Answer:
Forces in our Universe
Step-by-step explanation:
a)
First of all we have,
and,
We need to define a function that allows us to find said change based on r, so one of the functions that shows that change is,
That is,
For this case F is a conservative field and the line integral is independent of the path. Thus, defining 
and 
. So the amount of work on the movement of the object from P1 to P2 is,
2) The gravitational force field is given by,
The maximum distance from the earth to the sun is 
km and the minimum distance is 
km. The mass values of the bodies are given by m = 
kg, M = 
kg and the constant G is 
In this way we raise the problem like this,
If you would like to simplify <span>4 + (-3) - 2 * (-6), you can do this using the following steps:
</span><span>4 + (-3) - 2 * (-6) = 4 - 3 + 2 * 6 = 1 + 12 = 13
</span>
The correct result would be 13.
Answer:
x=36
Step-by-step explanation:
The 2 angles, ∠EAF and ∠FAB are on a straight line. This means they are supplementary, and add to 180 degrees.
So,
∠EAF +∠FAB =180
We know that ∠EAF is 3x and ∠FAB is 2x, so we can substitute them in
3x+2x=180
Combine like terms
5x=180
Divide by 5 on both sides
x=36
So, x=36 degrees, or the last choice
Answer:
The functions are inverses; f(g(x)) = x ⇒ answer D
⇒ answer D
Step-by-step explanation:
* <em>Lets explain how to find the inverse of a function</em>
- Let f(x) = y
- Exchange x and y
- Solve to find the new y
- The new y = 
* <em>Lets use these steps to solve the problems</em>
∵ 
∵ f(x) = y
∴ 
- Exchange x and y
∴ 
- Square the two sides
∴ x² = y - 3
- Add 3 to both sides
∴ x² + 3 = y
- Change y by
∴ 
∵ g(x) = x² + 3
∴ 
∴ <u><em>The functions are inverses to each other</em></u>
* <em>Now lets find f(g(x))</em>
- To find f(g(x)) substitute x in f(x) by g(x)
∵
∵ g(x) = x² + 3
∴ 
∴ <u><em>f(g(x)) = x</em></u>
∴ The functions are inverses; f(g(x)) = x
* <em>Lets find the inverse of h(x)</em>
∵ h(x) = 3x² - 1 where x ≥ 0
- Let h(x) = y
∴ y = 3x² - 1
- Exchange x and y
∴ x = 3y² - 1
- Add 1 to both sides
∴ x + 1 = 3y²
- Divide both sides by 3
∴ 
- Take √ for both sides
∴ ± 
∵ x ≥ 0
∴ We will chose the positive value of the square root
∴
- replace y by 
∴
The first and last choices are true.
