{dt}\left(1.006^t\right)\\\\\mathrm{Apply\:the\:derivative\:exponent\:rule}:\quad \frac{d}{dx}\left(a^x\right)=a^x\ln \left(a\right)\\\\1.394\cdot \:1.006^t\ln \left(1.006\right)\\\\\frac{d}{dt}\left(1.394\cdot \:1.006^t\right)=(1.394\cdot \ln \left(1.006\right))\cdot 1.006^t

To find the population growing at the start of 2014 we say t = 0

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(0)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^0\\P(0)' = 0.00833901 \:Billion/year

To find the population growing at the start of 2015 we say t = 1

P(t)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^t\\P(1)' = (1.394\cdot \ln \left(1.006\right))\cdot 1.006^1\\P(1)' = 0.00838904 \:Billion/year

To convert billion to million you multiple by 1000

P(0)' = 0.00833901 \:Billion/year \cdot 1000 = 8.34 \:Million/year \\P(1)' = 0.00838904 \:Billion/year \cdot 1000 = 8.39 \:Million/year

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Kim loves to read. She reads at least one book every week. On Monday, Kim read 1/ 4 of her new book. On Tuesday, she read 1/ 5 o
mixer [17]

Answer:

Step-by-step explanation:

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3 years ago
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