The LCM is the lowest number that is a multiple of all three numbers.
First, list the multiples of each number
8: 8, 16, 24, 32,40 48, 56, 64, 72, 80, 88, 96, 104, 112, 120
10: 10, 20, 30 40, 50, 60, 70, 80, 90, 100, 110, 120
12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120
The LCM is 120 because there is no lower number that is a multiple of all three numbers.
Hope this helped!
We are given an angle of elevation of 2 degrees and distance in the x axis of 5280 feet and we are asked in the problem to determine the height of the building. We use the tangent function to determine the height: that is tan 2 = h / 5280; h is equal then to 184 ft.
<span>Simplifying
(6a + -8b)(6a + 8b) = 0
Multiply (6a + -8b) * (6a + 8b)
(6a * (6a + 8b) + -8b * (6a + 8b)) = 0
((6a * 6a + 8b * 6a) + -8b * (6a + 8b)) = 0
Reorder the terms:
((48ab + 36a2) + -8b * (6a + 8b)) = 0
((48ab + 36a2) + -8b * (6a + 8b)) = 0
(48ab + 36a2 + (6a * -8b + 8b * -8b)) = 0
(48ab + 36a2 + (-48ab + -64b2)) = 0
Reorder the terms:
(48ab + -48ab + 36a2 + -64b2) = 0
Combine like terms: 48ab + -48ab = 0
(0 + 36a2 + -64b2) = 0
(36a2 + -64b2) = 0
Solving
36a2 + -64b2 = 0
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '64b2' to each side of the equation.
36a2 + -64b2 + 64b2 = 0 + 64b2
Combine like terms: -64b2 + 64b2 = 0
36a2 + 0 = 0 + 64b2
36a2 = 0 + 64b2
Remove the zero:
36a2 = 64b2
Divide each side by '36'.
a2 = 1.777777778b2
Simplifying
a2 = 1.777777778b2
Take the square root of each side:
a = {-1.333333333b, 1.333333333b}</span>
Answer:
![\boxed{4 \sqrt[8]{ {d}^{3} } }](https://tex.z-dn.net/?f=%20%5Cboxed%7B4%20%5Csqrt%5B8%5D%7B%20%7Bd%7D%5E%7B3%7D%20%7D%20%7D%20)
Step-by-step explanation:
![= > 4 {d}^{ \frac{3}{8} } \\ \\ = > 4({d}^{3 \times \frac{1}{8} }) \\ \\ = > 4( {d}^{3} \times {d}^{ \frac{1}{8} } ) \\ \\ = > 4( {d}^{3} \times \sqrt[8]{d} ) \\ \\ = > 4 \sqrt[8]{ {d}^{3} }](https://tex.z-dn.net/?f=%20%3D%20%20%3E%204%20%7Bd%7D%5E%7B%20%5Cfrac%7B3%7D%7B8%7D%20%7D%20%20%20%5C%5C%20%20%5C%5C%20%3D%20%20%20%3E%204%28%7Bd%7D%5E%7B3%20%5Ctimes%20%20%5Cfrac%7B1%7D%7B8%7D%20%7D%29%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%204%28%20%7Bd%7D%5E%7B3%7D%20%20%5Ctimes%20%20%20%7Bd%7D%5E%7B%20%5Cfrac%7B1%7D%7B8%7D%20%7D%20%29%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%204%28%20%7Bd%7D%5E%7B3%7D%20%20%5Ctimes%20%20%5Csqrt%5B8%5D%7Bd%7D%20%29%20%5C%5C%20%20%5C%5C%20%20%3D%20%20%3E%204%20%20%5Csqrt%5B8%5D%7B%20%7Bd%7D%5E%7B3%7D%20%7D%20)
