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2 years ago

Find the equation of a line that passes through the given points(-6,-5) and (6,-13)

Mathematics

2 answers:

NeTakaya2 years ago

5 0

Answer:

y+5=-3/4(x+6)

or in slope intercept

y= -3/4x-38/4

Step-by-step explanation:

To write the equation of a line we must have a slope and a point. To find the slope we use the slope formula and substitute (x,y) points in it as shown below:

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{-5--13}{-6-6}=\frac{-5+13}{-6+-6}=\frac{8}{-12}=\frac{-3}{4}$

Now that we have the slope, plug in the slope and choose one point to plug into the point slope formula. Use the point-slope form to write the equation, then simplify and convert into the slope intercept form.

(y--5)=-3/4(x--6)

y+5=-3/4(x+6)

y+5=-3/4x-18/4

y=-3/4x-18/4-20/4

y= -3/4x-38/4

Evgen [1.6K]2 years ago

4 0

Hello there,

Find the equation of a line that passes through the given points

(-6,-5) and (6,-13)

Answer: -3/4x-38/4

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At what points does the curve r(t) = ti + (5t − t2)k intersect the paraboloid z = x2 + y2? (if an answer does not exist, enter d

Sergeu [11.5K]

Answer : curve r(t) = t i + (2t - t 2)k intersect the paraboloid z = x 2 + y 2

By the equation of r(t), x = t, y = 0, and z = $5t - t^{2}$ .

Thus, z = $x^{2} + y^{2}$

on solving we get,

$5t - t^{2}$ = $t^{2} + 0^{2}$

Now, we can solve for t

$t^{2} + t^{2} -5t$ = 0

So, $2t^2 - 5t$ = 0

2t ( t - 5/2) = 0

t = 0 , t = 5

plugging these values in t = 0 into r(t)

r(0) = <0 , 0 , 0>

r(5) = < 5, 0 , 25 >

6 0

2 years ago

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A paint machine dispenses dye into paint cans to create different shades of paint. The amount of dye dispensed into a can is kno

Anton [14]

Answer:

4.464 ml

Step-by-step explanation:

Given that:

mean (μ) = 5 mm, standard deviation (σ) = 0.4 ml

The z score is a score in statistics used to determine by how many standard deviation the raw score is above or below the mean. If the z score is positive then the raw score is above the mean and if the z score is negative then the raw score is below the mean It is given by:

$z=\frac{x-\mu}{\sigma}$