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3 years ago

Really easy question I’m Just really tired

Mathematics

1 answer:

alex41 [277]3 years ago

4 0

Answer:

4.5

Step-by-step explanation:

So the ladder is 4 feet from the wall and 18 feet tall. This can translate to negative 4 spaces on the x-axis and 18 spaces on the y-axis. The slope of a line is rise over run which is 18/4 or 4.5

I hope the answer is right and I hope I helped. Have fun with the rest of your math :)

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For each vector field f⃗ (x,y,z), compute the curl of f⃗ and, if possible, find a function f(x,y,z) so that f⃗ =∇f. if no such f

butalik [34]

$\vec f(x,y,z)=(2yze^{2xyz}+4z^2\cos(xz^2))\,\vec\imath+2xze^{2xyz}\,\vec\jmath+(2xye^{2xyz}+8xz\cos(xz^2))\,\vec k$

Let

$\vec f=f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k$

The curl is

$\nabla\cdot\vec f=(\partial_x\,\vec\imath+\partial_y\,\vec\jmath+\partial_z\,\vec k)\times(f_1\,\vec\imath+f_2\,\vec\jmath+f_3\,\vec k)$

where $\partial_\xi$ denotes the partial derivative operator with respect to $\xi$ . Recall that

$\vec\imath\times\vec\jmath=\vec k$

$\vec\jmath\times\vec k=\vec i$

$\vec k\times\vec\imath=\vec\jmath$

and that for any two vectors $\vec a$ and $\vec b$ , $\vec a\times\vec b=-\vec b\times\vec a$ , and $\vec a\times\vec a=\vec0$ .

The cross product reduces to

$\nabla\times\vec f=(\partial_yf_3-\partial_zf_2)\,\vec\imath+(\partial_xf_3-\partial_zf_1)\,\vec\jmath+(\partial_xf_2-\partial_yf_1)\,\vec k$

When you compute the partial derivatives, you'll find that all the components reduce to 0 and

$\nabla\times\vec f=\vec0$

which means $\vec f$ is indeed conservative and we can find $f$ .

Integrate both sides of

$\dfrac{\partial f}{\partial y}=2xze^{2xyz}$

with respect to $y$ and

$\implies f(x,y,z)=e^{2xyz}+g(x,z)$

Differentiate both sides with respect to $x$ and

$\dfrac{\partial f}{\partial x}=\dfrac{\partial(e^{2xyz})}{\partial x}+\dfrac{\partial g}{\partial x}$

$2yze^{2xyz}+4z^2\cos(xz^2)=2yze^{2xyz}+\dfrac{\partial g}{\partial x}$

$4z^2\cos(xz^2)=\dfrac{\partial g}{\partial x}$

$\implies g(x,z)=4\sin(xz^2)+h(z)$

Now

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+h(z)$

and differentiating with respect to $z$ gives

$\dfrac{\partial f}{\partial z}=\dfrac{\partial(e^{2xyz}+4\sin(xz^2))}{\partial z}+\dfrac{\mathrm dh}{\mathrm dz}$

$2xye^{2xyz}+8xz\cos(xz^2)=2xye^{2xyz}+8xz\cos(xz^2)+\dfrac{\mathrm dh}{\mathrm dz}$

$\dfrac{\mathrm dh}{\mathrm dz}=0$

$\implies h(z)=C$

for some constant $C$ . So

$f(x,y,z)=e^{2xyz}+4\sin(xz^2)+C$

3 0

4 years ago

Tammi deposited $520 into a bank account that earned simple interest each year. After 5 years, she had earned $156 in interest.

Sveta_85 [38]

Answer:

Step-by-step explanation:

Interest = Principal * rate * time

156 = 520(r)(5)

156 = 2600r

r = 0.06 or 6%

6 0

3 years ago

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Help!! This doesn't make any sense to me. Can anyone help me solve for the value of x?

notsponge [240]

<em>Exterior angle of the triangle is equal to the sum of the opposite angles.</em>

9x = 5x + 9 + x

<em>Combine like terms:</em>
9x = 6x + 9

<em>Take away 6x from both sides:</em>
3x = 9

<em>Divide by 3 on both sides:</em>
x = 3

Answer: x = 3

6 0

3 years ago

What is the MAD of this data ? Round to the nearest hundredth. 7, 14, 15, 9, 11, 14, 11, 10, 17

Vladimir79 [104]

Step 1 :

Find the mean of the data :

(2+4+6+8) / 4 = 20/4 = 5

Step 2 :

Find the distance between each data and mean.

Distance between 2 and 5 is 3

Distance between 4 and 5 is 1

Distance between 6 and 5 is 1

Distance between 8 and 5 is 3

Step 3 :

Add all the distances :

3+1+1+3 = 8

Step 4 :

Divide it by the number of data :

8 / 4 = 2

2 is the average absolute deviation.

<h2>So hence, your answer is 2.67</h2>

"The beautiful thing about learning is that no one can take it away from YOU"

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3 0

2 years ago

Work out the percentage change when a price of £50 is decreased to £40.

Ivanshal [37]

So the formula for price change is amount of change / original price * 100
50-40
= 10
10/50*100
= 1/5*100
= 20%

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3 years ago

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