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3 years ago

Write the equation for a parabola with a focus at (9,0) and a directrix at y = -4.

Mathematics

2 answers:

Alika [10]3 years ago

8 0

Answer:

Step-by-step explanation-3:

kondor19780726 [428]3 years ago

4 0

Answer:

(x-9)^2/8 -2 is the correct answer.

Step-by-step explanation:

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Find the equation of the line through (2,4) and (3,-1)

Natasha2012 [34]

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3 years ago

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The triangle T has vertices at (-2, 1), (2, 1) and (0,-1). (It might be an idea to

Firdavs [7]

Rewrite the boundary lines y = -1 - x and y = x - 1 as functions of y :

y = -1 - x ==> x = -1 - y

y = x - 1 ==> x = 1 + y

So if we let x range between these two lines, we need to let y vary between the point where these lines intersect, and the line y = 1.

This means the area is given by the integral,

$\displaystyle\iint_T\mathrm dA=\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy$

The integral with respect to x is trivial:

$\displaystyle\int_{-1}^1\int_{-1-y}^{1+y}\mathrm dx\,\mathrm dy=\int_{-1}^1x\bigg|_{-1-y}^{1+y}\,\mathrm dy=\int_{-1}^1(1+y)-(-1-y)\,\mathrm dy=2\int_{-1}^1(1+y)\,\mathrm dy$

For the remaining integral, integrate term-by-term to get

$\displaystyle2\int_{-1}^1(1+y)\,\mathrm dy=2\left(y+\frac{y^2}2\right)\bigg|_{-1}^1=2\left(1+\frac12\right)-2\left(-1+\frac12\right)=\boxed{4}$

Alternatively, the triangle can be said to have a base of length 4 (the distance from (-2, 1) to (2, 1)) and a height of length 2 (the distance from the line y = 1 and (0, -1)), so its area is 1/2*4*2 = 4.

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3 years ago

Show how to write, evaluate and simply an expression to represent and solve this problem: Jeff and his friend each text four cla

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Answer:

Step-by-step explanation:

It is given that Jeff and his friend each text four classmates about an concert that is two people texts four classmates then 2×4=8 people are notified about the concert, then according to question, each 8 of them texts 4 more students from a different school about the concert, so the total number of people from the other school which are being notified about the concert will be 8×4=32.

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3 years ago

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Answer:

If Regina wants a mean of 90, she needs to sell 94 books on the 5th day.

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3 years ago

Jeff can weed the garden twice as fast as his sister Julia. Together they can weed the garden in 3 hours. How long would it take

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