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3 years ago

Find the equation of the circle that passes through the point (-3,1) and has its center at C(-4,6)

Mathematics

1 answer:

qaws [65]3 years ago

5 0

Answer:

(x+4)^2 + (y-6)^2 = 29

Step-by-step explanation:

The center-radius form of the circle equation is in the format (x – h)^2 + (y – k)^2 = r^2, with the center being at the point (h, k)

Replacing the center C(-4,6):

(x+4)^2 + (y-6)^2 = r^2

then replacing the point (-3,1):

(-3+4)^2 + (1-6)^2 = r^2

1 + 25 = r^2

then the equation of the circle is:

(x+4)^2 + (y-6)^2 = 29

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Please Help Quicly The equation 8x - 4y = 5 is dilated by a scale factor of 8 centered at the origin. What is the new slope and

Rzqust [24]

For new line, slope m=2 and y-intercept c=(-10)

Step-by-step explanation:

Note : Figure given is for reference to understand better.

Where redline is for given line and blueline for new line

The equation of given line 8x-4y=5 and it is dilated by a scale factor of 8 centered at the origin.

Step 1 : Find two points on given line.

When x=0, y=?

$8x-4y=5$

$8(0)-4y=5$

$y=\frac{-5}{4}$

When y=0, x=?

$8x-4y=5$

$8x-4(0)=5$

$x=\frac{5}{8}$

We get points $A(0,\frac{-5}{4}), B(\frac{5}{8},0)$

Step 2: Find distance from centered and scale it.

Now, It is said that line 8x-4y=5 dilated by a scale factor of 8 centered at the origin and point A and point B is on same.

So that point A and point B will also get dilated by a scale factor of 8 centered at the origin or distance of points from origin will be scaled by 8.

For point A:

Distance of point $A(0,\frac{-5}{4})$ from origin is $( \frac{-5}{4})$ unit in x-direction and zero $\frac{-5}{4})$ unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is $A'(0,-10)$

For point B:

Distance of point $B(\frac{5}{8},0)$ from origin is $(\frac{5}{8})$ unit in x-direction and zero unit in y-direction.

After scaled by factor of 8, the distance will multipy by 8 and new location is $B'(5,0)$

Step 3: Find Equation of new line.

Points $A'(0,-10)$ and $B'(5,0)$ make a new line

The equation of given as

$\frac{y-Y1}{x-X1} = \frac{Y2-Y1}{X2-X1}$

$\frac{y-(-10)}{x-0} = \frac{0-(-10)}{5-0}$

$\frac{y+(10)}{x} = 2$

$y+10= 2x$

$y= 2x-10$

Now, Comparing with the equation of the line : y=mx + c

Where m=slope and c is the y-intercept

We get, Slope m=2 and y-intercept c=(-10)

8 0

3 years ago

You and your friend rent a canoe. The canoe costs 10 dollars per half hour plus 5 dollars per day for each life vest. Life vests

REY [17]

The greatest range....the range is ur y value, it will be the total cost...the x is gonna be the number of 1/2 hrs. And the 5 per life vest has to be multiplied by 2 because there is 2 people, making it 10
y = 10x + 10

the greatest range will be when u rent the canoe for the longest.
8 a.m to 6 p.m......thats 10 hrs....20 half hrs...so the greatest range is when u rent the canoe for 20 half hrs.

y = 10(20) + 10
y = 200 + 10
y = 210 <=== the greatest range

3 0

3 years ago

From the set 1/2/3/4/5 which values make the inequality n + 1 > true?

saul85 [17]

Hi there!

To make n+1>4 true, you must have n be a numebr greater than 3...

The reason why is because if it is less than 3 or 3, it’ll have to be <.

The two numbers that can make this equation true is 4 and 5...

$4+1=5>4$

$5+1=6>4$

And if it is 1,2, and 3 it would be:

$1+1=2$

$2+1=3$

$3+1=4=4$

7 0

3 years ago

A metallic sphere is immersed in water in a cylindrical container causing a rise in the level of water by 7.5cm if the cylinder

SVETLANKA909090 [29]

Answer:

6.51 cm

Step-by-step explanation:

Since the sphere causes the water level in the cylindrical container to rise and thus increase by its own volume, the volume of the sphere is V = 4πr³/3 where r = radius of sphere. The volume rise of the container is thus V' = πR²h where R = radius of base of cylinder = 7 cm and h = height of water level = 7.5 cm.

Since V = V',

4πr³/3 = πR²h

dividing through by π, we have

4r³/3 = R²h

multiplying both sides by 3/4, we have

r³ = 3R²h/4

taking cube-root of both sides, we have

r = ∛(3R²h/4)

Substituting the values of the variables into the equation, we have

r = ∛(3(7 cm)² × 7.5 cm/4)

r = ∛(3 × 49 cm² × 7.5 cm/4)

r = ∛(1102.5cm³/4)

r = ∛(275.625 cm³)

r = 6.508 cm

r ≅ 6.51 cm to 2 decimal places

3 0

3 years ago

How do you use equivalent fractions to compare the fractions in each pair

Alenkasestr [34]

Firstly you need to to reduce to a common denominator by multiplYing the whole fraction. This way you have to multiply 4/5 by 2 (both numerator and denominator). so 4/5 = 8/10. And now you have 8/10 and 9/10. You compare only numerators. This way you have 8/10 <9/10. Same goes for 2/3 and 5/8. Only here you need to multiply both fractions. The common denominator here is 24. So you have to multiply 2/3 by 8 and 5/8 by 3. You now have to compare 16/24 and 15/24. 16/24>15/24.

8 0

3 years ago