Find the equation of the line in slope-intercept form. m=− 4 7 through (14, 3)

If the endpoints of the diameter of a circle are (−8, −6) and (−4, −14), what is the standard form equation of the circle?

kondaur [170]

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

Solution:

The endpoints of the diameter of a circle are (–8, –6) and (–4, –14).

Center of the circle = Mid point of the diameter

Mid point formula:

$$P(x, y)=\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$

Here, $x_1=-8, y_1=-6, x_2=-4, y_2=-14$

$$P(x, y) =\left(\frac{-8-4}{2}, \frac{-6-14}{2}\right)$

$$P(x, y) =\left(\frac{-12}{2}, \frac{-20}{2}\right)$

$$P(x, y) =(-6, -10)$

Center of the circle = (–6, –10)

Radius is the distance between center and any endpoint of the diameter.

To calculate the radius using distance formula.

$r=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}$

Here, $x_1=-6, y_1=-10, x_2=-8, y_2=-6$

$r=\sqrt{\left(-8-(-6)\right)^{2}+\left(-6-(-10)}\right)^{2}}$

$r=\sqrt{(-8+6)^{2}+(-6+10)^{2}}$

$r=\sqrt{(-2)^{2}+(4)^{2}}$

$r=\sqrt{20}$ units

The standard form of the equation of a circle is

$(x-a)^{2}+(y-b)^{2}=r^{2}$ , where (a, b) are center and r is the radius.

Here, center = (–6, –10) and $r=\sqrt{20}$

$(x-(-6))^{2}+(y-(-10))^{2}={(\sqrt{20})} ^{2}$

$(x+6)^{2}+(y+10)^{2}=20$

Equation of the circle is $(x+6)^{2}+(y+10)^{2}=20$ .

4 0

3 years ago

Because Charles David Keeling and his new colleagues began measuring CO2 in 1958, we now have an excellent record of how CO2 con

Alecsey [184]

Answer:

1. 516 ppm; 2. 561 ppm

Step-by-step explanation:

1. CO₂ increase at old rate

Time = 2100 - 2010 = 90 years

Increase in CO₂ = 90 yr × (1.4 ppm/1 yr) = 126 ppm

CO₂ in 2010 = 390 + 126 = 516 ppm

At the old rate, the CO₂ concentration in 2100 will be 516 ppm.

2. CO₂ increase at new rate

Time = 2100 - 2010 = 90 years

Increase in CO₂ = 90 yr × (1.9 ppm/1 yr) = 171 ppm

CO₂ in 2010 = 390 + 171 = 561 ppm

At the new rate, the CO₂ concentration in 2100 will be 561 ppm.

6 0

3 years ago

Use the Change of Base Formula to evaluate log5 92. Then convert log5 92 to a logarithm in base 3. Round to the nearest thousand

ANTONII [103]

I was thinking that the answer could be

2.810; log3 21.903

OR

<span> 2.810; log3 55.2 </span>

So,<span> log5 of 92 is between 2.5 and 3 Correct answer is A</span>

6 0

3 years ago

Read 2 more answers

Help? Meeeeeeeeeeeeeeeeeeeeeeeee e

Setler79 [48]

Answer:

a or d im very positive that is d

Step-by-step explanation:

5 0

3 years ago

Han drinks three gallons of iced tea each day. Each gallon of iced tea contains ¾ cups of sugar. How much sugar does Han drink w

erica [24]

Answer:

3 cups of sugar.

Step-by-step explanation:

Han drinks 3/4 of a cup of sugar each day when she drinks iced tea. She drinks 3 gallons, and each contains 3/4. If each contains only 3/4, we will have to multiply 3/4 by 3 gallons to find our answer to this question.

$\frac{3}{4} = 1 \text{-gallon}$

So, now we will have to multiply 3/4 by the number 3.

$\frac{3}{4}$ × $3$ = $\frac{12}{4}$

12/4 is equal to 3, so the answer is 3.

7 0

2 years ago