Ask question

Ask question

All categories

3 years ago

12

Find the equation of the circle if one of the endpoints of the diameter is (-2,-3) and the midpoint of the circle's diameter is

(4,5).

1 answer:

tankabanditka [31]3 years ago

8 0

Answer:

The answer to your question is (x - 4)² + (y - 5)² = 100

Step-by-step explanation:

Data

Point = (-2, -3)

Midpoint = (4, 5)

Process

1.- Find the length of the radius using the formula of the distance between two points.

dPM = $\sqrt{(x2 - x1)^{2}+ (y2 - y1)^{2}}$

x1 = -2 y1 = -3 x2 = 4 y2 = 5

dPM = $\sqrt{(4 + 2)^{2} + (5 + 3)^{2}}$

dPM = $\sqrt{(6)^{2} + (8)^{2}}$

dPM = $\sqrt{36 + 64}$

dPM = $\sqrt{100}$

dPM = 10

2.- Find the equation of the line

(x - h)² + (y - k)² = r²

h = 4

k = 5

r = 10

(x - 4)² + (y - 5)² = 10²

(x - 4)² + (y - 5)² = 100

You might be interested in

on the first play of a game , a football team gained 23 yards and then lost 10 yards due to penalty during the second play the t

zepelin [54]

-1 Let's say the set of downs starts at the 20 yard line (maybe the kicking team kicked deep, the receiving team took a knee and so play starts at the 20).
Ok - we're at the 20. First down - they advance 5 yards. So we're now at the 25. We can write that mathematically as:
20
+
5
=
25
So the second play they get sacked deep and lose 6 yards. So we subtract 6:
25
−
6
=
19
So what's the change in yardage for the 2 plays? We are on the 19 and started at the 20, so we can write:
19
−
20
=
−
1
and this makes sense because we know we advanced 5 and fell back 6

3 0

3 years ago

All of the picture please help

Sonbull [250]

A. She needs 16 quarter cups of milk.
B. Equation: 4 cups multiplied by 4(four quarter cups per cup) = 16 quarter cups

Hope this helps!!

5 0

3 years ago

Without graphing, determine whether the following pair of lines are parallel, perpendicular, or neither parallel nor perpendicul

Tomtit [17]

Write the equation of the lines in slope-intercept form (y=mx+b)

First equation: It is already in slope-intercept form

$y=\frac{2}{5}x-4$

Second equation: solve y:

$\begin{gathered} 4x-10y=-7 \\ 4x-4x-10y=-4x-7 \\ -10y=-4x-7 \\ \frac{-10}{-10}y=\frac{-4}{-10}x-\frac{7}{-10} \\ \\ y=\frac{4}{10}x+\frac{7}{10} \\ \\ y=\frac{2}{5}x+\frac{7}{10} \end{gathered}$

Identify the slope of each line:

If two or more lines have the same slope then the lines are parallel

If two lines have slopes that are negative reciprocals then the lines are perpendicular

The two given lines have the same slope: 2/5. Then, they are parallel lines

4 0

1 year ago

An electrician charges a $100 flat fee, plus $75 per hour to work on a house.

jek_recluse [69]

Answer:

y=75x+100

Step-by-step explanation:

8 0

2 years ago

The Slow Ball Challenge or The Fast Ball Challenge.

cupoosta [38]

Answer:

Fast ball challenge

Step-by-step explanation:

Given

Slow Ball Challenge

$Pitches = 7$

$P(Hit) = 80\%$

$Win = \$60$

$Lost = \$10$

Fast Ball Challenge

$Pitches = 3$

$P(Hit) = 70\%$

$Win = \$60$

$Lost = \$10$

Required

Which should he choose?

To do this, we simply calculate the expected earnings of both.

Considering the slow ball challenge

First, we calculate the binomial probability that he hits all 7 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 7$ --- pitches

$x = 7$ --- all hits

$p = 80\% = 0.80$ --- probability of hit

So, we have:

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

$P(7) =^7C_7 * 0.80^7 * (1 - 0.80)^{7 - 7}$

$P(7) =1 * 0.80^7 * (1 - 0.80)^0$

$P(7) =1 * 0.80^7 * 0.20^0$

Using a calculator:

$P(7) =0.2097152$ --- This is the probability that he wins

i.e.

$P(Win) =0.2097152$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 -0.2097152$

$P(Lose) = 0.7902848$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.2097152 * \$60 + 0.7902848 * \$10$

Using a calculator, we have:

$Expected = \$20.48576$

Considering the fast ball challenge

First, we calculate the binomial probability that he hits all 3 pitches

$P(x) =^nC_x * p^x * (1 - p)^{n - x}$

Where

$n = 3$ --- pitches

$x = 3$ --- all hits

$p = 70\% = 0.70$ --- probability of hit

So, we have:

$P(3) =^3C_3 * 0.70^3 * (1 - 0.70)^{3 - 3}$

$P(3) =1 * 0.70^3 * (1 - 0.70)^0$

$P(3) =1 * 0.70^3 * 0.30^0$

Using a calculator:

$P(3) =0.343$ --- This is the probability that he wins

i.e.

$P(Win) =0.343$

The probability that he lose is:

$P(Lose) = 1 - P(Win)$ ---- Complement rule

$P(Lose) = 1 - 0.343$

$P(Lose) = 0.657$

The expected value is then calculated as:

$Expected = P(Win) * Win + P(Lose) * Lose$

$Expected = 0.343 * \$60 + 0.657 * \$10$

Using a calculator, we have:

$Expected = \$27.15$

So, we have:

$Expected = \$20.48576$ -- Slow ball

$Expected = \$27.15$ --- Fast ball

<em>The expected earnings of the fast ball challenge is greater than that of the slow ball. Hence, he should choose the fast ball challenge.</em>

5 0

3 years ago