Answer:
12.12ft
Step-by-step explanation:
14² = 7² + x²
x² = 14² - 7²
x² = 196 - 49
x² = 147
x = √147
x = 12.12ft
All the components in the state vector need to sum to 1. You're given that component corresponding to state 1 is 0.2, and that the component for state 3 is 0.
That leaves states 2 and 4, for which you're told that the component for state 2 is four times as large. If

is the component for state

, then you have

which means

. So the state vector is

.
Answer:

Step-by-step explanation:
Given



Required
Determine the measure of side XY
To do this, we make use of sine law. This is as follows:

In this case:

Cross Multiply


Make XY the subject



-- <em>approximated</em>
Answer:
-6 1/8
Step-by-step explanation:
=-7/3 *21/8
=147/24
=-6 3/24
=-6 1/8
We need to find two numbers that multiply to 24 (last coefficient) and add to 10 (middle coefficient). Through trial and error, the two values are 6 and 4
6 + 4 = 10
6*4 = 24
So we can break up the 10ab into 6ab+4ab and then use factor by grouping
a^2 + 10ab + 24b^2
a^2 + 6ab + 4ab + 24b^2
(a^2+6ab) + (4ab+24b^2)
a(a+6b) + 4b(a+6b)
(a+4b)(a+6b)
Therefore, the original expression factors completely to (a+4b)(a+6b)