Factor the following expression
20u^5v8-24u^3v^2w^9
To factor the expression 20u^5v^8 - 24u^3v^2w^9, we can first look for common factors among the terms.
The common factors among the terms are:
- 4u^3v^2, which can be factored out of both terms.
Factoring out 4u^3v^2, we get:
4u^3v^2(5u^2v^6 - 6w^9)
Thus, the expression 20u^5v^8 - 24u^3v^2w^9 can be factored as 4u^3v^2(5u^2v^6 - 6w^9).
Graph the parabola y=2x^2+4x+4
Plot the 5 points
1)the vertex
2)two points to the left of the vertex
3)two points to the right of the vertex
To graph the parabola y = 2x^2 + 4x + 4, we can start by finding the vertex.
The x-coordinate of the vertex can be found using the formula x = -b/2a, where a = 2 and b = 4 in this case.
x = -4/2(2) = -1
Substituting x = -1 into the equation, we can find the y-coordinate of the vertex.
y = 2(-1)^2 + 4(-1) + 4 = 2 - 4 + 4 = 2
Therefore, the vertex is (-1, 2).
To find two points to the left of the vertex, we can substitute x = -2 and x = -3 into the equation.
For x = -2, y = 2(-2)^2 + 4(-2) + 4 = 8 - 8 + 4 = 4
For x = -3, y = 2(-3)^2 + 4(-3) + 4 = 18 - 12 + 4 = 10
So the two points to the left of the vertex are (-2, 4) and (-3, 10).
To find two points to the right of the vertex, we can substitute x = 0 and x = 1 into the equation.
For x = 0, y = 2(0)^2 + 4(0) + 4 = 0 + 0 + 4 = 4
For x = 1, y = 2(1)^2 + 4(1) + 4 = 2 + 4 + 4 = 10
So the two points to the right of the vertex are (0, 4) and (1, 10).
Now we can plot these points on a graph:
The vertex (-1, 2) is located at the minimum point of the parabola.
Two points to the left of the vertex are (-2, 4) and (-3, 10).
Two points to the right of the vertex are (0, 4) and (1, 10).
The graph of the parabola y = 2x^2 + 4x + 4 will have a "U" shape and will pass through these points.
Simplify secxcotx use algebra and fundamental trigonometric identities
To simplify sec(x) * cot(x), we can use the fundamental trigonometric identities.
We know that:
sec(x) = 1/cos(x)
cot(x) = cos(x)/sin(x)
Substituting these values into sec(x) * cot(x), we get:
(1/cos(x)) * (cos(x)/sin(x))
The cosine terms cancel out, leaving us with:
1/sin(x)
Recall that the reciprocal of sine is cosecant, so we can rewrite 1/sin(x) as:
cosec(x)
Therefore, sec(x) * cot(x) simplifies to:
cosec(x)
To factor the expression 20u^5v^8 - 24u^3v^2w^9, we can start by looking for common factors among the terms:
The common factors among the terms are 4u^3v^2:
20u^5v^8 - 24u^3v^2w^9 = 4u^3v^2(5u^2v^6 - 6w^9)
So the factored form of the expression is 4u^3v^2(5u^2v^6 - 6w^9).
To factor the expression 20u^5v^8 - 24u^3v^2w^9, we can first look for any common factors. In this case, we can see that 4 is a common factor between 20 and 24, u^3 is a common factor between u^5 and u^3, and v^2 is a common factor between v^8 and v^2. Let's factor out these common terms:
20u^5v^8 - 24u^3v^2w^9
= 4u^3v^2(5u^2v^6 - 6w^9)
Now we have factored out the common terms. The expression inside the parentheses cannot be further factored because the terms do not have any common factors. Therefore, the factored form of the original expression is:
4u^3v^2(5u^2v^6 - 6w^9)