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1 year ago

A varies inversely as the square of b. If a is 1 when b is 4, find a when b is 4. with solution

Mathematics

1 answer:

inn [45]1 year ago

5 0

Answer:

a=k/b squared when a=1,b=4 k=16

When b=4 a=1

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Write the equation of a parabola having the vertex (1, −2) and containing the point (3, 6) in vertex form. Then, rewrite the equ

In-s [12.5K]

PART A

The equation of the parabola in vertex form is given by the formula,

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

where

$(h,k)=(1,-2)$

is the vertex of the parabola.

We substitute these values to obtain,

$y + 2 = a {(x - 1)}^{2}$

The point, (3,6) lies on the parabola.

It must therefore satisfy its equation.

$6 + 2 = a {(3 - 1)}^{2}$

$8= a {(2)}^{2}$

$8=4a$

$a = 2$
Hence the equation of the parabola in vertex form is

$y + 2 = 2 {(x - 1)}^{2}$

PART B

To obtain the equation of the parabola in standard form, we expand the vertex form of the equation.

$y + 2 = 2{(x - 1)}^{2}$

This implies that

$y + 2 = 2(x - 1)(x - 1)$

We expand to obtain,

$y + 2 = 2( {x}^{2} - 2x + 1)$

This will give us,

$y + 2 = 2 {x}^{2} - 4x + 2$

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

This equation is now in the form,

$y = a {x}^{2} + bx + c$
where

$a=1,b=-4,c=0$

This is the standard form

7 0

2 years ago

Which of the following expressions has a coefficient of 6 and a constant of 9?

Tcecarenko [31]

It would be C because a coefficient is always with a variable and 6 is with a variable which makes it a coefficient

Hope this helps

Have a great day/night

6 0

2 years ago

Read 2 more answers

Find the midpoint of the line segment joining the points (5,6) and (-1,-6).

kumpel [21]

Answer:

The midpoint is (2,0)

Step-by-step explanation:

To find the x coordinate of the midpoint, add the x coordinates of the endpoint and divide by 2

(5+-1)/2 =4/2 =2

To find the y coordinate of the midpoint, add the y coordinates of the endpoint and divide by 2

(6+-6)/2 =0/2 =0

The midpoint is (2,0)

8 0

2 years ago

On a certain game show, contestants pick 5 number balls from a bag containing 20 numbered balls (0-19). After each draw, the bal

Gnoma [55]

Answer:

5/20 or 25% probability of winning $1,000,000

Step-by-step explanation:

How many numbered balls do they need to win?

How many balls are there?

Therefor your answer is (balls need to win/number of balls).

4 0

1 year ago

Help me with 5 and 6 please I really don’t get it

alekssr [168]

Answer:

5 is congruent, 6 is not congruent

Step-by-step explanation:

In 5, both shapes have the same side lengths. This means their areas are the same, making them congruent.

In 6, the shapes do not have the same side lengths. This means their areas are not the same, making them not congruent.

6 0

2 years ago