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2 years ago

What is the equation of a parabola with vertex (0, 0) and directrix x = -3.

Mathematics

1 answer:

miv72 [106K]2 years ago

3 0

Answer:

${y}^{2}= 12x$

Step-by-step explanation:

The standard equation of a parabola with vertex at the origin and and directix x=-p is of the form

${y}^{2} = 4{p}x$

Where p is simplify the distance from the origin to the directrix.

That is

$p = 3$

${y}^{2} = 4 \times 3x$

This simplifies to

${y}^{2}= 12x$

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10x + 8 = 3(x - 2)<br> 10x + 8 = 3x

lisabon 2012 [21]

Answer:

1) -2

2) 8/7

Step-by-step explanation:

1) 10x+8=3(x-2)

10x+8=3x-6

10x-3x=-6-8

7x=-14

x=-2

2) 10x+8=3x

10x-3x=8

7x=8

x=8/7

Hope it helps

5 0

2 years ago

Show with work please.

kolbaska11 [484]

Answer:

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

Step-by-step explanation:

The identity you will use is:

$\csc \left(x\right)=\frac{1}{\sin \left(x\right)}$

So,

$\csc \left(\theta-\frac{\pi }{2}\right)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{\sin \left(-\frac{\pi }{2}+\theta\right)}$

Now, using the difference of sin

Note: state that $\text{sin}(\alpha\pm \beta)=\text{sin}(\alpha) \text{cos}(\beta) \pm \text{cos}(\alpha) \text{sin}(\beta)$

$\csc \left(\theta-\frac{\pi }{2}\right)=\frac{1}{-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)}$

Solving the difference of sin:

$-\cos \left(\theta\right)\sin \left(\frac{\pi }{2}\right)+\cos \left(\frac{\pi }{2}\right)\sin \left(\theta\right)$

$-\cos \left(\theta\right) \cdot 1+0\cdot \sin \left(\theta\right)$

$-\text{cos} \left(\theta\right)$

Then,

$\csc \left(\theta-\frac{\pi }{2}\right)=-\frac{1}{\cos \left(\theta\right)}$

Once

$\text{sec}(-\theta)=\text{sec}(\theta)$

And, $\text{sec}(\theta)=-0.73$

$-\frac{1}{\cos \left(\theta\right)}=-\text{sec}(\theta)$

$-\frac{1}{\cos \left(\theta\right)}=-(-0.73)$

$-\frac{1}{\cos \left(\theta\right)}=0.73$

Therefore,

$\csc \left(\theta-\frac{\pi }{2}\right)=0.73$

3 0

2 years ago

Write the standard form of a line that passes through the given points (4,7) and (0,7)

VARVARA [1.3K]

The slope-intercept form:

$y=mx+b$

m - slope

b - y-intercept → (0, b).

We have the points (4, 7) and (0, 7) → b = 7.

Calculate the slope:

$m=\dfrac{7-7}{0-4}=\dfrac{0}{-4}=0$

Therefore we have $y=0x+7=7$

The standard form: $Ax+By=C$

<h3>Answer: y = 7.</h3><h3><em>It's a horizontal line.</em></h3>

4 0

2 years ago

I need help with the answer.

ivolga24 [154]

Answer:

Step-by-step explanation:

5x6-c

5x6=30

30-c

c=7

30-7=23

5 0

3 years ago

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Find the area of the semicircle. Round your answer to the nearest hundredth. YEAH IVE BEEN STUCK ON THIS help please I need the

aivan3 [116]

Answer:

your answer will be 127.17 sq in

Step-by-step explanation:

hope it helps you

have a wonderful day!!!

7 0

2 years ago

Read 2 more answers