27.09.2020

Write an equation in standard form of the hyperbola described. Focus (4, 0); vertex (2, 0); center (0, 0)

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09.07.2023, solved by verified expert
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Check the picture below, so the hyperbola looks more or less like so, so let's find the length of the conjugate axis, or namely let's find the "b" component.

Write an equation in standard form of the hyperbola, №18011067, 27.09.2020 02:07

Write an equation in standard form of the hyperbola, №18011067, 27.09.2020 02:07


Write an equation in standard form of the hyperbola, №18011067, 27.09.2020 02:07
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Mathematics
Step-by-step answer
P Answered by Specialist

Check the picture below, so the hyperbola looks more or less like so, so let's find the length of the conjugate axis, or namely let's find the "b" component.

\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill

\begin{cases} h=0\\ k=0\\ a=2\\ c=4 \end{cases}\implies \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 4^2=2^2+b^2\implies 16=4+b^2\implies \underline{12=b^2} \\\\\\ \cfrac{(x-0)^2}{2^2}-\cfrac{(y-0)^2}{12}\implies \boxed{\cfrac{x^2}{4}-\cfrac{y^2}{12}}


Write an equation in standard form of the hyperbola described.

Focus (4, 0); vertex (2, 0); center
Mathematics
Step-by-step answer
P Answered by Master

Check the picture below, so the hyperbola looks more or less like the one below, let's find the conjugate axis or namely the "b" component.

\textit{hyperbolas, horizontal traverse axis } \\\\ \cfrac{(x- h)^2}{ a^2}-\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2} \end{cases} \\\\[-0.35em] ~\dotfill

\begin{cases} h=0\\ k=0\\ a=10\\ c=26 \end{cases}\implies \cfrac{(x-0)^2}{10^2}-\cfrac{(y-0)^2}{b^2} \\\\\\ c^2=a^2+b^2\implies 26^2=10^2+b^2\implies 676=100+b^2\implies \underline{576=b^2} \\\\\\ \cfrac{(x-0)^2}{10^2}-\cfrac{(y-0)^2}{576}\implies \boxed{\cfrac{x^2}{100}-\cfrac{y^2}{576}}


Write an equation in standard form of the hyperbola described.

Vertex (10, 0); focus (-26, 0); cen
Mathematics
Step-by-step answer
P Answered by PhD

SI=(P*R*T)/100

P=2000

R=1.5

T=6

SI=(2000*1.5*6)/100

=(2000*9)/100

=180

Neil will earn interest of 180

Mathematics
Step-by-step answer
P Answered by PhD

For 1 flavor there are 9 topping

Therefore, for 5 different flavors there will be 5*9 choices

No of choices= 5*9

=45 

Mathematics
Step-by-step answer
P Answered by PhD

The solution is in the following image

The solution is in the following image
Mathematics
Step-by-step answer
P Answered by PhD
The answer is in the image 

The answer is in the image 

Mathematics
Step-by-step answer
P Answered by PhD

F=ma

where F=force

m=mass

a=acceleration

Here,

F=4300

a=3.3m/s2

m=F/a

    =4300/3.3

    =1303.03kg

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