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harkovskaia [24]
3 years ago
14

Which is the standard form of the equation of the parabola that has a vertex of (3, 1) and a directric of x = -2?

Mathematics
2 answers:
vagabundo [1.1K]3 years ago
8 0
Check the picture below.  So,the parabola looks like so, notice the distance "p". since the parabola is opening to the right, then "p" is positive, thus is 5.

\bf \textit{parabola vertex form with focus point distance}\\\\
\begin{array}{llll}
\boxed{(y-{{ k}})^2=4{{ p}}(x-{{ h}})} \\\\
(x-{{ h}})^2=4{{ p}}(y-{{ k}}) \\
\end{array}
\qquad 
\begin{array}{llll}
vertex\ ({{ h}},{{ k}})\\\\
{{ p}}=\textit{distance from vertex to }\\
\qquad \textit{ focus or directrix}
\end{array}\\\\

\bf -------------------------------\\\\
\begin{cases}
h=3\\
k=1\\
p=5
\end{cases}\implies (y-1)^2=4(5)(x-3)\implies (y-1)^2=20(x-3)
\\\\\\
\cfrac{1}{20}(y-1)^2=x-3\implies \boxed{\cfrac{1}{20}(y-1)^2+3=x}

fgiga [73]3 years ago
3 0

Answer:

20(x-3) = (y-1)^2

Step-by-step explanation:

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The perimeter of a rectangle is 120 inches. The length is 10 more than the width. Find the length and width
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The formula of a perimeter of a rectangle:

P=2(l+w)

We have:

P=120\ in\\\\l=w+10

Substitute

2(w+10+w)=120\\\\2(2w+10)=120\ \ \ \ |:2\\\\2w+10=60\ \ \ \ |-10\\\\2w=50\ \ \ \ |:2\\\\w=25\\\\l=25+10=35

<h3>Answer: Length = 35 in, Width = 25 in.</h3>
4 0
3 years ago
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denis23 [38]
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4 0
3 years ago
Given () = −^3 + 2^2 +(3/2) be the position of a particle moving along the x-axis at time t. At what time will the instantaneous
cestrela7 [59]

Answer:

5.266 secs

Step-by-step explanation:

Lets assume ; p(t) = t^-3 + 2^2 + ( 3/2 ) is the particle position along x-axis

time interval [ 0, 4 ]

Average velocity = Displacement / time

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where a = 0 , b = 4 ( time intervals )

Back to equation 1

Average velocity = [ ( 4^-3 + 4 + (3/2) ) - ( 0 +  4 + (3/2) ) ] / 4

                             = 3.9 * 10^-3 ----- ( 2 )

Instantaneous velocity = d/dx p(t)

                                      = - 3/t^4  ------ ( 3 )

To determine the time that the instanteous velocity = average velocity

equate equations (2) and (3)

3.9*10^-3 = - 3 / t^4

t^4 = - 3 / ( 3.9 * 10^-3 ) = - 769.231

hence t = \sqrt[4]{- 769.231 } = 5.266 secs

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3 years ago
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The equation is:

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Step-by-step explanation:

6 0
3 years ago
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