Mathematics, 01.07.2019 09:30 kony345p

Write the equation in standard form for the circle that has a diameter with endpoints (0,8) and (0, - 8)

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Answer from: danuwell

Hello!

Explanation:

Slope-intercept form: → y=mx+b

m: represents the slope and is constant.

b: represents the y-intercept.

Used rise/run.

$\frac{rise}{run}$

$Slope=\frac{y^2-y^1}{x^2-x^1}$

(x^1,y^1)=(0,8)

(x^2,y^2)=(0,-8)

rise=y^2-y^1=-8-8=-16

run=x^2-x^1=0-0=0

$=\frac{-16}{0}$

Undefined is -16/0

But the slope is -16

And the y-intercept is 0.

Hope this helps!

Answer from: unkown77

so the endpoints are at (0,8) and (0,-8) for the diameter, meaning half-way in between those points, is the center of the circle, and the distance of between those points, is the diameter, but half of that, is its radius.

so let's find the center of it and radius then.

$\bf ~~~~~~~~~~~~\textit{middle point of 2 points } \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-8}) \qquad \left(\cfrac{ x_2 + x_1}{2}~~~ ,~~~ \cfrac{ y_2 + y_1}{2} \right) \\\\\\ \left( \cfrac{0+0}{2}~,~\cfrac{-8+8}{2} \right)\implies (0,0)$

so the center is at the origin, now

$\bf ~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{0}~,~\stackrel{y_1}{8})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ \stackrel{diameter}{d}=\sqrt{(0-0)^2+(-8-8)^2}\implies d=\sqrt{(-16)^2} \implies d=16 \\\\\\ \textit{so then the radius is half that }\cfrac{16}{2}\implies r=8 \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{0}{ k})\qquad \qquad radius=\stackrel{8}{ r} \\\\\\ (x-0)^2+(y-0)^2=8^2\implies \boxed{x^2+y^2=64}$

Answer from: Quest

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

$m\angle qrt=156^o$

$m\angle qst=156^o$

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.