Answer:
p(x) = (5x - 1) (x + 4) (x - 2)
Answer:
First, let's define an arithmetic sequence:
In an arithmetic sequence, the difference between any two consecutive terms is always the same.
Then we can write it in a general way as:
aₙ = a₁ + (n - 1)*d
where:
aₙ is the n-th term of the sequence.
d is the constant difference between two consecutive terms.
a₁ is the initial term of our sequence.
Now in this case we know that the first terms of our sequence are:
84, 77, ...
Then we know the initial term of our sequence:
a₁ = 84.
And the value of d can be calculated as:
d = a₂ - a₁ = 77 - 84 = -7
Then the general way of writing this sequence is:
aₙ = 84 + (n - 1)*(-7)
And the recursion relation is:
aₙ = aₙ₋₁ - 7
So for the n-th term, we must subtract 7 of the previous term.
Answer:
A.
![f(x) = \frac{ \sqrt[3]{x} }{5} \: { \bf{and}} \: g(x) = 5 {x}^{3}](https://tex.z-dn.net/?f=f%28x%29%20%3D%20%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7Bx%7D%20%7D%7B5%7D%20%20%5C%3A%20%7B%20%5Cbf%7Band%7D%7D%20%5C%3A%20g%28x%29%20%3D%205%20%7Bx%7D%5E%7B3%7D%20)
Step-by-step explanation:
Consider f(x) as the original function:
![{ \tt{f(x) = \frac{ \sqrt[3]{x} }{5} }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bf%28x%29%20%3D%20%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7Bx%7D%20%7D%7B5%7D%20%7D%7D)
Let the inverse be m:
![{ \tt{g(x) = f {}^{ - 1} (x) = m}} \\ { \tt{m = \frac{ \sqrt[3]{x} }{5} }} \\ { \tt{5m = \sqrt[3]{x} }} \\ { \tt{x = 5m {}^{3} }} \\ therefore : \\ { \tt{g(x) = 5 {x}^{3} }}](https://tex.z-dn.net/?f=%7B%20%5Ctt%7Bg%28x%29%20%3D%20f%20%7B%7D%5E%7B%20-%201%7D%20%28x%29%20%3D%20m%7D%7D%20%5C%5C%20%7B%20%5Ctt%7Bm%20%3D%20%20%5Cfrac%7B%20%5Csqrt%5B3%5D%7Bx%7D%20%7D%7B5%7D%20%7D%7D%20%5C%5C%20%7B%20%5Ctt%7B5m%20%3D%20%20%5Csqrt%5B3%5D%7Bx%7D%20%7D%7D%20%5C%5C%20%7B%20%5Ctt%7Bx%20%3D%205m%20%7B%7D%5E%7B3%7D%20%7D%7D%20%5C%5C%20therefore%20%3A%20%20%5C%5C%20%7B%20%5Ctt%7Bg%28x%29%20%3D%205%20%7Bx%7D%5E%7B3%7D%20%7D%7D)
The answer you are looking for is the last option, PR and CR form right angles.
Hope this helps
