All categories

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

You might be interested in

Show work and explain with formulas.

3241004551 [841]

14 Answer: 28

Step-by-step explanation:

$S_\infty=\dfrac{a_1}{1-r}\\\\\sum\limits^\infty_{n=1} 35\bigg(-\dfrac{1}{4}\bigg)^n\implies a_1=35,\ r=-\dfrac{1}{4}\\\\\\S_\infty=\dfrac{35}{1-\bigg(-\dfrac{1}{4}\bigg)}=\dfrac{35}{\dfrac{5}{4}}=35\times \dfrac{4}{5}=7\times 4=\large\boxed{28}$

15A Answer: 49

Step-by-step explanation:

$S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\\sum\limits^7_{i=1} i+3\\\\a_1=1+3\quad =4\\a_7=7+3\quad =10\\n=7\\\\\\S_7=\dfrac{a_1+a_7}{2}\cdot 7\\\\\\.\ =\dfrac{4+10}{2}\cdot 7\\\\\\.\ =\dfrac{14}{2}\cdot 7\\\\\\.\ =7\cdot 7\\\\.\ =\large\boxed{49}$

15B Answer: 12

Step-by-step explanation:

$S_n=\dfrac{a_1+a_n}{2}\cdot n\\\\\\\sum\limits^{10}_{k=3} k-5\\\\a_3=3-5\quad =-2\\a_{10}=10-5\quad =5\\n=8\\\\\\S_8=\dfrac{a_3+a_{10}}{2}\cdot 8\\\\\\.\ =\dfrac{-2+5}{2}\cdot 8\\\\\\.\ =\dfrac{3}{2}\cdot 8\\\\\\.\ =3\cdot 4\\\\.\ =\large\boxed{12}$

16 Answer: $\sum\limits^5_{n=1} 3n-2$

Step-by-step explanation:

$\{1, 4, 7, 10, 13\}\implies a_1=1,\ d=3,\ n=5\\\\\text{The explicit rule for an arithmetic sequence is: }a_n=a_1+d(n-1)\\\\a_n=1+3(n-1)\\\\.\ =1+3n-3\\\\.\ =3n-2\\\\\large\boxed{\sum\limits^5_{n=1} 3n-2}$

8 0

3 years ago

Help, which one should I choose

tekilochka [14]

Answer:

Step-by-step explanation:

u can calculate it using the md point 3 times Soo it is actually easy but the answer is 6

5 0

2 years ago

The length of a rectangle is 6 centimeters less than twice its width. The perimeter of the rectangle is 48 cm. What are the

fomenos

Answer:

the length is 12 and the width is 9.

Step-by-step explanation:

The first step is always to assign letters to the variables. We can call length L and width W.

Since all units are in cm, unit conversion is unnecessary.

Next, set up some equations. L=2W-6 because of the first sentence of the problem. Length times width equals area, so L*W=108.

Now that there are two equations and two variables, the next step is to solve the system. I'm going to solve it by plugging in the right side of the first equation in for L in the second equation. This gives me (2W-6)*W=108. Distributing the W gives me 2W^2-6W=108, or W^2-3W-54=0. Using the quadratic formula, I get that W=9. Using the first equation, L=2*9-6=12. So the length is 12 and the width is 9.

6 0

2 years ago

Which of the following is an arithmetic sequence?

masha68 [24]

Answer:

Step-by-step explanation:

And arithmetic sequence is a sequence in which the difference between each of the numbers are constant.

It is not A, because the difference between 3 and 9 is positive 6, and the difference between 9 and 81 is positive 72.

It is not C, because the difference between 4 and 1 is -3, and the difference between 1 and 4 is positive 3.

It is not D, because the difference between 2 and -2 is -4, and the difference between -2 and 2 is positive 4.

And it is B because the numbers maintain a constant difference between each other, which is -3.

3 0

2 years ago

Read 2 more answers

8.76× 10 6 is times than 8.76× 10 2 .

VashaNatasha [74]

10^6 = 10 *10*10*10*10*10 = 1,000,000

10^2 = 10*10 = 100

1000000/100 = 10,000 times larger

4 0

3 years ago