Answer:
33.49 cubic inches
Step-by-step explanation:
The parent function, f(x) = 5x, has been vertically compressed by a factor of one-half, shifted to the right three units and up
two units.
1 answer:
I'm guessing you want to know what the new function looks like.
Compression takes place when you have a function that constant is between 0 and 1
so f(x) = 1/2 5x We'd best not do any more to it for now because it will be altered by the next two transformations.
You want to shift this to the right two units.
That means f(x-2) will bu put into x on the right. You will get
f(x - 2) = 1/2*5(x - 2)
Finally, we want to go up 2 units. That's done by adding another term on what we have already.
f(x -2) = 1/2 * 5(x - 2) + 2
A line is not a very good example to be showing these transformations. I'll include a graph.
The red line is f(x) = 5x
The blue line is f(x - 2) = 1/2 * 5(x -2) + 2
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<h2>Hello!</h2>
Since there is no additional information, we can assume that the given angles are respect to the horizontal axis (x), so
The answer is:
Magnitude: 95.14 lbs
Direction: 80° respect to the x-axis
<h2>Why?</h2>Since there is no additional information about the given angles, we can assume that both angles are respect to the horizontal axis (x), positive direction to x-axis positive directions (right) and above x-axis.
<h2>Calculations:</h2>100 pounds (lb) force, 50° angle:
50 pounds (lb) force, 160° angle:
So,
For x-axis forces we have:
64.28lbs (positive direction)
-46.98lbs (negative direction)
Then,
(positive direction)
Fox y-axis forces we have:
76.60lbs (positive direction)
17.10 lbs (positive direction)
Then,
(positive direction)
So, we have the two components values of the acting force:
17.3 lbs for the x-axis and 93.7 lbs for the y-axis.
Therefore,
We have to calculate the angle between both resultant force components:
Let's calll it α
So,
Hence, the angle between both resultant force components is 80 °, meaning that the resultant force direction is positive, above the x-axis.
Now we have to calculate the magnitude of the resultant force since the sum of both resultant force components is equal to the hypotenuse of the formed triangle, we have that:
So, we have that:
- Resultant force magnitude is equal to 95.14 lbs
- Direction is 80° respect to the x-axis.
Have a nice day!
I hope this helps you
