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Whitepunk [10]
3 years ago
11

Can someone help explain how to solve this problem please? It would be very helpful.

Mathematics
1 answer:
ladessa [460]3 years ago
7 0
Z=180-84-50
x=180-84-63
y=180-33-13

z=46
x=33
y=134
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Write an equation of the hyperbola given that the center is at (2, -3), the vertices are at (2, 3) and (2, - 9), and the foci ar
zavuch27 [327]
Check the picture below.

so, the hyperbola looks like so, clearly a = 6 from the traverse axis, and the "c" distance from the center to a focus has to be from -3±c, as aforementioned above, the tell-tale is that part, therefore, we can see that c = 2√(10).

because the hyperbola opens vertically, the fraction with the positive sign will be the one with the "y" in it, like you see it in the picture, so without further adieu,

\bf \textit{hyperbolas, vertical traverse axis }
\\\\
\cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1
\qquad 
\begin{cases}
center\ ( h, k)\\
vertices\ ( h,  k\pm a)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2 + b ^2}\\
asymptotes\quad  y= k\pm \cfrac{a}{b}(x- h)
\end{cases}\\\\
-------------------------------

\bf \begin{cases}
h=2\\
k=-3\\
a=6\\
c=2\sqrt{10}
\end{cases}\implies \cfrac{[y- (-3)]^2}{ 6^2}-\cfrac{(x- 2)^2}{ b^2}=1
\\\\\\
\cfrac{(y+3)^2}{ 36}-\cfrac{(x- 2)^2}{ b^2}=1
\\\\\\
c^2=a^2+b^2\implies (2\sqrt{10})^2=6^2+b^2\implies 2^2(\sqrt{10})^2=36+b^2
\\\\\\
4(10)=36+b^2\implies 40=36+b^2\implies 4=b^2
\\\\\\
\sqrt{4}=b\implies 2=b\\\\
-------------------------------\\\\
\cfrac{(y+3)^2}{ 36}-\cfrac{(x- 2)^2}{ 2^2}=1\implies \cfrac{(y+3)^2}{ 36}-\cfrac{(x- 2)^2}{ 4}=1

3 0
2 years ago
Liz flips a coin 40 times. The coin lands heads up 24 times and tails up 16 times. What is the theoretical probability of the co
Semenov [28]

Answer:50

Step-by-step explanation:

Because I just got it right

4 0
3 years ago
Express the probability that a die wil land on a number less than 5 as a fraction
Rashid [163]

Answer:

\frac{2}{3}

Step-by-step explanation:

Values less than 5 on a die are 1, 2, 3, 4 ← 4 values out of a possible 6

P( < 5) = \frac{4}{6} = \frac{2}{3} in simplest form


7 0
3 years ago
What are the slope and the y-intercept of the linear function that is represented by the equation y=-10x+1
RUDIKE [14]
<h3>Answer:</h3>

The slope is -10 and the y-intercept is 1.

<h3>Explanation:</h3>

This function is written in slope-intercept form, which is y=mx+b.  In this form, m is the slope and b is the y-intercept.

In this case, m=-10 and b=1, so those are the answers to this problem.

6 0
3 years ago
Read 2 more answers
The angle of elevation from an observer to the bottom edge of the Delaware River drawbridge observation deck located 200 feet fr
aleksklad [387]

The height of the chimney above the floor of the observation deck is 52.4 ft

Two right angle triangle will be formed.

<h3>Right angle triangle:</h3>

Right angle triangle are triangle that has one of its angle as 90 degrees.

Therefore, using trigonometric ratio,

adjacent side = distance of observer from the bottom edge of the Delaware River drawbridge observation deck

Therefore,

tan 40 = opposite / adjacent

Where

x = height of the observer to the top of the observation deck

tan 40 = x / 200

x = 200 tan 40

x = 167.819926235

x = 167.82 ft

tan 30 = opposite / adjacent

y = height of the observer to the bottom of the observation deck

tan 30 = y / 200

y = 200 tan 30

y = 115.470053838

y = 115.47 ft

The height of the chimney above the floor of the observation deck = height of the observer to the top of the observation deck - height of the observer to the bottom of the observation deck

The height of the chimney above the floor of the observation deck = 167.82 - 115.47 = 52.35 ft

learn more on trigonometric ratio here: brainly.com/question/23854119

5 0
2 years ago
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