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3 years ago

What is the radius of a circle whose equation is x2 y2 8x – 6y 21 = 0?

Mathematics

2 answers:

andrew11 [14]3 years ago

8 0

we know that

the standard form of the equation of the circle is

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

where

(h,k) is the center of the circle

r is the radius of the circle

In this problem we have

$x^{2} +y^{2} +8x-6y+21=0$

<u>Convert to standard form</u>

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$(x^{2}+8x) +(y^{2}-6y)=-21$

Complete the square twice. Remember to balance the equation by adding the same constants to each side.

$(x^{2}+8x+16) +(y^{2}-6y+9)=-21+16+9$

$(x^{2}+8x+16) +(y^{2}-6y+9)=4$

Rewrite as perfect squares

$(x+4)^{2} +(y-3)^{2}=4$

$(x+4)^{2} +(y-3)^{2}=2^{2}$

the center of the circle is $(-4,3)$

the radius of the circle is $2\ units$

therefore

<u>the answer is</u>

the radius of the circle is $2\ units$

uranmaximum [27]3 years ago

6 0

Answer:

Should be (A) on ED

Step-by-step explanation:

You might be interested in

Evaluate the following expression:<br> 62 − 7(8 + 6 − 32)

Alex Ar [27]

Answer:

188

Step-by-step explanation:

<u>Step 1: Distribute</u>

62 − 7(8 + 6 − 32)

62 + (-7 * 8) + (-7 * 6) + (-7 * -32)

62 + (-56) + (-42) + (224)

<u>Step 2: Combine the first two numbers</u>

(62 - 56) - 42 + 224

6 - 42 + 224

<u>Step 3: Combine the next two number</u>

(6 - 42) + 224

-36 + 224

<u>Step 4: Combine the last two number</u>

-36 + 224

188

Answer: 188

3 0

3 years ago

A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas

Fittoniya [83]

Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

$#V=pi r^2 h#$

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

$#V=pi (5m)^2 h#$

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

$#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#$

In the problem, we are given $#3(m^3)/min# which is #(dV)/(dt)#.$

So we need to substitute this in:

$#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#$

Hence, Height of the water increasing is at rate of $#(dh)/(dt)=3/(25 pi)m/(min)#$

<h3>Formula used: </h3>

$#V=pi r^2 h#$

To Learn more visit:

brainly.com/question/4313883

#SPJ4

4 0

2 years ago

Read 2 more answers

Use 45-45-90 & 30-60-90 Special Right Triangles to Solve. find the missing sir length. Leave you answers as radicals in simp

horsena [70]

Answer:5) x=y=7×6^1/2,6)x=38,y=19×3^1/2

7)m=n=18,8)u= 2×5^1/2,v=3

Step-by-step explanation: use trigonometry laws

8 0

3 years ago

The regular price of a TV is $475. It's currently on sale for 30% off. What is

Hitman42 [59]

Answer:

You will pay $332.50 for a item with original price of $475 when discounted 30%

meaning the discount is $142.50

Step-by-step explanation:

if you buy an item at $475 with 30% discount, you will pay 475 - 142.5 = 332.5 dollars.

please give brainliest and thanks if possible

7 0

2 years ago

In the diagram below, the perimeter of the triangle is equal to the perimeter of the square. What is the length of a side of the

kondaur [170]

The perimeter of each is the sum of the lengths of its sides.

Triangle Perimeter = 16 + 4x-3 +3x = 7x+13

Square Perimeter = 2x +2x +2x +2x = 8x

If these are equal, you have

$7x+13=8x\\\\13=x\qquad \mbox{subtract 7x}\\\\26=2x\qquad \mbox{multiply by 2}$

The length of a side of the square is 26 units.

3 0

3 years ago