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2 years ago

What is the equation of a parabola if the vertex is (1, 4) and the directrix is located at y = 7?

Mathematics

1 answer:

Oksana_A [137]2 years ago

4 0

According to the vertex and the directrix of the given parabola, the equation is:

$y = \frac{3}{4}(x - 1)^2 + 4$

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

The equation of a quadratic function, of vertex (h,k), is given by:

$y = a(x - h)^2 + k$

In which a is the leading coefficient.

The directrix is at y = k + 4a.

In this problem, the vertex is (1,4), hence:

$h = 1, k = 4$

The directrix is at y = 7, hence:

$4 + 4a = 7$

$a = \frac{3}{4}$

Hence, the equation is:

$y = a(x - h)^2 + k$

$y = \frac{3}{4}(x - 1)^2 + 4$

More can be learned about the equation of a parabola at brainly.com/question/26144898

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Differentiate y=x⁴(1-2x⁵)⁶(5-8x³)².

Liula [17]

Step-by-step explanation:

Let $y(x)=f(x)g(x)h(x)$ where

$f(x) = x^4$

$g(x)= (1 -2x^5)^6$

$h(x)= (5 - 8x^3)^2$

so that

$y(x) = x^4(1 -2x^5)^6(5 - 8x^3)^2$

Recall that the derivative of the product of functions is

$y'(x)=f'(x)g(x)h(x)+f(x)g'(x)h(x)+f(x)g(x)h'(x)$

so taking the derivatives of the individual functions, we get

$f'(x) = 4x^3$

$g'(x) = 6(1 - 2x^5)^5(-10x^4)$

$h'(x) = 2(5 - 8x^3)(-24x^2)$

So the derivative of y(x) is given by

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2 + x^4 6(1 -2x^5)^5(-10x^4)(5 - 8x^3)^2 + x^4(1 -2x^5)^6 2(5 - 8x^3)(-24x^2)$

$y'(x) = 4x^3(1 -2x^5)^6(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 60x^8(1 -2x^5)^5(5 - 8x^3)^2$

$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:- 48x^6(1 -2x^5)^6 2(5 - 8x^3)$

3 0

2 years ago

Connie collected 50 seashells during her 5-day vacation. Each day she collected 3 more than the previous day. How many seashells

vfiekz [6]

Answer:

The number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively

Step-by-step explanation:

This is a question that deals with consecutive numbers.

Let x represent the number of seashells collected on her first day.

Given that she collected 3 more each day, then

On day 2, she collected x + 3

On day 3, she collected x + 6

On day 4, she collected x + 9

On day 5, she collected x + 12

Adding up the above will give the number of sea shells collected on day 1;

i.e.

x + x + 3 + x + 6 + x + 9 + x + 12 = 50

Collect like terms

x + x + x + x + x + 3 + 6 + 9 + 12 = 50

5x + 30 = 50

5x = 50 - 30

5x = 20

Multiply ⅕ to both sides

⅕ * 5x = ⅕ * 20

x = 4.

This mean that she found 4 seashells on day 1;

Recall that day 2 = x + 3

So, day 2 = 4 + 3 = 7 seashells

day 3 = x + 6

day 3 = 4 + 6 = 10 seashells

day 4 = x + 9

day 4 = 4 + 9 = 13 seashells

day 5 = x + 12

day 5 = 4 + 13 = 16 seashells

Hence, the number of seashells collected on day 1 to day 5 is 4, 7, 10, 13 and 16 respectively

6 0

2 years ago

Find the area of a square whose side is 4xy.

ruslelena [56]

Step-by-step explanation:

Given,

Side of a square = 4xy

Therefore, area of the square = side × side

= 4xy × 4xy

$16 {x}^{2} {y}^{2} (ans)$

6 0

2 years ago

Read 2 more answers

On a track and field team, 8% of the members run only long-distance, 32% compete only in field events, and 12% are sprinters onl

kondor19780726 [428]

Answer:

0.40

Step-by-step explanation:

Members who run only long distance = 8%

So, probability that a member will run only long distance = P(A) = 0.08

Members who compete only in field events = 32%

So, probability that a member will compete only in field events = P(B) 0.32

Members who are sprinters = 12%

So, probability that a member is sprinter = P(C) 0.12

We have to calculate the probability that a randomly chosen team member runs only long-distance or competes only in field events. i.e we have to find P(A or B). Since these events cannot occur at the same time, we can write:

P(A or B) = P(A) + P(B)

Using the values, we get:

P(A or B) = 0.08 + 0.32 = 0.40

Thus, the probability that a randomly chosen team member runs only long-distance or competes only in field events is 0.40

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3 years ago

Consider the following pair of equations: y = −2x + 8 y = x − 1 Explain how you will solve the pair of equations by substitution

Rzqust [24]

Y = -2x +8
y = x-1

y=y

-2x+8 = x-1

-3x = -1 -8

-3x = -9

3x = 9

x = 3

6 0

3 years ago