Aldo works as a busboy making

The endpoints of a diameter of a circle are A(2,1) and B(5,5). Find the area of the circle in terms of pi.

Tcecarenko [31]

Answer:

The area of the circle is $A=6.25\pi\ units^{2}$

Step-by-step explanation:

step 1

Find the diameter of circle

we know that

The diameter of the circle is equal to the distance AB

the formula to calculate the distance between two points is equal to

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

substitute the values

$AB=\sqrt{(5-1)^{2}+(5-2)^{2}}$

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

$AB=\sqrt{25}$

$AB=5\ units$

therefore

the diameter of the circle is

$D=5\ units$

step 2

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

$r=5/2=2.5\ units$ ----> the radius is half the diameter

substitute

$A=\pi (2.5)^{2}$

$A=6.25\pi\ units^{2}$

4 0

3 years ago

What type of symmetry is shown in this picture (point, line, or rotational)? Explain your answer and identify the line of symmet

ludmilkaskok [199]

Answer:

symmetry about the y-axis is shown

Step-by-step explanation:

Points on the right of the line of symmetry (x=0, the y-axis) are the same distance from that line as the corresponding points on the left. (That is what makes it a line of symmetry.)

There is no point of rotation that will map one figure to the other after rotation, hence no point or rotational symmetry.

8 0

3 years ago

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How do I solve this <br> 5{6x(5x +78) -10000

patriot [66]

Answer:

150x^2+2340x-50000

Step-by-step explanation:

5[6x(5x+78)-10000]

5[30x^2+468x-10000]

150x^2+2340x-50000

6 0

3 years ago

An experiment consists of drawing a marble out of a bag, observing the color, and then placing it back in the bag. Suppose the e

Elan Coil [88]

The experimental data suggest that

$\mathbb P(\text{red})\approx\dfrac{38}{75}$
$\mathbb P(\text{blue})\approx\dfrac{23}{75}$
$\mathbb P(\text{green})\approx\dfrac{11}{75}$
$\mathbb P(\text{yellow})\approx\dfrac3{75}$

Because the marble is replaced after being drawn, and so the number of marbles of a given color remains the same, the event of drawing any given color is independent of what was drawn before. So

$\mathbb P(\text{2 consecutive yellows})\approx\dfrac3{75}\cdot\dfrac3{75}=\dfrac1{625}$

5 0

4 years ago

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Find an equation of the line that passes through the points (-5, -3) and (3, 1)

Mkey [24]

$\bf (\stackrel{x_1}{-5}~,~\stackrel{y_1}{-3})\quad (\stackrel{x_2}{3}~,~\stackrel{y_2}{1}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{1}-\stackrel{y1}{(-3)}}}{\underset{run} {\underset{x_2}{3}-\underset{x_1}{(-5)}}}\implies \cfrac{1+3}{3+5}\implies \cfrac{4}{8}\implies \cfrac{1}{2}$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-3)}=\stackrel{m}{\cfrac{1}{2}}[x-\stackrel{x_1}{(-5)}]\implies y+3=\cfrac{1}{2}(x+5) \\\\\\ y+3=\cfrac{1}{2}x+\cfrac{5}{2}\implies y=\cfrac{1}{2}x+\cfrac{5}{2}-3\implies y = \cfrac{1}{2}x-\cfrac{1}{2}$

6 0

3 years ago

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