What are the domain and range of the exponential function below F(x)=4^x+3
1 answer:
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Answer:
(A) Set A is linearly independent and spans . Set is a basis for
.
Step-by-Step Explanation
<u>Definition (Linear Independence)</u>
A set of vectors is said to be linearly independent if at least one of the vectors can be written as a linear combination of the others. The identity matrix is linearly independent.
<u>Definition (Span of a Set of Vectors)</u>
The Span of a set of vectors is the set of all linear combinations of the vectors.
<u>Definition (A Basis of a Subspace).</u>
A subset B of a vector space V is called a basis if: (1)B is linearly independent, and; (2) B is a spanning set of V.
Given the set of vectors , we are to decide which of the given statements is true:
In Matrix , the circled numbers are the pivots. There are 3 pivots in this case. By the theorem that The Row Rank=Column Rank of a Matrix, the column rank of A is 3. Thus there are 3 linearly independent columns of A and one linearly dependent column.
has a dimension of 3, thus any 3 linearly independent vectors will span it. We conclude thus that the columns of A spans
.
Therefore Set A is linearly independent and spans . Thus it is basis for
.
Answer: The correct options are (1) (5,10), (2) (3,-3), (3) x = -1, (4) , (5) 21s and (6) 0, -1, and 5.
Explanation:
Te standard form of the parabola is,
.....(1)
Where, (h,k) is the vertex of the parabola.
(1)
The given equation is,
Comparing this equation with equation (1),we get,
and
Therefore, the vertex of the graph is (5,10) and the fourth option is correct.
(2)
The given equation is,
To make perfect square add , i.e.,
. Since there is factor 3 outside the parentheses, so subtract three times of 9.
Comparing this equation with equation (1),we get,
and
Therefore, the vertex of the graph is (3,-3) and the fourth option is correct.
(3)
The given equation is
To make perfect square add , i.e.,
. Since there is factor 4 outside the parentheses, so subtract three times of 1.
Comparing this equation with equation (1),we get,
and
The vertex of the equation is (-1,3) so the axis is x=-1 and the correct option is 2.
(4)
The given equation is,
To make perfect square add , i.e.,
.
Therefore, the correct option is 4.
(5)
The given equation is,
It can be written as,
It is a downward parabola. so the maximum height of the function is on its vertex.
The x coordinate of the vertex is,
Therefore, after 21 seconds the projectile reach its maximum height and the correct option is first.
(6)
The given equation is,
Use factoring method to find the factors of the equation.
Equate each factor equal to 0.
Therefore, the zeros of the given equation is 0, -1, 5 and the correct option is 2.
The graphs arey=(1/3)x^2
and y=3
they intersect at x=3
so the limits are x=0 and 3
to rotate it about y=k, minus k from every function
which evaluates to 72/5pi
A is asnwer
and y=3
they intersect at x=3
so the limits are x=0 and 3
to rotate it about y=k, minus k from every function
which evaluates to 72/5pi
A is asnwer