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3 years ago

If f(x) = (x3 + 25), find the inverse of f.

Mathematics

1 answer:

irakobra [83]3 years ago

3 0

Answer:

Dear user,

Answer to your query is provided below

Inverse is 3√(x-25)

Step-by-step explanation:

Explanation of the same is attached in image

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barxatty [35]

$z=f(x(u,v),y(u,v)),\begin{cases}x(u,v)=2u+v^2\\y(u,v)=3u-v\end{cases}$

We're given that $f_x(6,1)=3$ and $f_y(6,1)=-1$ , and want to find $\frac{\partial z}{\partial v}(1,2)$ .

By the chain rule, we have

$\dfrac{\partial z}{\partial v}=\dfrac{\partial z}{\partial x}\dfrac{\partial x}{\partial v}+\dfrac{\partial z}{\partial y}\dfrac{\partial y}{\partial v}$

and

$\dfrac{\partial x}{\partial v}=2v$

$\dfrac{\partial y}{\partial v}=-1$

Then

$\dfrac{\partial z}{\partial v}(1,2)=\dfrac{\partial z}{\partial x}(6,1)\dfrac{\partial x}{\partial v}(1,2)+\dfrac{\partial z}{\partial y}(6,1)\dfrac{\partial y}{\partial v}(1,2)$

(because the point $(x,y)=(6,1)$ corresponds to $(u,v)=(1,2)$ )

$\implies\dfrac{\partial z}{\partial v}(1,2)=3\cdot2\cdot2+(-1)\cdot(-1)=\boxed{13}$

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3 years ago

What are the coordinates of the point (-4,-10) after a 180 rotation about the orgin and then a translation 1 unit right

goblinko [34]

1. Rotation by 180° (clockwise or anti-clockwise) about the origin has a rule:

(x,y)→(-x,-y).

Then

(-4,-10)→(4,10).

2. Translation 1 unit to the right has a rule:

(x,y)→(x+1,y).

Then

(4,10)→(5,10).

3. After rotation and translation the image of point (-4,-10) is point (5,10).

Answer: (5,10).

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3 years ago

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Answer:

6 3/8 pizzas

Step-by-step explanation:

She estimates that each player will eat three eighths if a pizza and there are 17 players.

Therefore, we have to multiply 3/8 by 17:

3 / 8 * 17 = 6.375 pizzas = 6 3/8 pizzas

They will eat 6 3/8 pizzas.

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3 years ago

Bob is going to China, and he wants to bring some DVDs on the airplane. If Bob has a collection of 15 DVDs, in how many ways can

Ksju [112]

There would be "five ways" to bring three DVD's. If you divide fifteen by three there would be five.

$15/3=5


$

To prove your work:

$3 * 5 = 15$

Hope this helps!

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3 years ago

Jose invested $5000 into a fund with an interest rate of 4.8%. How much interest would he earn after 2 years? A) $240 B) $24,000

pogonyaev

Answer: C) $480

Step-by-step explanation:

Given: Jose invested $5000 into a fund with an interest rate of 4.8%.

Therefore, Principal amount (P)$5000

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We know that the simple interest is given by

$S.I.=Prt\\\Rightarrow\ S.I.=5000\times0.048\times2\\\Rightarrow\ S.I.=\$480$

Hence, the interest after 2 years = $480

6 0

4 years ago