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2 years ago

What is the equation of the line that is parallel to the line y = -1/3x+4 and passes through the point (6,5)

Mathematics

1 answer:

inn [45]2 years ago

3 0

Answer:

$\sf y =\dfrac{-1}{3}x + 7$

Step-by-step explanation:

Equation of line: y =mx +b

Here, m is the slope and b is the y-intercept.

Parallel lines have same slope.

$\sf y =\dfrac{-1}{3}x + 4$

So, the slope of the required line = -1/3

Equation of the required line:

$\sf y =\dfrac{-1}{3}x + b$

Point(6,5) goes through the line. substitute x = 6 and y =5 in the above equation and then we can find the value of y-intercept 'b'

$\sf 5 =\dfrac{-1}{3}*6 +b\\\\ 5 = -2 + b\\\\5+2 = b\\\\\boxed{b = 7}$

Equation of the require line:

$\sf \boxed{\bf y =\dfrac{-1}{3}x+7}$

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If the equal sides of an isosceles right triangle measure 12 units then the measure of the hypotenuse is

Nata [24]

Answer:

16.97056275

Step-by-step explanation:

12 squared + 12 squared = 288

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7 0

3 years ago

Write the equation of the line in fully simplified slope-intercept form. y intercept = -2 (GIVE EXPLANATION)

nekit [7.7K]

Answer:

See Below:

Step-by-step explanation:

So, first of all. to find the equation of the line, the equation has to be in $y=mx+b$ form. In this for the following are:

$m$ is the slope of the line
$b$ is the y intercept

Solving

So, first of all, to find the equation of the line, we can get two points from the line, you can pick any points you want, but for this case, I will be using (0,-2) and (-2,0).

To solve for the slope, we can use rise over run to find the equation.

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Upon inserting our points into the equation, we get a slope of -1.

$\frac{0-(-2)}{-2-0}=\frac{2}{-2}=-1$

Creating The Equation

To create the equation in $y=mx+b$ form, we need to know what the intercept and the slope are, for which we solved above. We can now put in the things we found to get our final equation.

$y=-1x-2$

We know the slope has to be -1 as we solved for that, and because the line is decending downwards, we can interpret the slope as down 1 right 1.

We know that b is -2 because the y intercept is -2 and b is equal to the y intercept. Therefore the b cation is -2.

Cheers!

5 0

3 years ago

Use the divergence theorem to calculate the surface integral s f · ds; that is, calculate the flux of f across s. f(x, y, z) = x

valkas [14]

$\mathbf f(x,y,z)=x^4\,\mathbf i-x^3z^2\,\mathbf j+4xy^2z\,\mathbf k$
$\mathrm{div}(\mathbf f)=\dfrac{\partial(x^4)}{\partial x}+\dfrac{\partial(-x^3z^2)}{\partial y}+\dfrac{\partial(4xy^2z)}{\partial z}=4x^3+0+4xy^2=4x(x^2+y^2)$

Let $\mathcal D$ be the region whose boundary is $\mathcal S$ . Then by the divergence theorem,

$\displaystyle\iint_{\mathcal S}\mathbf f\cdot\mathrm d\mathbf S=\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV$

Convert to cylindrical coordinates, setting

$x=r\cos\theta$
$y=r\sin\theta$

and keeping $z$ as is. Then the volume element becomes

$\mathrm dV=r\,\mathrm dr\,\mathrm d\theta\,\mathrm dz$

and the integral is

$\displaystyle\iiint_{\mathcal D}4x(x^2+y^2)\,\mathrm dV=\int_{\theta=0}^{\theta=2\pi}\int_{r=0}^{r=1}\int_{z=0}^{z=r\cos\theta+7}4r\cos\theta\cdot r^2\cdot r\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\displaystyle4\iiint_{\mathcal D}r^4\cos\theta\,\mathrm dz\,\mathrm dr\,\mathrm d\theta$
$=\dfrac{2\pi}3$

4 0

4 years ago

A two-word phrase used to show division in a word problem.

fomenos

Division phrases:
-divided by
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5 0

3 years ago

Read 2 more answers

What is the value of x?<br> 4 cm<br> 32 cm<br> 40 cm

Luba_88 [7]

Answer:

x=5