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3 years ago

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Section 1 - Topic 5 Compositions of Functions 1. Consider f(x) = x + 3x - 70 and g(x) - 4(x-3). Part A: Find (fog)(3). ( Part B:

Find g(f (3)). Bg() Part C: Find f(g(-2)). Part D: Find (g.(-2). (( 2. Given the functions f(x) = 3x and g(x) = x + 1, find [(g(x)] - [(fºg)(x)]

1 answer:

SCORPION-xisa [38]3 years ago

7 0

Answer:

part c. find f(g(-2))Sana maka tulong

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ruslelena [56]

Answer: With that assumption, we have a square, whose area is given by the formula Asquare=a2, and two semicircles. The distance D is simply the square's diagonal. The area of each semicircle is given by the formula Asemicircle=π*r2/2. then you will get your answer!

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3 years ago

Question 2. Do I divide 9.76 by 8 or the opposite?

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3 years ago

Read 2 more answers

At Greenwood Landscaping, rock costs $47.50 per ton. How much would 2.5 tons cost?

Grace [21]

Answer:

Hey!

Your answer is $118.75!

Step-by-step explanation: How did I get this?

<u>STEP 1:</u> So we know that for a ton of rock costs us $47.50...

To get 2 tons all we have to do is to MULTIPLY $47.50 by 2...

<em><u>(47.50 x 2 = 95)</u></em>

<u>STEP 2: </u>So for $95, you will get 2 tons of rock!

Now to get the .5 tons of rock in price form, we have to get the price of the whole 2.5 tons and DIVIDE BY 2

<em><u>(47.50 ÷ 2 = 23.75)</u></em>

<u>STEP 3:</u> So now we have the costs for 2 tons and the price for HALF a ton.

What we do now is easy...we ADD THE VALUES TOGTHER!

<em><u>(95 + 23.75 = $118.75)</u></em>

The result of $118.75 after adding them together is the PRICE OF 2 TONS!

<u>I HOPE THIS HELPED YOU!</u>

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4 0

3 years ago

For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential f

Phantasy [73]

The key idea is that, if a vector field is conservative, then it has curl 0. Equivalently, if the curl is not 0, then the field is not conservative. But if we find that the curl is 0, that on its own doesn't mean the field is conservative.

1.

$\mathrm{curl}\vec F=\dfrac{\partial(5x+10y)}{\partial x}-\dfrac{\partial(-6x+5y)}{\partial y}=5-5=0$

We want to find $f$ such that $\nabla f=\vec F$ . This means

$\dfrac{\partial f}{\partial x}=-6x+5y\implies f(x,y)=-3x^2+5xy+g(y)$

$\dfrac{\partial f}{\partial y}=5x+10y=5x+\dfrac{\mathrm dg}{\mathrm dy}\implies\dfrac{\mathrm dg}{\mathrm dy}=10y\implies g(y)=5y^2+C$

$\implies\boxed{f(x,y)=-3x^2+5xy+5y^2+C}$

so $\vec F$ is conservative.

2.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(-2y)}{\partial z}-\dfrac{\partial(1)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x)}{\partial z}-\dfrac{\partial(1)}{\partial z}\right)\vec\jmath+\left(\dfrac{\partial(-2y)}{\partial x}-\dfrac{\partial(-3x)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x\implies f(x,y,z)=-\dfrac32x^2+g(y,z)$

$\dfrac{\partial f}{\partial y}=-2y=\dfrac{\partial g}{\partial y}\implies g(y,z)=-y^2+h(y)$

$\dfrac{\partial f}{\partial z}=1=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=z+C$

$\implies\boxed{f(x,y,z)=-\dfrac32x^2-y^2+z+C}$

so $\vec F$ is conservative.

3.

$\mathrm{curl}\vec F=\dfrac{\partial(10y-3x\cos y)}{\partial x}-\dfrac{\partial(-\sin y)}{\partial y}=-3\cos y+\cos y=-2\cos y\neq0$

so $\vec F$ is not conservative.

4.

$\mathrm{curl}\vec F=\left(\dfrac{\partial(5y^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial y}\right)\vec\imath+\left(\dfrac{\partial(-3x^2)}{\partial z}-\dfrac{\partial(5z^2)}{\partial x}\right)\vec\jmath+\left(\dfrac{\partial(5y^2)}{\partial x}-\dfrac{\partial(-3x^2)}{\partial y}\right)\vec k=\vec0$

Then

$\dfrac{\partial f}{\partial x}=-3x^2\implies f(x,y,z)=-x^3+g(y,z)$

$\dfrac{\partial f}{\partial y}=5y^2=\dfrac{\partial g}{\partial y}\implies g(y,z)=\dfrac53y^3+h(z)$

$\dfrac{\partial f}{\partial z}=5z^2=\dfrac{\mathrm dh}{\mathrm dz}\implies h(z)=\dfrac53z^3+C$

$\implies\boxed{f(x,y,z)=-x^3+\dfrac53y^3+\dfrac53z^3+C}$

so $\vec F$ is conservative.

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4 years ago

I will give brainliest! In the figure, the circle has a center O and has a radius of 10. If the length of arc AB is between 5 an

Softa [21]

Answer:

any integer in between 29,30,31,32,33,34 will work.

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3 years ago