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3 years ago

a circle is centered at (-4,9)and has a radius of 11. what is the equation of the circle. use x and y

Mathematics

1 answer:

Sholpan [36]3 years ago

3 0

Answer:

(x + 4)^2 + (y-9)^2 = 121

Step-by-step explanation:

We can write the equation of a circle as

(x-h)^2 + (y-k) ^2 = r^2 where (h,k) is the center and r is the radius

(x - -4)^2 + (y-9)^2 = 11 ^2

(x + 4)^2 + (y-9)^2 = 11 ^2

(x + 4)^2 + (y-9)^2 = 121

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At 2 PM, a thermometer reading 80°F is taken outside where the air temperature is 20°F. At 2:03 PM, the temperature reading yiel

Alexeev081 [22]

Use Law of Cooling:
$T(t) = (T_0 - T_A)e^{-kt} +T_A$
T0 = initial temperature, TA = ambient or final temperature

First solve for k using given info, T(3) = 42
$42 = (80-20)e^{-3k} +20 \\ \\ e^{-3k} = \frac{22}{60}=\frac{11}{30} \\ \\ k = -\frac{1}{3} ln (\frac{11}{30})$

Substituting k back into cooling equation gives:
$T(t) = 60(\frac{11}{30})^{t/3} + 20$

At some time "t", it is brought back inside at temperature "x".
We know that temperature goes back up to 71 at 2:10 so the time it is inside is 10-t, where t is time that it had been outside.
The new cooling equation for when its back inside is:
$T(t) = (x-80)(\frac{11}{30})^{t/3} + 80 \\ \\ 71 = (x-80)(\frac{11}{30})^{\frac{10-t}{3}} + 80$
Solve for x:
$x = -9(\frac{11}{30})^{\frac{t-10}{3}} + 80$
Sub back into original cooling equation, x = T(t)
$-9(\frac{11}{30})^{\frac{t-10}{3}} + 80 = 60 (\frac{11}{30})^{t/3} +20$
Solve for t:
$60 (\frac{11}{30})^{t/3} +9(\frac{11}{30})^{\frac{-10}{3}}(\frac{11}{30})^{t/3} = 60 \\ \\ (\frac{11}{30})^{t/3} = \frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}} \\ \\ \\ t = 3(\frac{ln(\frac{60}{60+9(\frac{11}{30})^{\frac{-10}{3}}})}{ln (\frac{11}{30})}) \\ \\ \\ t = 4.959$

This means the exact time it was brought indoors was about 2.5 seconds before 2:05 PM

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3 years ago

Sonja's house is 4 blocks west and 1 block south of the center of town. Her school is 3 blocks east and 2 blocks north of the ce

adoni [48]

Answer:

The answer is √58 = 7.62

Step-by-step explanation:

So, if you draw this down, you will see that the direct distance is hypotenuse c of a right triangle which sides are 3 blocks (1 south and 2 north) and 7 blocks (4 west and 3 east).

Use the Pythagorean theorem:

c² = a² + b²

a = 3

b = 7

c² = 3² + 7²

c² = 9 + 49

c² = 58

c = √58

c = 7.62

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3 years ago

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The radius of a sphere is 1/3 ft what is the approximate volume of the sphere

Katen [24]

Answer:

0.16 ft

Step-by-step explanation:

v = 4/3 πr³

v = 4/3 × 3.142 × 1/3 × 1/3 × 1/3

v = 0.16 ft

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2 years ago

The circumference is __

Anestetic [448]

Answer:

As we know that there is a radius which is 2 cm

so 

circumference = 2 π r

 = 2 * 22/7 * 2

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it's circumference is 12.57 cm

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Which ordered pair is a solution to the system of inequalities? y< 3x y< 5

tatyana61 [14]

Answer:

Step-by-step explanation:

Split it into two:

Y<3x

Y<5

X = 1

Y = 3

(1,3)

X = 2

Y = 6

(2, 6)

Plot the line up to y = 4.999999999999999999999 and not higher.

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3 years ago

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a circle is centered at (-4,9)and has a radius of 11. what is the equation of the circle. use x and y​

a circle is centered at (-4,9)and has a radius of 11. what is the equation of the circle. use x and y