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5 months ago

What is the directrix of a parabola whose equation is (y+3)^3=8(x-3)?

Mathematics

2 answers:

Zanzabum5 months ago

5 0

Considering the equation of the parabola, the directrix is: x = 1.

<h3>What is the equation of a parabola given it’s vertex?</h3>

The equation of an horizontal parabola, of vertex (h,k), is given by:

(y - k)² = 4p(x - h).

The directrix is at x = h - p.

For this problem, the equation is:

(y + 3)² = 8(x - 3).

The relevant coefficients for this problem are:

4p = 8 -> p = 2, h = 3.

Hence the directrix is:

x = h - p = 3 - 2 = 1.

More can be learned about the equation of a parabola at brainly.com/question/17987697

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Leya [2.2K]5 months ago

4 0

The equation of the parabola whose equation $(y + 3)^3 = 8(x - 3).$ , the directrix exists x = 1.

<h3>What is the equation of a parabola given its vertex?</h3>

The equation of a horizontal parabola, of vertex (h, k), exists given by:

(y - k)² = 4p(x - h).

The directrix exists at x = h - p.

For this problem, the equation exists:

$(y + 3)^3 = 8(x - 3).$

The appropriate coefficients for this problem exist:

4p = 8

p = 8/4 = 2 and h = 3.

Hence the directrix exists:

x = h - p = 3 - 2 = 1.

Therefore, the directrix exists at x = 1.

To learn more about the equation of a parabola refer to:

brainly.com/question/17987697

#SPJ9

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1. The science club constructed a pyramid with a square base out of paper clips. The height of the pyramid is 2.5 feet. One side

elena-14-01-66 [18.8K]

Answer:

Part 1) The slant height of the pyramid is $2.80\ ft$

Part 2) The length of the third side of the window is $20.78\ in$

Part 3) The building's slant height is $53.85\ ft$

Step-by-step explanation:

Part 1) we know that

To find out the slant height of the pyramid, apply the Pythagorean Theorem

Let

l ----> the slant height of the pyramid

h ---> the height of the pyramid

b ---> the length side of the square base

$l^2=h^2+(b/2)^2$

we have

$h=2.5\ ft\\b=2.5\ ft$

substitute the given values

$l^2=2.5^2+(2.5/2)^2$

$l^2=2.5^2+(1.25)^2$

$l^2=7.8125$

$l=2.80\ ft$

Part 2) Let

c ----> the hypotenuse of a right triangle (the greater side)

a ---> the measure of one leg of the right triangle

b ---> the measure of the other leg of the right triangle

Applying the Pythagorean Theorem

$c^2=a^2+b^2$

we have

$c=24\ in\\a=12\ in$

substitute the given values and solve for b

$24^2=12^2+b^2$

$b^2=24^2-12^2$

$b^2=432$

$b=20.78\ in$

Part 3) Let

l ----> the building's slant height

h ---> the height of the building

r ---> the radius of the base of the building

Applying the Pythagorean Theorem

$l^2=h^2+r^2$

we have

$h=50\ ft\\r=20\ ft$

substitute the given values

$l^2=50^2+20^2$

$l^2=2,900$

$l=53.85\ ft$

4 0

3 years ago

Find the measure of e. (Please explain how you got your answer thanks!)

Amanda [17]

Angle e=88 this is because a straight line is always equal to 180. So 180-92 is equal to 88

7 0

3 years ago

Consider the figure shown on the coordinate plane. What are the coordinates of the midpoint of line segment CB?

Digiron [165]

I would say b or d....

5 0

3 years ago

Read 2 more answers

Renee says that y = mx can be rewritten in the form y = mx + b. Is she right? Explain why or why not

adelina 88 [10]

Answer - yes it can
Say you have y=2x with no y intercept (b)
You can still write it as y=2x +0 or assume the y intercept (b) is zero by writing it as y=2x

8 0

1 year ago

A plane decides to travel along AB towards the North with a velocity of V.

Maru [420]

Step-by-step explanation:

The wind has a speed of w and a direction α with the vertical. The x component of that speed is w sin α. The y component is -w cos α.

In order to stay on the north trajectory AB, the plane must have a horizontal speed of -w sin α. The plane's speed is v, so using Pythagorean theorem, the y component of the plane's speed is:

v² = (-w sin α)² + vᵧ²

v² = w² sin²α + vᵧ²

vᵧ = √(v² − w² sin²α)

The total vertical speed is therefore √(v² − w² sin²α) − w cos α.

If a is the length of AB, then the time is:

t = a / [√(v² − w² sin²α) − w cos α]

To rationalize the denominator, we multiply by the conjugate.

t = a / [√(v² − w² sin²α) − w cos α] × [√(v² − w² sin²α) + w cos α] / [√(v² − w² sin²α) + w cos α]

t = a [√(v² − w² sin²α) + w cos α] / (v² − w² sin²α − w² cos²α)

t = a [√(v² − w² sin²α) + w cos α] / (v² − w²)

8 0

2 years ago