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Sergeu [11.5K]
3 years ago
7

What is the equation for a circle with a center at (-2,-4) that passes through the point (3,8)?

Mathematics
2 answers:
Schach [20]3 years ago
5 0

Answer:

(x+2)²+(y+4)²=169

Step-by-step explanation:

In simplest terms

Margarita [4]3 years ago
3 0
Check the picture below.

so, the center of the circle is the midpoint of that diametrical segment, and half that length is the radius.

\bf ~~~~~~~~~~~~\textit{middle point of 2 points }
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -2 &,& -4~) 
%  (c,d)
&&(~ 3 &,& 8~)
\end{array}\qquad
%   coordinates of midpoint 
\left(\cfrac{ x_2 +  x_1}{2}\quad ,\quad \cfrac{ y_2 +  y_1}{2} \right)
\\\\\\
\left( \cfrac{3-2}{2}~~,~~\cfrac{8-4}{2} \right)\implies \left( \frac{1}{2}~,~2 \right)\impliedby center

\bf ~~~~~~~~~~~~\textit{distance between 2 points}
\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ -2 &,& -4~) 
%  (c,d)
&&(~ 3 &,& 8~)
\end{array}~~~ 
%  distance value
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
d=\sqrt{[3-(-2)]^2+[8-(-4)]^2}\implies d=\sqrt{(3+2)^2+(8+4)^2}
\\\\\\
d=\sqrt{25+144}\implies d=\sqrt{169}\implies d=13\qquad\qquad \qquad  \stackrel{radius}{\frac{13}{2}}

\bf \textit{equation of a circle}\\\\ 
(x- h)^2+(y- k)^2= r^2
\qquad 
center~~(\stackrel{\frac{1}{2}}{ h},\stackrel{2}{ k})\qquad \qquad 
radius=\stackrel{\frac{13}{2}}{ r}
\\\\\\
\left( x-\frac{1}{2} \right)^2+(y-2)^2=\left( \frac{13}{2} \right)^2\implies \left( x-\frac{1}{2} \right)^2+(y-2)^2=\frac{169}{4}

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Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T
Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180                      ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}

105^{\circ}+ m\angle B=180^{\circ}

Simplify:

m\angle B=75^{\circ}

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle  to the sines of its angles.

\frac{\sin A}{BC} = \frac{\sin C}{AB}

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}

then,

BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}

BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798 unit

Similarly for  AC:

\frac{\sin B}{AC} = \frac{\sin C}{AB}

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}

then,

AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}

AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283 unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

A = \frac{1}{2} \times AB \times AC \times \sin A

Substitute the values in above formula to get area;

A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}

A = 4 \times 10.9283 \times 0.86602540378

Simplify:

Area of triangle ABC = 37.856 (approx) square unit





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Suppose these show number of hours each student in a class slept last night:
Olin [163]

⊂ Hey, rosedalphinis ⊃

Answer:

Mean: 6.9 hours; Median 7 hours

Step-by-step explanation:

<u><em>⇒ Given:</em></u>

<em>-------------------------------------------------------------------------------------------------------------</em>

<em>Suppose these show number of hours each student in a class slept last night:</em>

<em>8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6</em>

<em>What is the mean of these numbers (rounded to the nearest tenth)?</em>

<em>What is the median?</em>

<em>Mean: 6.9 hours; Median 7 hours</em>

<em>Mean: 6.9 hours; Median 7.5 hours</em>

<em>Mean: 7 hours; Median 6.9 hours</em>

<em>Mean: 7.2 hours; Median 7 hours</em>

<em>-------------------------------------------------------------------------------------------------------------</em>

<u><em>⇒ Solution~:</em></u>

<em>-------------------------------------------------------------------------------------------------------------</em>

<em>Let's first define "Median".</em>

<em>You may be wondering "What is median/What is mean?".</em>

<em>When it asking for "Mean" It asking for the average.</em>

<em>When it asking for "Median" It asking for the middle number.</em>

<em>The formula for "Mean" is : M = sum of the terms/number of terms</em>

<em />

<em>According to the given we have;</em>

<em>8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6</em>

<em />

<em>Let's first find the "Mean":</em>

<em>First, add all the number together.</em>

<em>8 + 4 + 8 + 7 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6</em>

<em>12 + 8 + 7 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6</em>

<em>20 + 7 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6</em>

<em>27 + 7 + 9 + 6 + 5 + 10 + 7 + 6 + 6</em>

<em>34 + 9 + 6 + 5 + 10 + 7 + 6 + 6</em>

<em>43+ 6 + 5 + 10 + 7 + 6 + 6</em>

<em>49+ 5 + 10 + 7 + 6 + 6</em>

<em>54+ 10 + 7 + 6 + 6</em>

<em>64 + 7 + 6 + 6</em>

<em>71+ 6 + 6</em>

<em>77 + 6</em>

<em>= 83</em>

<em>Now let's count how many numbers of hours each student in a class slept.</em>

<em>8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6 = 12</em>

<em>Now 83 divide by 12:</em>

<em>83/12 = 6.9166666666667 {Round}</em>

<em>6.9166666666667 = 6.9</em>

<em>Therefore, Mean = 6.9</em>

<em>-------------------------------------------------------------------------------------------------------------</em>

<em>Next, Let's find the "Median":</em>

<em>To find the Median, place the numbers in value order and find the middle.</em>

<em>⇒ 8, 4, 8, 7, 7, 9, 6, 5, 10, 7, 6, 6</em>

<em>⇒ 4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10</em>

<em>Now we have them in order:</em>

<em>4, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 10</em>

<em>Then, we find the middle number:</em>

<u><em>4,</em></u><em> 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, </em><u><em>10</em></u>

<u><em>4, 5,</em></u><em> 6, 6, 6, 7, 7, 7, 8, 8, </em><u><em>9, 10</em></u>

<u><em>4, 5, 6,</em></u><em> 6, 6, 7, 7, 7, 8, </em><u><em>8, 9, 10</em></u>

<u><em>4, 5, 6, 6, </em></u><em>6, 7, 7, 7, </em><u><em>8, 8, 9, 10</em></u>

<u><em>4, 5, 6, 6, 6, </em></u><em>7, 7,</em><u><em> 7, 8, 8, 9, 10</em></u>

<em />

<em>Now You see that there two's 7 left.</em>

<em> If there is an even number of numbers add the two middles and divide by 2</em>

<em>Thus,</em>

<em>7 + 7 = 14</em>

<em>14/2 = 7</em>

<em>Therefore, Median = 7.</em>

<em>-------------------------------------------------------------------------------------------------------------</em>

<em>According to the solving above we can conclude that:</em>

<em>Mean: 6.9 hours; Median 7 hours</em>

<em>-------------------------------------------------------------------------------------------------------------</em>

<em />

<u><em>xcookiex12</em></u>

<em>9/4/2022</em>

<em>#Learnwithxcookiex12</em>

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