Answer:
Step-by-step explanation:
We want to solve the equation:
In the interval [0, 2π).
Notice that this is in quadratic form. Namely, by letting u = sin(θ), we acquire:
Factor:
By the Zero Product Property:
Solve for each case:
Back-substitute:
Use the Unit Circle. Hence, our three solutions in the interval [0, 2π) are:
Answer:
Step-by-step explanation:
Domain : Set of all possible input values (x-values) on a graph
Codomain : Set of all possible out values for the input values (y-values) on the graph
Range : Actual output values for the input values (x-values) given on the graph.
Therefore, for the given graph,
Domain : (-∞, ∞)
Codomain : (-∞, 2]
Range : (-∞, 2]
From the given graph every input value there is a image or output value.
Therefore, the given function is onto.
Distance from Supermarket to Bank = 3 miles.
Distance from the Bank to the library = 4 miles.
Distance from the library back to supermarket =
Total Distance = 3 + 4 + 5 = 12 miles.
Answer: 12 miles
Answer:
the first one and the last one
Step-by-step explanation:
Answer:
True
True
False
Step-by-step explanation:
TRUE
If the equation Ax = 0 has only the trivial solution, then A is row equivalent to the n × n identity matrix
Here's why
If the equation Ax = 0 has only the trivial solution the determinant of the matrix is NOT 0 and the matrix is invertible therefore it is row equivalent to the nxn identity matrix.
TRUE
If the columns of A span ℝ^n , then the columns are linearly independent
Here's why
Remember that the rank nullity theorem states that
According to the information given we know that
Therefore you have
and
Which is equivalent to the problem we just solved.
FALSE
If A is an n × n matrix, then the equation Ax = b has at least one solution for each b in ℝ^n
Here's why
Take b as a non null vector and A=0, then Ax = 0 and Ax=b will have no solution.