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White raven [17]
3 years ago
15

Which of the following is the equation of a circle with a radius of 10 cm and center at (–3, 6)?

Mathematics
1 answer:
Volgvan3 years ago
4 0

The equation of the circle:

(x-h)^2+(y-k)^2=r^2

(h, k) - center

r - radius

We have:

r=10\\(-3,\ 6)\to h=-3,\ k=6

Substitute:

(x-(-3))^2+(y-6)^2=10^2\\\\(x+3)^2+(y-6)^2=100

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Give the equation for a circle with the given center and radius.Center at (-10, -4), radius = 5A. (x−10)^2+(y−4)^2=25B. (x−4)^2+
BaLLatris [955]

D)(x+10)^2+(y+4)^2=5^2=25

Explanation

Step 1

We know that the general equation for a circle is

\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\  \end{gathered}

where

(h,k) is the center of the circel

and r is the radius

then, all we need to do is replace

Let

\begin{gathered} \text{center}\Rightarrow(h,k)\Rightarrow(-10,-4) \\ \text{radius}\Rightarrow r\Rightarrow5 \end{gathered}

replace the values

\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ (x-(-10))^2+(y-(-4))^2=5^2 \\ (x+10)^2+(y+4)^2=5^2=25 \end{gathered}

therefore, the answer is

D)(x+10)^2+(y+4)^2=5^2=25

I hope this helps you

7 0
1 year ago
A store buys 17 sweaters for $204 and sells them for $646. how much profit does the store make per sweater?
uranmaximum [27]

Total profit: 646 - 204 = 442


profit per shirt = 442 / 17 = 26


Answer: $26

6 0
2 years ago
Find the number b such that the line y = b divides the region bounded by the curves y = 36x2 and y = 25 into two regions with eq
Gemiola [76]

Answer:

b = 15.75

Step-by-step explanation:

Lets find the interception points of the curves

36 x² = 25

x² = 25/36 = 0.69444

|x| = √(25/36) = 5/6

thus the interception points are 5/6 and -5/6. By evaluating in 0, we can conclude that the curve y=25 is above the other curve and b should be between 0 and 25 (note that 0 is the smallest value of 36 x²).

The area of the bounded region is given by the integral

\int\limits^{5/6}_{-5/6} {(25-36 \, x^2)} \, dx = (25x - 12 \, x^3)\, |_{x=-5/6}^{x=5/6} = 25*5/6 - 12*(5/6)^3 - (25*(-5/6) - 12*(-5/6)^3) = 250/9

The whole region has an area of 250/9. We need b such as the area of the region below the curve y =b and above y=36x^2 is 125/9. The region would be bounded by the points z and -z, for certain z (this is for the symmetry). Also for the symmetry, this region can be splitted into 2 regions with equal area: between -z and 0, and between 0 and z. The area between 0 and z should be 125/18. Note that 36 z² = b, then z = √b/6.

125/18 = \int\limits^{\sqrt{b}/6}_0 {(b - 36 \, x^2)} \, dx = (bx - 12 \, x^3)\, |_{x = 0}^{x=\sqrt{b}/6} = b^{1.5}/6 - b^{1.5}/18 = b^{1.5}/9

125/18 = b^{1.5}/9

b = (62.5²)^{1/3} = 15.75

8 0
3 years ago
True or false: “If a positive integer is divisible by both 2 and 3, then it is divisible by 12.”
Julli [10]
False because 6 is divisible by 2 and 3, but not 12
4 0
3 years ago
17. Find the value of the function h(x) = 7x - 11 given that = 8m +3
Naya [18.7K]

Answer:

the answer is d

Step-by-step explanation:

thank you please follow me

4 0
3 years ago
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