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2 years ago

Find the inverse of the function. y = 2x²-4

Mathematics

1 answer:

N76 [4]2 years ago

7 0

Answer:

Below in bold.

Step-by-step explanation:

y = 2x²-4

First find x in terms of y:

2x² = y - 4

x² = (y - 4)/2

x = √ [(y - 4)/2]

Now replace x by the inverse f-1(x) and y by x:

f-1(x) = √ [(x - 4)/2] (Note: it's the positive square root only)

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An election ballot asks voters to select three city commissioners from a group of six candidates, in how many ways can this be d

slava [35]

20 possibilities based on this as a combination not a permutation, 6 nCr 3 = 20

6 0

3 years ago

*ANSWER ASAP* Earth has a diameter of approximately 7926 miles. Determine the volume of Earth.

frutty [35]

Answer:

Rounding to the nearest whole number, 49 moons can fit in the earth.

Rounding to the tenth place, 50 moons can fit in the earth.

Step-by-step explanation:

To find how approximately how many moons could fit inside the earth, you would need yo find the volumes the earth and the moon.

V = 4/3 π r^3

Earth:

d = 2r

d = 7926 miles

7926 = 2r

3963 miles = r

V = 4/3 π (3963)^3

V = 4/3 π (62240377347)

V = 82987169796π cubic miles

Moon:

d = 2r

d = 2159 miles

2159 = 2r

1079.5 miles = r

V = 4/3 π (1079.5)^3

V = 4/3 π (1257963209.88)

V = 1677284279.83π cubic miles

Now you divide the volume of earth by the volume of moon to find how many moons can fit in earth

82987169796π ÷ 1677284279.83π =

approx 49

6 0

3 years ago

You spend £41.01 on groceries, £49.54 on fuel, and £12.50 on lottery tickets, how much do you have left from £105?

Maksim231197 [3]

Answer:

£1.95

Step-by-step explanation:

£41.01 + £49.54 + £12.50 = £103.05

£105 - £103.05 = £1.95

4 0

3 years ago

It is given that m=3x+1 and y= (5/1+m^2).<br>Find dy/dx in terms of x.<br>

DiKsa [7]

Answer:

${ \underline{ \bf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}}$

Step-by-step explanation:

${ \bf{m = 3x + 1}} \\ { \sf{ \frac{dm}{dx} = 3 }} \\ \\ { \bf{y = \frac{5}{1 + {m}^{2} } }} \\ \\ { \tt{ \frac{dy}{dm} = \frac{ - 10m}{ {(1 + {m}^{2} )}^{2} } }}$

Using chain rule:

${ \boxed{ \bf{ \frac{dy}{dx} = \frac{dy}{dm}. \frac{dm}{dx} }}}$

${ \sf{ \frac{dy}{dx} = - \frac{10m}{ {(1 + {m}^{2}) }^{2} } \times 3}} \\ \\ { \sf{ \frac{dy}{dx} = - \frac{30m}{ {(1 + {m}^{2}) }^{2} } }}$

${ \underline{ \sf{ \blue{christ \:† \: alone }}}}$

8 0

3 years ago

Read 2 more answers

The lengths of three sides of a quadrilateral are shown below:

pentagon [3]

In part A, we need to solve for the total length of sides 1, 2 and 3.
Since all three sides measurements are given, we have the solution below:
Sides123 = Side 1 + Side 2 + Side 3
Sides123 = (3y² + 2y - 6) + (4y² + 3y -7) + (5y² + 4y -8)
Sides123 = 12y² + 9y - 21
This is the total length of sides 1,2 and 3 "12y² + 9y - 21"

In part B, we need to solve for the length of the fourth side and the solution is shown below:
Side 4 = Perimeter / Sides123
Side 4 = (4y³ + 18y² + 16y -26) / 12y² + 9y -21

3 0

3 years ago