Answer:
See Below.
Step-by-step explanation:
Problem A)
We have:
When in doubt, convert all reciprocal trig functions and tangent into terms of sine and cosine.
So, let cscθ = 1/sinθ and tanθ = sinθ/cosθ. Hence:
Cancel:
Let 1/cosθ = secθ:
From the Pythagorean Identity, we know that tan²θ + 1 = sec²θ. Hence, sec²θ - 1 = tan²θ:
Problem B)
We have:
Factor out a sine:
From the Pythagorean Identity, sin²θ + cos²θ = 1. Hence, sin²θ = 1 - cos²θ:
Distribute:
Problem C)
We have:
Recall that cos2θ = cos²θ - sin²θ and that sin2θ = 2sinθcosθ. Hence:
From the Pythagorean Identity, sin²θ + cos²θ = 1 so cos²θ = 1 - sin²θ:
Cancel:
By definition:
4 goes into 4 once, and then into 16 4 times. Making the final answer 1/4
I think its D <em>(or #4 - He Should use the mean because there are no outliers that affect the mean)</em> because the Median would be $175,000 but the Mean would be $638,400. It's honestly almost up to you.
Use the Pyth. Thm. to calculate the length of MO:
6^2 + 8^2 = |MO| = 36 + 64 = 100. Therefore, |MO| = 10.
In linear algebra, the rank of a matrix
A
A is the dimension of the vector space generated (or spanned) by its columns.[1] This corresponds to the maximal number of linearly independent columns of
A
A. This, in turn, is identical to the dimension of the vector space spanned by its rows.[2] Rank is thus a measure of the "nondegenerateness" of the system of linear equations and linear transformation encoded by
A
A. There are multiple equivalent definitions of rank. A matrix's rank is one of its most fundamental characteristics.
The rank is commonly denoted by
rank
(
A
)
{\displaystyle \operatorname {rank} (A)} or
rk
(
A
)
{\displaystyle \operatorname {rk} (A)}; sometimes the parentheses are not written, as in
rank
A
{\displaystyle \operatorname {rank} A}.
