Answer:
Step-by-step explanation:
Attached above
Answer:
Step-by-step explanation:
r = 8 in
h = 5 in
Volume of cylinder = πr²h
= π * 8 * 8* 5
= 320π in³
There are 2 possibilities for where A can be: one where C is 30° (and A is 60°) and another where C is 60° (and A is 30°). Since it's not specified, we can find both.
30°:
drawing the triangle on a graph, you can see that point C is 4 units above point B, so we know that one side of the triangle is 4. Once we find the other "leg" of the triangle (the one that's parallel to the x-axis), we can just add that value to B to find the x coordinate of A.
If angle C is 30°, using the side ratios of a 30-60-90 triangle, that side is "a√3", and the side we're looking for is a. So, to find a, we just divide 4 by √3. In that case, point A is 4/(√3) units to the right of -2√3. We can rationalize 4/(√3) like this:
(4√3)/3
and then add that to 2√3:
(4√3)/3 + -2√3
(4√3)/3 + (-6√3)/3 = (-2√3)/3
We know that the x-coordinate of A is (-2√3)/3, and the y-coordinate is -1 because B is a right angle and we're just moving horizontally. So, if C is 30° and A is 60°, point A is at ((-2√3)/3, -1).
60°:
in this case, the leg we know is "a" and the leg we're looking for is "a√3". So, we can multiply 4 by √3 to get the distance from B:
4 x √3 = 4√3
4√3 + -2√3 = 2√3
So the x-coordinate of A here is 2√3, and the y-coordinate is still -1: (2√3, -1).
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Answer:
x = 7
General Formulas and Concepts:
Order of Operations: BPEMDAS
Step-by-Step Explanation:
Step 1: Define
5(x - 3) = 2(x + 3)
Step 2: Solve for x
1. Distribute: 5x - 15 = 2x + 6
2. Subtract 2x on both sides: 3x - 15 = 6
3. Add 15 on both sides: 3x = 21
4. Divide both sides by 3: x = 7
