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3 years ago

Richard and teo have combined age of 36 Richard is 9 years older than twice

Mathematics

1 answer:

Juliette [100K]3 years ago

5 0

Answer:

27 years old

Step-by-step explanation:

So if they are 9 years old you can do 36 minus 9. You get 27. And it said the Ages combined, so if we combine/plus 27 and 9 then you get 36.

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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.

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

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.

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

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.

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

so $\vec F$ is not conservative.

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

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.

4 0

3 years ago

(PLEASE HELP!) (IM GIVING GOOD POINTS!)

morpeh [17]

Answer:

No, he incorrectly rounded 1.25 to 2

Step-by-step explanation:

hope this helps :)

7 0

2 years ago

Read 2 more answers

2) In August, Emily's Clothing Store sold 460 shirts with the ratio of short sleeve to long

aivan3 [116]

Answer:

138

Step-by-step explanation:

We know that there are at least 3 short sleeved shirts and there are at least 7 long sleeved shirts. And we know it's in that ratio. So the best way to start this is to divide 460 by 7+3 to get the single unit amount of both shirts.

46 is the single unit amount. So 46 * 3 will get us our short sleeved shirts:

46 * 3 = 138

To check our answer, we'll take 460-138 and divide that by 7 to see if we get 46:

322/7 = 46

So the answer is correct!

4 0

3 years ago

How do you solve this

beks73 [17]

Answer:

In all x keep the value of x 5 then the answer can get.

4 0

2 years ago

The perimeter of a basketball court is 278ft. The length is 41ft longer than the width. Find the dimensions of the court.

inysia [295]

Since Perimeter is Length+ Width, and there are "two lengths" and "two widths", the formula needed here is p=2l+2w. We have the P, so using that, along with knowing that l is 41ft longer than w;
p = 278 , l = w+41
278 = 2l + 2w

278 = 2(w+41) + 2w

We'll use the DISTRIBUTIVE PROPERTY first: 278 = 2w + 82 + 2w

Then we'll COMBINE LIKE TERMS: 278 = 4w + 82

Next we'll subtract 82 from both sides: 196 = 4w

And finally divide both sides by 4:
49 = w

Since the length is w+41 and we now know the width, we can see what the length is: l = w+41 , l = 49 + 41 , l = 90.

Now that we know the length, we can see what the dimensions of the court are:
Perimeter is 278ft
Width is 49ft
And the Length is 90ft.

7 0

3 years ago