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4 years ago

What is the slope of the line represented by the equation y=-1/2x+1/4

Mathematics

1 answer:

ahrayia [7]4 years ago

3 0

I’m pretty sure the slope is -1/2

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Ariana plans to use $260 less than three-fourths of savings to buy a car. If the purchase price of the car is 9,340, how much do

tangare [24]

She has $12,488 in savings

Step-by-step explanation:

Ariana plans to use $260 less than three-fourths of savings to buy a car.

If the purchase price of the car is 9,340, we need to find how much

she has in savings

To find the savings

Assume that she has $x in savings
Write an equation of x
Solve the equation to find x

∵ She has $x in savings

∵ She plans to use $260 less than three-fourths of savings

- Three-fourths means $\frac{3}{4}$ and less than means subtract

∴ She plans to use $\frac{3}{4}$ x - 26

∵ The purchase price of the car is 9,340

- Equate the expression of x by 9,340

∴ $\frac{3}{4}$ x - 26 = 9,340

Now let us solve the equation

∵ $\frac{3}{4}$ x - 26 = 9,340

- Add 26 to both sides

∴ $\frac{3}{4}$ x = 9,366

- Divide both sides by $\frac{3}{4}$

∴ x = $12,488

She has $12,488 in savings

Learn more:

You can learn more about word problems in brainly.com/question/3950386

#LearnwithBrainly

7 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

4 years ago

the area of a rectangle hall is the same as the area of a square field of side 56 m. if the lenght of hall is 112m. find its bre

Semmy [17]

Step-by-step explanation:

please subscribe to my mom channel please

7 0

3 years ago

Help me!! need help!!!!! 10 minutes due!

Aleks04 [339]

Answer:

Step-by-step explanation:

The slope is 3 because the equation is y=mx+b. If you add in the terms m=3 and b=0. It is y=3x. M is the slope, so the slope is 3!

6 0

3 years ago

Read 2 more answers

Slope intercept form: passes through (1, -3), slope = -1

Zigmanuir [339]

Answer:

y=-x-2

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7 0

3 years ago