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3 years ago

The student council at Spend too much High School is planning a school dance. The table below shows the budget for the dance.

1 answer:

Pie3 years ago

4 0

The dance would /cost/ the school 50 dollars, making the profit -50. The dance tickets make 300, and the DJ takes away 250, making a 50 profit. However, the decorations cost 100, taking away that from 50, making -50.

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Y=x.arctan(x)^1/2. find dy/dx. pls show steps

Whitepunk [10]

$y=x(\arctan x)^{1/2}$

Use the product rule first:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dx}{\mathrm dx}(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+x\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}$

Use the chain rule to compute the derivative of $(\arctan x)^{1/2}$ . Let $z=(\arctan x)^{1/2}$ and take $u=\arctan x$ , so that by the chain rule

$\dfrac{\mathrm dz}{\mathrm dx}=\dfrac{\mathrm dz}{\mathrm du}\dfrac{\mathrm du}{\mathrm dx}$

$\dfrac{\mathrm dz}{\mathrm du}=\dfrac{\mathrm du^{1/2}}{\mathrm du}=\dfrac12u^{-1/2}$

$\dfrac{\mathrm du}{\mathrm dx}=\dfrac{\mathrm d\arctan x}{\mathrm dx}=\dfrac1{1+x^2}$

$\implies\dfrac{\mathrm d(\arctan x)^{1/2}}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}(1+x^2)}$

So we have

$\dfrac{\mathrm dy}{\mathrm dx}=(\arctan x)^{1/2}+\dfrac x{2(\arctan x)^{1/2}(1+x^2)}$

You can rewrite this a bit by factoring $(\arctan x)^{-1/2}$ , just to make it look neater:

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac1{2(\arctan x)^{1/2}}\left(2\arctan x+\dfrac x{1+x^2}\right)$

3 0

3 years ago

Round 481 to the nearest<br> tens place?

nydimaria [60]

480.

There is 1 before 8. And 1 is below not 5 or more in order to round up to 490. So, the only choice is to stay at 480. Therefore, the answer is 480.

4 0

3 years ago

What best describes the expression y over 3?

Leya [2.2K]

The answer would be C, some number divided by 3.

A represents addition, y + 3
B represents multiplication, y * 3
D represents subtraction, y - 3

4 0

4 years ago

Expand this expression by using the distributive property. 4( -2g + 4 -3t)

Ilia_Sergeevich [38]

Answer:

-8g + 16 + 12t

Step-by-step explanation:

multiply 4 with -2g

multiply 4 with 4

multiply 4 with -3t

4 0

3 years ago

a maze at a country fair is made from 275 bales of hay. the maze at the state fair is made from 4 times as many bales of hay. ho

tia_tia [17]

For this, you simply multiply 275 bye 4 as it says 4 times as many bales of hay.
275*4=1100

4 0

3 years ago

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