Answer:
![\left[\begin{array}{c}-\frac{8}{\sqrt{117} } \\\frac{7}{\sqrt{117} }\\\frac{2}{\sqrt{117} }\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-%5Cfrac%7B8%7D%7B%5Csqrt%7B117%7D%20%7D%20%5C%5C%5Cfrac%7B7%7D%7B%5Csqrt%7B117%7D%20%7D%5C%5C%5Cfrac%7B2%7D%7B%5Csqrt%7B117%7D%20%7D%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
We are required to find a unit vector in the direction of:
![\left[\begin{array}{c}-8\\7\\2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-8%5C%5C7%5C%5C2%5Cend%7Barray%7D%5Cright%5D)
Unit Vector, 
The Modulus of 
=
Therefore, the unit vector of the matrix is given as:
To start this is a ratio, and the goal is to get at least 1 to be a whole number so first lets get the number below 1 to 1.
0.75 : 2 5/16 ---> (x1.3333 on both sides) ---> 1 : 3 1/12.
Next, if needed for your answer, lets get the other number to be a whole number as well. We can do this my multiplying both sides by 12 since the fraction on 3 1/12 is 1/12.
1 : 3 1/12 --> (x12 on both sides) ---> 12 : 37
Your final answer will either be 1 : 3 1/12 or 12 : 37, depending on the formatting expected for your homework assignment.
The domain is all real numbers except -6 and 0. Hence, domain D: {x ∈ ℝ| x ≠ –6, 0}
Hence the range is all real numbers except -3 and 3. Hence, range R: (–∞, –3) ∪ (3, ∞)
Given the following functions:
First we need to get the composite function f(g(x))
Get the domain
The domain the values of x for which the function exists. The function cannot exists at when x = -6 and x = 0
- Hence the domain is all real numbers except -6 and 0. Hence, domain D: {x ∈ ℝ| x ≠ –6, 0}
The range is the value of y for which the function exists. The function cannot exists at when x = -6 and x = 0
- Hence the range is all real numbers except -3 and 3. Hence, range R: (–∞, –3) ∪ (3, ∞)
Learn more here: brainly.com/question/20838649
Answer: F. Initially the pipe leaks at 17 gallons per minute.
Step-by-step explanation:
Given the equation below:
R = 17 + 4t
Where R is the rate of leakage in gallons per minute,
And t is the age of pipe in years.
The rate of leakage at time t = 0 ( initial rate of leakage )
R(0)= 17 + 4(0)
R(0)= 17 gallons per minute.
Therefore the initial rate of leakage is 17gallons per minute
[2+(9x3)]x3
Solve for parentheses
[2+(27)]x3
Brackets are solved before the rest of the equation, but always parentheses first
[29]x3=81
The answer is 81.
Hope this helps, and hope I was the brainliest! :)
