All categories

4 years ago

Determine the center and radius of the following circle equation: x^2+y^2-6x-8y+24=0

Mathematics

1 answer:

slega [8]4 years ago

6 0

Center is (3, -4) and radius is 1

Step-by-step explanation:

Step 1: Find center and radius of the circle with equation x² + y² - 6x - 8y + 24 = 0

The standard form of the equation of a circle is x² + y² + 2gx +2fy + c = 0, where center is (-g, -f) and radius = √g² + f² - c

By comparing the 2 equations, 2g = -6, 2f = 8 and c = 24

⇒ g = -6/2 = -3

⇒ f = 8/2 = 4

⇒ c = 24

Step 2: Find center.

Center = (-g. -f) = (3, -4)

Step 3: Find radius.

Radius = √g² + f² - c = √3² + (-4)² - 24

= √9 + 16 - 24 = √1 = 1

You might be interested in

-17/30 write a fraction as a decimal

Whitepunk [10]

As a decimal the answer would be −0.566666666666667

7 0

3 years ago

Lisa wants to use her calculator to square a two-digit positive integer, but she accidentally enters the tens digit incorrectly.

Svetradugi [14.3K]

Answer: Correct two digit number= 24

Step-by-step explanation:

Let

x= tens digit (wrong one)

and y= zeroes digit

and z= tens digit (right one)

Now according to the statement,

(10x+y)² - (10z+y)² = 2340

Simplifying this we get

(x-z)(5x+y+5z)= 117= 1 * 3 * 3 * 13

So it could either be

x-z=1 or x-z=3

If we take the x-z=1

then 5x+y+5z=117

which is not possible as maximum value we can get from this is 99.

This leaves us with x-z=3

so 5x+y+5z= 39

Put x=3+z

We get,

y+10z= 24

Now as y and z both are single digits so the only possible numbers to fit these are y=4 and z=2.

Put z=2 in x=3+z , we get x=5

So the numbers become 10x+y= 54

and 10z+y= 24

Their sum is 54+24=78

Check

54²-24²= 2340 so it is correct.

7 0

3 years ago

1. Manufacturing Process Incorporation plan to produce a new ergonomic chair. Before the company starts producing this chair the

Oduvanchick [21]

Answer:

1. cost per chair: $86.40

2. selling price per chair: $146.88

Step-by-step explanation:

1. The total cost per chair will be the sum of the cost of materials and the overhead cost (equipment, energy, labor, marketing). The cost of materials is ...

$500/(16 chairs) = $31.25/chair

So, the total cost is ...

cost of each chair = material cost + overhead cost

= $31.25 +55.15

cost of each chair = $86.40

2. We assume the markup is 70% of the cost, so will be ...

0.70 · $86.40 = $60.48

Then the selling price of the chair will be ...

selling price = cost + markup

selling price = $86.40 +60.48

selling price = $146.88

3 0

3 years ago

What is the volume, in cubic in, of a cylinder with a height of 8 in and a base radius of

densk [106]

Answer:

V=100.5

Step-by-step explanation:

hopes this helps

5 0

3 years ago

Thaddeus already has $5 saved. He wants to save more to buy a book . Complete the table , and graph the ordered pairs on the coo

Fed [463]

We are going to need to see the table

8 0

4 years ago