Which equation represents the volume of a cone with the same base and height as the cylinder below?

Write an equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the l

mamaluj [8]

The equation in slope-intercept form for the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5 is $y = \frac{3}{4}x - \frac{5}{4}$

Solution:

The slope intercept form is given as:

y = mx + c ----- eqn 1

Where "m" is the slope of line and "c" is the y - intercept

Given that the line that passes through the point ( -1 , -2 ) and is perpendicular to the line − 4 x − 3 y = − 5

Given line is perpendicular to − 4 x − 3 y = − 5

− 4 x − 3 y = − 5

-3y = 4x - 5

3y = -4x + 5

$y = \frac{-4x}{3} + \frac{5}{3}$

On comparing the above equation with eqn 1, we get,

$m = \frac{-4}{3}$

We know that product of slope of a line and slope of line perpendicular to it is -1

$\frac{-4}{3} \times \text{ slope of line perpendicular to it}= -1\\\\\text{ slope of line perpendicular to it} = \frac{3}{4}$

Given point is (-1, -2)

Now we have to find the equation of line passing through (-1, -2) with slope $m = \frac{3}{4}$

Substitute (x, y) = (-1, -2) and m = 3/4 in eqn 1

$-2 = \frac{3}{4}(-1) + c\\\\-2 = \frac{-3}{4} + c\\\\c = - 2 + \frac{3}{4}\\\\c = \frac{-5}{4}$

$\text{ substitute } c = \frac{-5}{4} \text{ and } m = \frac{3}{4} \text{ in eqn 1}$

$y = \frac{3}{4} \times x + \frac{-5}{4}\\\\y = \frac{3}{4}x - \frac{5}{4}$

Thus the required equation of line is found

8 0

2 years ago

Find the length of the arc shown in red. Leave your answer in terms of .

docker41 [41]

Answer:

red segment = 25.12 ft

Step-by-step explanation:

circumference of full circle = (3.14)(24) = 75.36 ft

semi circle = 75.36/2 = 37.68 ft

60° segment = (60/360)(75.36) = 12.56 ft

red segment = 37.68 - 12.56 = 25.12 ft

8 0

3 years ago

Write the number seven and one - third as a decimal rounded to the nearest hundredth

bagirrra123 [75]

Well you know you keep the 7. 1/3 well you see it as .3333 so just go 7.33 because 7.333 and since it's a 3 you keep it.

4 0

3 years ago

Read 2 more answers

How would I simplify number 3) ?

Anna [14]

You wouldn’t because 3 is the base number and cannot be simplified anymore

6 0

2 years ago

Read 2 more answers

Is the mean age at which American children learn to walk less than 15 months? A study of 40 American children found a mean walki

Sonbull [250]

Answer:

We define the random variable X as the walking age and we are interested if American children learn to walk less than 15 months so then that would be the alternative hypothesis and the complement would be the null hypothesis.

Null hypothesis: $\mu \geq 15$

Alternative hypothesis: $\mu$

And for this case the best answer would be:

H 0 : μ ≥ 15 vs. Ha : μ < 15