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3 years ago

A circle is centered at (-6,3) and has a radius of 11. Where does the point (3,-3) lie?

Mathematics

1 answer:

makvit [3.9K]3 years ago

8 0

As we can see that the distance of the given point is less than the radius,

The point lies inside the circle

Step-by-step explanation:

We will use the distance formula to find the distance between the centre of the circle and the given point. If the distance is less than the radius, the point lies inside the circle. If the distance is equal to the radius then the point lies on the circle. If the distance is greater than the radius of the circle, then the point will be out of the circle.

Given

(-6,3) = (x1,y1)

(3,-3) = (x2, y2)

The distance formula is:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\= \sqrt{(3-(-6))^2+(-3-3)^2}\\=\sqrt{(3+6)^2+(-6)^2}\\=\sqrt{(9)^2+36}\\=\sqrt{81+36}\\=\sqrt{117}\\=10.81$

As we can see that the distance of the given point is less than the radius,

The point lies inside the circle

Keywords: Circle, Equation of circle

Learn more about circle at:

#LearnwithBrainly

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If (ax+2)(bx+7)=15x2+cx+14 for all values of x, and a+b=8, what are the 2 possible values fo c

dolphi86 [110]

Given:

$(ax+2)(bx+7)=15x^2+cx+14$

And

$a+b=8$

Required:

To find the two possible values of c.

Explanation:

Consider

$\begin{gathered} (ax+2)(bx+7)=15x^2+cx+14 \\ abx^2+7ax+2bx+14=15x^2+cx+14 \end{gathered}$

$\begin{gathered} ab=15-----(1) \\ 7a+2b=c \end{gathered}$

And also given

$a+b=8---(2)$

Now from (1) and (2), we get

$\begin{gathered} a+\frac{15}{a}=8 \\ \\ a^2+15=8a \\ \\ a^2-8a+15=0 \end{gathered}$ $a=3,5$

Now put a in (1) we get

$\begin{gathered} (3)b=15 \\ b=\frac{15}{3} \\ b=5 \\ OR \\ b=\frac{15}{5} \\ b=3 \end{gathered}$

We can interpret that either of a or b are equal to 3 or 5.

When a=3 and b=5, we have

$\begin{gathered} c=7(3)+2(5) \\ =21+10 \\ =31 \end{gathered}$

When a=5 and b=3, we have

$\begin{gathered} c=7(5)+2(3) \\ =35+6 \\ =41 \end{gathered}$

Final Answer:

The option D is correct.

31 and 41

8 0

10 months ago

Question

nika2105 [10]

Answer:

y = -1

Step-by-step explanation:

(y+1)/(x-8) = (-1+1)/(-2-8)

(y+1)/(x-8) = 0

y+1 =0

y= -1

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2 years ago

claudia is making a gelatin desseert for a party.She plans on making 12 servings for every 5 people.If each pan claudia uses to

prisoha [69]

First we need to find the total amount of servings needed.

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Now we can find the amount of pans needed

24 servings/8 servings (1 pan)
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She needs at least 3 pans

5 0

3 years ago

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Mkey [24]

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