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3 years ago

HELP!! 15 POINTS

Mathematics

1 answer:

babymother [125]3 years ago

5 0

Answer:

2 and 9 are correct. The remainder need to be reconsidered.

Step-by-step explanation:

Your answer to 9 is correct, which means you have the appropriate signs for the point coordinates. In your other point-slope questions, one or more of the signs is incorrect. Use your good work as an example of how to choose the correct answers elsewhere.

1) When you have y = kx, you can find the value of k from ...

... k = y/x

When the variation is direct, this works for any (x, y) pair.

3) A unit rate is called a unit rate because it has 1 (a unit) in the denominator.

4a, 4b, ... all slope calculations. You managed to get it right in problem 9. Watch your signs.

10, 11 ... It can work well to put the x term on the same side with the y-term, then multiply the equation by the denominator value.

... (2/3)x + y = 7 . . . . add (2/3)x to both sides of the equation

... 2x + 3y = 21 . . . . . multiply by 3. (Standard form always has the leading coefficient positive.)

_____

Whenever you consider making a term disappear from one side of the equation, think in terms of adding its opposite to both sides of the equation. This will give the result you want and is consistent with the properties of equality: whatever you do to one side of the equation you must also do to the other side of the equation. Other wording may have been used by your teacher or friends. This is the one true statement about transforming equations.

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3 years ago

Read 2 more answers

Explain how to write 45,100,000 in scientific notation.

Komok [63]

Step-by-step explanation:

$45,100,000 \\ = 4.51 \times {10}^{7}$

5 0

3 years ago

The dimensions of the nations smallest post office are 8 feet 4 inches by 7 feet 3 inches why would you use the measurement 8 fe

viva [34]

Answer:

Because 16 inches is one foot and 4 inches, as there are 12 inches in a foot. So this one foot is added to the 7 inches. Or otherwise we can say: a hundred inches (100 in).

Step-by-step explanation:

If we tell the length in feet, only the rest of the integer number of feet is expressed in inches.

4 0

3 years ago

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

3 years ago

Gordon, Henry and Sarah share £48 in a ratio 2:3:1. How much money does each person get?

Alinara [238K]

Answer:

Gordon gets 16£, Henry gets 24£ and Sarah gets 8£

Step-by-step explanation:

Let the ratio be 2x + 3x + 1x

Total amount = £48

So;

2x + 3x + x = 48

6x = 48

x = 48 / 6

x = 8

Now

2x = 16

3x = 24

x = 8

5 0

3 years ago