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2 years ago

What is the equation of the circle with center (−3, 1) that passes through the point (−5, 3)?

Mathematics

1 answer:

Mariulka [41]2 years ago

6 0

Answer:

( x + 3)^2 + ( y - 1)^2 = 8

Step-by-step explanation:

The equation of a circle with a center and a point

( x - a) ^2 + ( y - b) ^2 = r^2

( x , y) - any point on the circle

( a, b) - center of the circle

r^2 - radius of the circle

( -3 , 1) - center - ( a, b)

a = -3

b = 1

( -5 , 3) - point - ( x, y)

x = -5

y = 3

Step 1: substitute the center into the equation

( x -(-3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + ( y - 1)^2 = r^2

Step 2 : sub the point into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( -5 + 3)^2 + ( 3 - 1)^2 = r^2

(-2)^2 + 2^2 = r^2

4 + 4 = r^2

8 = r^2

Step 3 : sub the radius into the equation

( x + 3)^2 + ( y - 1)^2 = r^2

( x + 3)^2 + (y - 1)^2 = 8

Therefore, the equation of the circle is

( x + 3)^2 + (y - 1)^2 = 8

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a sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. turning the radius-reduction screw on t

Zarrin [17]

Answer:

1590.4 square ft

Step-by-step explanation:

r=30 so you need to multiply that by 25% (30*.25=7.5)

30-7.5=22.5

A= pi(r)^2

A=pi*(22.5)^2

A=506.25pi

A=1590.43 or 1590.4 (to the nearest tenth)

4 0

3 years ago

Read 2 more answers

40 pts!! please help T^T

viva [34]

Answer:

30%

Step-by-step explanation:

If a football quarterback enjoys practicing his long passes over 40 yards and misses the first pass 40% of the time, but when he misses on the first pass, he misses the second pass 20% of the time. The probability of missing two passes in a row is 30%.

First pass: 40%

Second pass: 20%

40% and 20% combined/average is 30%.

Therefore, the probability of missing two passes in a row is 30%.

3 0

2 years ago

Read 2 more answers

A fire hydrant with a blue cap provides water at a rate of 1,500 gallons per minute. A fire hydrant with a green cap provides wa

lapo4ka [179]

Answer:

a) 2b = 3g

b) 3p = b

Step-by-step explanation:

Given:

Fire hydrant with a blue cap, b, provides water at a rate = 1500 gallons per min

Fire hydrant with a green cap, g, provides water at a rate = 1000 gallons per min

Fire hydrant with a purple cap, p, provides water at a rate = ½g = $\frac{1}{2}*1000 = 500$

a) The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g.

Given flow of blue hydrant, b = 500

Simplifying, we have:

b = 3*500

$b = 3 * \frac{1000}{2}$

Since the flow rate of green hydrant, g, is 1000, let's replace 1000 with g above.

Therefore,

$b = 3 * \frac{g}{2}$

$b = \frac{3}{2}g$

Cross multuply

$2b = 3g$

The equation to relate the flow of water from the blue hydrant, b, to the flow from the green hydrant, g is 2b=3g.

b) An equation to relate the flow of water from the purple hydrant, p, to the flow from the blue hydrant, b.

Given flow rate of purple hydrant, p = 500

It could also be re-written as:

$\frac{3}{3} * 500$

$p = \frac{1500}{3}$

Since the flow rate of blue hydrant, b, is 1500, let's replace 1500 with b above.

$p = \frac{b}{3}$

Cross multiply

3p = b

8 0

2 years ago

Which is a factor of 2n^2-5n-42 A 2n-7 B 3 - 2n C 3-2n^2 D 4-2n^2

Kaylis [27]

Split the middle term.

(2n²-5n)-42

Multiply the coefficient of the first term (2 is the coefficient of 2n²) by the constant (-42, it's constant because there are no variables attached).

2 x (-42) = -84

Find the factor of -84 that equals your middle term (-5)

The factors of 84 are as follows (remember that if either number is negative, you'll get -84):
84*1
42*2
28*3
21*4
14*6
12*7

What two numbers, when added or subtracted, equal the middle term? 12-7 = 5, but your number is a negative, so how do you do get that 5 to be negative? -12+7 = -5, but make that easier to understand 7-12 = -5, and now add your variable back to get 7n-12n = -5n

Rewrite your equation using the split middle term.

2n²+7n-12n-42

Pull out the factors and add up the first two terms.

n*(2n+7) = 2²+7n

-6(2n+7) = -12n-42

The numbers inside the parenthesis give you one half of your new equation, combine the numbers outside the parentheses to get your second half.

(n-6) (2n+7)

In regards to your answer, there are three possibilities:

1) You wrote the initial equation incorrectly
2) You wrote the answers incorrectly
3) Whoever created the question wrote the equation or the answers wrong, and the answer is not present.

6 0

2 years ago

A= 49 sq. in. Find the value of x. If necessary, round to the nearest tenth.

BlackZzzverrR [31]

Answer:

9.90 inches

Step-by-step explanation:

Area of a triangle is equal to base times height divided by 2.

$bh/2$