8x-5x+7y-4y+6z-3z
3x+3y+3z
Answer:
The angle between them = 52.1°
Step-by-step explanation:
∵ The position vector of the first point is ![\left[\begin{array}{ccc}1\\5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%5C%5C5%5Cend%7Barray%7D%5Cright%5D)
∵ The position vector of the second point is ![\left[\begin{array}{ccc}6\\3\\\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D6%5C%5C3%5C%5C%5Cend%7Barray%7D%5Cright%5D)
∵ The magnitude of the first = √(1²+5²) = √26
∵ The magnitude of the second = √(6²+3²) = √45
∵ The scalar product of them = (1 × 6) + (5 × 3) = 6 + 15 = 21
∵ cosФ = scalar product/(magnitude 1st × magnitude 2nd)
∴ cosФ = 21/(√26 × √45) = 0.61394
∴ Ф = 52.1°
Answer: 114
Step-by-step explanation:
Plug in the numbers. 5*5+2*5*8/2*2+3*3=25+80+9=114
Answer:
x = 12.48
Step-by-step explanation:
Simplifying
12(x + -13) = 13(12 + -1x)
Reorder the terms:
12(-13 + x) = 13(12 + -1x)
(-13 * 12 + x * 12) = 13(12 + -1x)
(-156 + 12x) = 13(12 + -1x)
-156 + 12x = (12 * 13 + -1x * 13)
-156 + 12x = (156 + -13x)
Solving
-156 + 12x = 156 + -13x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '13x' to each side of the equation.
-156 + 12x + 13x = 156 + -13x + 13x
Combine like terms: 12x + 13x = 25x
-156 + 25x = 156 + -13x + 13x
Combine like terms: -13x + 13x = 0
-156 + 25x = 156 + 0
-156 + 25x = 156
Add '156' to each side of the equation.
-156 + 156 + 25x = 156 + 156
Combine like terms: -156 + 156 = 0
0 + 25x = 156 + 156
25x = 156 + 156
Combine like terms: 156 + 156 = 312
25x = 312
Divide each side by '25'.
x = 12.48
Simplifying
x = 12.48
Answer:
35.15
Step-by-step explanation:
There are 60 seconds in a minute so you divide 2,109 by 60 to get 35.15