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2 years ago

A circle has a diameter with endpoints

Mathematics

1 answer:

Mars2501 [29]2 years ago

4 0

Answer:

Step-by-step explanation:

Midpoint of diameter is a center of a circle.

Coordinates of midpoint are

( $x_{1}$ , $y_{1}$ )

( $x_{2}$ , $y_{2}$ )

( $\frac{x_{1} +x_{2} }{2}$ , $\frac{y_{1} +y_{2} }{2}$ )

d = $\sqrt{(x_{2} -x_{1})^2 +(y_{2} -y_{1})^2 }$

Equation of a circle with center at (h, k) and radius "r" is (x - h)² + (y - k)² = r²

~~~~~~~~~~

C(20, 21)

D(- 20, 21)

( $\frac{-20+20}{2}$ , $\frac{-21+21}{2}$ ) = (0, 0)

d = $\sqrt{(-20-20)^2 +(21+21)^2}$ = √3364 = 58

r = $\frac{d}{2}$ = 29

x² + y² = 29²

<em>x² + y² = 841</em>

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Can someone plz plz plz help me choose an answer for this idk what it is

shepuryov [24]

Answer:

Largest number ins scientific notation: 1.4 x 10⁹ (Diameter of sun)

Step-by-step explanation:

We need to find the largest number ins scientific notation.

The number which has highest degree would be the largest.

In the given options, Diameter of Sun has highest power i.e 10⁹

All other options have lower degrees.

So, largest number ins scientific notation: 1.4 x 10⁹ (Diameter of sun)

4 0

2 years ago

Find the vertices and foci of the hyperbola. 9x2 − y2 − 36x − 4y + 23 = 0

Xelga [282]

Hey there, hope I can help!

NOTE: Look at the image/images for useful tips
$\left(h+c,\:k\right),\:\left(h-c,\:k\right)$

$\frac{\left(x-h\right)^2}{a^2}-\frac{\left(y-k\right)^2}{b^2}=1\:\mathrm{\:is\:the\:standard\:equation\:for\:a\:right-left\:facing:H}$
with the center of (h, k), semi-axis a and semi-conjugate - axis b.
NOTE: H = hyperbola

$9x^2-y^2-36x-4y+23=0 \ \textgreater \ \mathrm{Subtract\:}23\mathrm{\:from\:both\:sides}$
$9x^2-36x-4y-y^2=-23$

$\mathrm{Factor\:out\:coefficient\:of\:square\:terms}$
$9\left(x^2-4x\right)-\left(y^2+4y\right)=-23$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}9$
$\left(x^2-4x\right)-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}$

$\mathrm{Divide\:by\:coefficient\:of\:square\:terms:\:}1$
$\frac{1}{1}\left(x^2-4x\right)-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}$

$\mathrm{Convert}\:x\:\mathrm{to\:square\:form}$
$\frac{1}{1}\left(x^2-4x+4\right)-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}+\frac{1}{1}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$\frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y^2+4y\right)=-\frac{23}{9}+\frac{1}{1}\left(4\right)$

$\mathrm{Convert}\:y\:\mathrm{to\:square\:form}$
$\frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y^2+4y+4\right)=-\frac{23}{9}+\frac{1}{1}\left(4\right)-\frac{1}{9}\left(4\right)$

$\mathrm{Convert\:to\:square\:form}$
$\frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y+2\right)^2=-\frac{23}{9}+\frac{1}{1}\left(4\right)-\frac{1}{9}\left(4\right)$

$\mathrm{Refine\:}-\frac{23}{9}+\frac{1}{1}\left(4\right)-\frac{1}{9}\left(4\right) \ \textgreater \ \frac{1}{1}\left(x-2\right)^2-\frac{1}{9}\left(y+2\right)^2=1 \ \textgreater \ Refine$
$\frac{\left(x-2\right)^2}{1}-\frac{\left(y+2\right)^2}{9}=1$

Now rewrite in hyperbola standardform
$\frac{\left(x-2\right)^2}{1^2}-\frac{\left(y-\left(-2\right)\right)^2}{3^2}=1$

$\mathrm{Therefore\:Hyperbola\:properties\:are:}\left(h,\:k\right)=\left(2,\:-2\right),\:a=1,\:b=3$
$\left(2+c,\:-2\right),\:\left(2-c,\:-2\right)$

Now we must compute c
$\sqrt{1^2+3^2} \ \textgreater \ \mathrm{Apply\:rule}\:1^a=1 \ \textgreater \ 1^2 = 1 \ \textgreater \ \sqrt{1+3^2}$

$3^2 = 9 \ \textgreater \ \sqrt{1+9} \ \textgreater \ \sqrt{10}$

Therefore the hyperbola foci is at $\left(2+\sqrt{10},\:-2\right),\:\left(2-\sqrt{10},\:-2\right)$

For the vertices we have $\left(2+1,\:-2\right),\:\left(2-1,\:-2\right)$

Simply refine it
$\left(3,\:-2\right),\:\left(1,\:-2\right)$
Therefore the listed coordinates above are our vertices

Hope this helps!

8 0

3 years ago

A running back is having a great day on the football field. It’s only the third quarter, and he’s already rushed for 203 yards.

Naddik [55]

Answer:

He needs to gain more than 26 yards in order to break his record

Step-by-step explanation:

Let y stand for the number of yards he’ll have to gain. The sum of y plus the number of yards he already has (203) must be greater than 229 in order for him to break the record.

203 + y > 229 Set up the inequality.

203 − 203 + y > 229 − 203 Subtract 203 from both sides of the inequality.

y > 26

8 0

3 years ago

How long does it take a car to travel 200 mi at a constant speed of 25 mi/h?

beks73 [17]

First you have to do $200/25=8$ .
Since the car is moving at a constant rate, the answer would be 8h.

7 0

3 years ago

Read 2 more answers

Find the slope of the line containing the given points

Luden [163]

Answer:

-9/8

Step-by-step explanation:

The two points given are

(1,6) and (9,-3)

The slope is given by

m = (y2-y1)/(x2-x1)

= (-3-6)/(9-1)

= -9/8

8 0

2 years ago