Answer:

Step-by-step explanation:
we are given
sequence is geometric
so, we can use nth term formula

we have


we have to find a9
so, we can plug n=9
we get



Answer:

Step-by-step explanation:
We will use the co-function identity for sine, where:

Since sin(21)=0.358=cos(x). This means that:

Solve for x. Add x to both sides:

Subtract 21 from both sides:

Hence:

(5,-3)(7,3)
slope = (y2 - y1) / (x2 - x1)
slope = (3 - (-3) / (7 - 5) = (3 + 3) / 2 = 6/2 = 3 <==
Answer:
x is approximately 2.220744
Step-by-step explanation:
This can be simplified a little using properties of logarithms, and then solve it by graphing:

So we use a graphing tool to find the intersection point of the graph of
, and the graph of 
Please see attached image for the graph and solution.
The value of x is approximately 2.220744
Assuming that an exponentiation sign is missing, all you need to know is that rational exponents work like this:
![a^{\frac{b}{c}}=\sqrt[c]{a^b}](https://tex.z-dn.net/?f=a%5E%7B%5Cfrac%7Bb%7D%7Bc%7D%7D%3D%5Csqrt%5Bc%5D%7Ba%5Eb%7D)
So, you have

And similarly,
![81^{\frac{7}{4}}=\sqrt[4]{25^7}=\sqrt[4]{(3^4)^7}=3^7](https://tex.z-dn.net/?f=81%5E%7B%5Cfrac%7B7%7D%7B4%7D%7D%3D%5Csqrt%5B4%5D%7B25%5E7%7D%3D%5Csqrt%5B4%5D%7B%283%5E4%29%5E7%7D%3D3%5E7)