We are given with
a1 = 2
r = 4
These are components of a geometric series. The first term is 2 and the common ratio is 4. To get the first six terms, we use the formula:
an = a1 r^(n-1)
a1 = 2 (4)^(1-1) = 2
a2 = 2 (4)^(2-1) = 8
a3 = 2 (4)^(3-1) = 32
a4 = 2 (4)^(4-1) = 128
a5 = 2 (4)^(5-1) = 512
a6 = 2 (4)^(6-1) = 2048
Answer:
<u>BC = 3.1666</u>
Step-by-step explanation:
To solve this you need to know that cosine∅ = adjacent/hypotenuse. We already know that hypotenuse = 5 and that ∅ = 70*. By substituting these in you will get cosine 70* = adjacent/5. Evaluate cosine 70* on the calculator and get 0.633... Multiply both sides by 5 and get adjacent is about equal to 3.1666. Because BC is the adjacent side of the triangle, this is the length of BC.
For any right triangle, we can use the Pythagorean Theorem. The Pythagorean Theorem states that for any right triangle, the legs when squared and added together will be equal to the hypotenuse squared.
In mathematical notation:
![a^2 + b^2 = c^2](https://tex.z-dn.net/?f=a%5E2%20%2B%20b%5E2%20%3D%20c%5E2)
Where the variables a and b are the legs and the variable c is the hypotenuse.
Because we know the two side lengths of the triangle, we can solve for the unknown side.
We know the length of one of the legs and the hypotenuse.
Plug in the values.
![10^2 + b^2 = 24^2 \\ \\ 100 + b^2 = 576 \\ \\ b^2 = 476 \\ \\ ](https://tex.z-dn.net/?f=10%5E2%20%2B%20b%5E2%20%3D%2024%5E2%20%5C%5C%20%5C%5C%20%0A100%20%2B%20b%5E2%20%3D%20576%20%5C%5C%20%5C%5C%20%0Ab%5E2%20%3D%20476%20%5C%5C%20%5C%5C%20%0A)
![b = \sqrt{476}](https://tex.z-dn.net/?f=b%20%3D%20%5Csqrt%7B476%7D)
So, the square root of 476 is the unknown length.