I need help proving a few trigonometric identities.

Find the slope of the line that is (a) parallel and (b) perpendicular to the line through the pair of points.

ddd [48]

Answer:

a) The slope of the line is parallel to the another line m=4

b) The slope of the line is perpendicular to the another line m= $\frac{-1}{4}$

Step-by-step explanation:

Step1:-

Slope of a line :-

If θ is the inclination of a line 'l' then tanθ is called the slope or gradient of the line 'l'.The slope of a line is denoted by m=tanθ

The slope of a line given two points m= $\frac{y_{2}-y_{1} }{x_{2} -x_{1} }$

Parallel lines:-

Two non-vertical lines are parallel if and only if their slopes are parallel

Perpendicular lines:-

Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

Step 2:-

a)The slope of a line when given two points (-1,-4) and (0,0)

$m = \frac{0-(-4)}{0-(-1)} =4$

Two non-vertical lines are parallel if and only if their slopes are parallel

$m_{1} = m_{2}$

Therefore the slope of the line that is parallel to the another line

$m_{1} =m_{2} =4$

Step 3:-

b) Two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other.

$m_{2} = \frac{-1}{m_{1} } \\$

$m_{2} =\frac{-1}{4}$

Therefore the slope of the line is perpendicular to the another line is

$m=\frac{-1}{4}$

3 0

3 years ago

Read 2 more answers

GIVEN THAT TITAN HAS A RADIUS OF 2575 KM WHICH IS COVERED BY 600 KM ATMOSPHERE. WHAT

Ber [7]

Answer:

87.4%

Step-by-step explanation:

The radius to the top of the atmosphere as a fraction of the moon's radius is ...

(2575 +600)/2575 ≈ 1.23301

The ratio of the moon's volume with atmosphere to the moon's volume without is the cube of this, or 1.87456

Then the ratio of the atmosphere's volume to the moon's volume is ...

(1.87456 -1)/1 = 0.87456

Atmospheric haze is about 87.4% of the moon's volume.

_____

We have assumed that the desired ratio is to the solid moon's volume, not the volume of moon and atmosphere together. The latter ratio would be 0.875 to 1.875 or about 46.7%.

3 0

4 years ago

What is the slope of the line that passes through the points (4, -9)(4,−9) and (8, -3) ?(8,−3)? Write your answer in simplest fo

faltersainse [42]

Answer:

$\frac{3}{2}$

Step-by-step explanation:

I am assuming that you mean (4,−9) and (8, -3).

$m=\frac{rise}{run}=\frac{-3+9}{8-4}=\frac{6}{4}=\boxed{\frac{3}{2}}$

Hope this helps.

6 0

3 years ago

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One root of f(x) = x + 10x2 – 25x – 250 is x = -10. What are all the roots of the function? Use the Remainder Theorem.

Natalka [10]

Answer:

-10

-5

5

Step-by-step explanation:

From the answers given, you probably mean f(x) = x^3 + 10x2 – 25x – 250

The Remainder Theorem is going to take a bit to solve.

You have to try the factors of 250. One way to make your life a lot easier is to graph the equation. That will give you the roots.

The graph appears below. Since the y intercept is -250 the graph goes down quite a bit and if you show the y intercept then it will not be easy to see the roots.

However just to get the roots, the graph shows that

x = -10

x = - 5

x = 5

The last answer is the right one. To use the remainder theorem, you could show none of the answers will give 0s except the last one. For example, the second one will give

f((10) = 10^3 + 10*10^2 - 25*10 - 250

f(10) = 1000 + 1000 - 250 - 250

f(10) = 2000 - 500

f(10) = 1500 which is not 0.

==================

f(1) = (1)^3 + 10*(1)^2 - 25(1) - 250

f(1) = 1 + 10 - 25 - 250

f(1) = -264 which again is not zero

3 0

3 years ago

Read 2 more answers

What is the value of 3 in the following numbers 6.13

expeople1 [14]

Answer:

3 hundredths or .03

Step-by-step explanation:

3 0

3 years ago