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2 years ago

Find f^-1(x) for f(x) = 1/x^3

Mathematics

1 answer:

kow [346]2 years ago

4 0

Answer: $f^{-1}(x) = \frac{\sqrt[3]{x^{2}}}{x}$

Step-by-step explanation:

$y = \frac{1}{x^{3}}$

Inverse is when you swap the x's and y's and then solve for "y":

$x = \frac{1}{y^{3}}$

$y^{3} = \frac{1}{x}$

$y = \frac{1}{\sqrt[3]{x}}$

$y = \frac{1}{\sqrt[3]{x}}*(\frac{\sqrt[3]{x}}{\sqrt[3]{x}})^{2}$

$y = \frac{\sqrt[3]{x^{2}}}{x}$

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A man invests his savings in two accounts ,one paying6% and the other paying 10% simple interest per year. He puts twice as much

AnnyKZ [126]

Answer: he invested $46062.5 at 6% and $23031.25 at 10%

Step-by-step explanation:

Let x represent the amount which he invested in the account paying 6% interest.

Let y represent the amount which he invested in the account paying 10% interest.

He puts twice as much in the lower-yielding account because it is less risky.. This means that

x = 2y

The formula for determining simple interest is expressed as

I = PRT/100

Considering the account paying 6% interest,

P = $x

T = 1 year

R = 6℅

I = (x × 6 × 1)/100 = 0.06x

Considering the account paying 10% interest,

P = $y

T = 1 year

R = 10℅

I = (y × 10 × 1)/100 = 0.1y

His annual interest is $7370dollars. it means that

0.06x + 0.2y = 7370 - - - - - - - - - -1

Substituting x = 2y into equation 1, it becomes

0.06 × 2y + 0.2y = 7370

0.12y + 0.2y = 7370

0.32y = 7370

y = 7370/0.32

y = $23031.25

x = 2 × 23031.25

x = 46062.5

6 0

2 years ago

A toy rocket is lunch vertically upward from ground level in into velocity of one 28 ft./s how long will it take for the rocket

pentagon [3]

Answer:

1.14 s

Step-by-step explanation:

Time, $t=\frac {d}{s}$

Here, d is the distance and s is the speed/velocity

Since we're given the velocity, s as 28 ft/s and the distance between the position of the rocket and ground as 32 ft then

$t=\frac {32}{28}=1.142857143\approx 1.14 s$

Therefore, it needs 1.14 seconds

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2 years ago

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Please help!!!!!! Rewrite this equation in terms of y 2x-3y=22

Leona [35]

The answer is y = 2/3x - 22/3

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1 year ago

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5. Henry hit 3 more than half as many home runs as Jack hit last season. Henry hit a total of 8 home runs. a. Make Sense and Per

Evgesh-ka [11]

Answer:

a. $3+\frac{x}{2} =8$

b. x = 10

Step-by-step explanation:

a. The number of home runs hit by Jack last season = x

It is given that Henry hit 3 more than half as many home runs as Jack hit.

Half of the runs hit by Jack = $\frac{x}{2}$

3 more than half the runs = $3+\frac{x}{2}$

So, the number of home runs hit by Henry = $3+\frac{x}{2}$

But, it is given that Henry hit a total of 8 runs.

Therefore, $3+\frac{x}{2} =8$

b. $3+\frac{x}{2} =8$

Subtract 3 from both sides.

$\frac{x}{2} =8-3$

= 5

x = 5 × 2

= 10

Hence, Jack hit 10 runs in the last season.

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2 years ago

Find the surface area of the composite solid. 6 ft 4 ft 1 5 ft 5 ft

likoan [24]

Sa Of Rectangular Prism - 65

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2 years ago