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skelet666 [1.2K]
1 year ago
13

Please help:

Mathematics
1 answer:
pentagon [3]1 year ago
7 0

A parabola with focus of (3, 4) and a directrix of y = 0 has the equation of the parabola as

  • y = 1/8(x - 3)²  + 2

<h3>How to write the equation of parabola </h3>

Quadratic equation is equal to  parabolic equation, when the directrix is at y direction is of the form:

(x - h)² =  4P (y - k)

OR

standard vertex form, y = a(x - h)² + k    

where a = 1/4p

The focus

F (h, k + p) = (3, 4)

h = 3

k + p = 4

P in this problem, is the midpoint between the focus and the directrix

P = (4 - 0) / 2 =  2

p = 2

the vertex

v(h, k)

h = 3

k + p = 4, k = 2

v(h, k) = v(3, 2)

substitution of the values into the equation gives

(x - h)² =  4P (y - k)

(x - 3)² =  4 * 2 (y - 2)

(x - 3)² =  8 (y - 2)

y = 1/8(x - 3)²  + 2

The quadratic equation is of the form y = 1/8(x - 3)²  + 2

Learn more about vertex of quadratic equations at:

brainly.com/question/29244327

#SPJ1

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Answer: E: 100%

Step-by-step explanation:

If the class average is currently 70% and she wants to increase it by 10% every week for 3 weeks, 10×3=30% and 70+30= 100%.

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What is the y-intercept of the following equation?<br> y=x2-3x-4
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Answer:

y- intercept is ( 0, -4 )  

Step-by-step explanation:

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Find the angle between u = (8.- 3) and v = (-3,- 8) Round to the nearest tenth of a degree.
Nimfa-mama [501]

Answer:

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Step-by-step explanation:

First you must calculate the module or the magnitude of both vectors

The module of u is:

|u|=\sqrt{(8)^2 + (-3)^2} \\\\|u|=\sqrt{64 + 9}\\\\|u|=8.544

The module of v is:

|v|=\sqrt{(-3)^2 + (-8)^2} \\\\|u|=\sqrt{9 + 64}\\\\|u|=8.544

Now we calculate the scalar product between both vectors

u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0

Finally we know that the scalar product of two vectors is equal to:

u*v = |u||v|*cos(\theta)

Where \theta is the angle between the vectors u and v. Now we solve the equation for \theta

0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°

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