A 45° angle turns through what fraction of a circle

Which equation represents the line that is parallel to segment RS in the triangle below and passes through point T?

mestny [16]

Answer:

$y = \frac{1}{2}x +4$

Step-by-step explanation:

Given:

$R = (0,0)$

$S= (8,4)$

$T = (-2,3)$

First, we have that the line is parallel to RS.

This means that the line has the same slope as RS and the slope of RS is calculated as follows:

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4-0}{8-0}$

$m = \frac{4}{8}$

$m = \frac{1}{2}$

So, the line has a slope of $m = \frac{1}{2}$

Next, we have that the line passes through $T = (-2,3)$ .

The equation of the line is then calculated using the following formula

$y - y_1 = m(x - x_1)$

$y - 3 = \frac{1}{2}(x - (-2))$

$y - 3 = \frac{1}{2}(x +2)$

Open bracket

$y - 3 = \frac{1}{2}x +1$

Make y the subject

$y = \frac{1}{2}x +1+3$

$y = \frac{1}{2}x +4$

8 0

3 years ago

A carpenter worked for 4 days to finish a repair job. She charged $825 for 15 hours plus $278 for materials. What is the carpent

harina [27]

29. A carpenter worked for 4 days to finish a repair job. She charged $825 for 15 hours plus $278 for materials. What is the carpenter's rate per hour? Let’s start solving: => 825 dollars + 278 dollars = 1 103 dollars is the total payment a carpenter have received => 15 hours is the total hours he worked => 1 103 / 15 = 73.5 dollars per hour. This is already including the material or equipment fee.

3 0

4 years ago

Read 2 more answers

What is the correct substitution? evaluate. 3m when m = -9 and n = -2

Vinvika [58]

Hi my name is Vanessa i'm Boribaby. I just wanted to let you know that answers A and C are the exact same thing.

I think I know your answer.... if any of your answers say 3(-9)(-2) then that is your answer.

Please know that the percentage of my answer is 50/50. I hope this help!!!! Good luck!!!!

8 0

3 years ago

Ex 7) Imagine a mile-long bar of metal such as the rail along railroad tracks. Suppose that the rail is anchored on both ends an

Fantom [35]

9514 1404 393

Answer:

about 44.5 feet

Step-by-step explanation:

We can write relations for the height of the rail as a function of initial length and expanded length, but the solution cannot be found algebraically. A graphical solution or iterative solution is possible.

Referring to the figure in the second attachment, we can write a relation between the angle value α and the height of the circular arc as ...

h = c·tan(α) . . . . . . where c = half the initial rail length

Then the length of the expanded rail is ...

s = r(2α) = (c/sin(2α)(2α) . . . . . . where s = half the expanded rail length

Rearranging this last equation, we have ...

sin(2α)/(2α) = c/s

It is this equation that must be solved iteratively. We find the solution to be ...

α ≈ 0.0168538794049 radians

So, the height of the circular arc is ...

h = 2640.5·tan(0.0168538794049) ≈ 44.4984550191 . . . feet

The rail will bow upward by about 44.5 feet.

_____

<em>Additional comments</em>

Note that s and c in the diagram are half the lengths of the arc and the chord, respectively. The ratio of half-lengths is the same as the ratio of full lengths: c/s = 2640/2640.5 = 5280/5281.

We don't know the precise shape the arc will take, but we suspect is is not a circular arc. It seems likely to be a catenary, or something similar.

__

We used Newton's method iteration to refine the estimate of the angle from that shown on the graph. The iterator used is x' = x -f(x)/f'(x), where x' is the next guess based on the previous guess of x. Only a few iterations are required obtain an angle value to full calculator precision.

3 0

3 years ago

How you explain the can you compare how you feel right now with how you felt before we started with the relaxation activity? On

DochEvi [55]

Answer:

I would rate my feelings 4 on a scale of 5

Step-by-step explanation:

Before exercising I usually feel low and heavily laden with overwhelming thoughts and the feeling doesn't seem to leave except in engage in some form of activities that will take my time and consciousness of time.

Like exercising does take time and it's very engaging one wouldn't know the passage of time while doing some physical task.

It's always relaxing after engaging in physical exercise,I also see it as physical therapy for mental health.

8 0

3 years ago