Answer:
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Answer:
To satisfy the hypotheses of the Mean Value Theorem a function must be continuous in the closed interval and differentiable in the open interval.
Step-by-step explanation:
As f(x)=2x3−3x+1 is a polynomial, it is continuous and has continuous derivatives of all orders for all real x, so it certainly satisfies the hypotheses of the theorem.
To find the value of c, calculate the derivative of f(x) and state the equality of the Mean Value Theorem:
dfdx=4x−3
f(b)−f(a)b−a=f'(c)
f(x)x=0=1
f(x)x=2=3
Hence:
3−12=4c−3
and c=1.
a. The first variable is x and the second variable is y.
b. The equations are
and 
Step-by-step explanation:
Step 1:
The first step is to define the variables. The variables can be any two symbols, letters, characters, etc.
Here let the first variable be x and the let the second variable be y.
So the variables are defined as x and y.
Step 2:
The sum of the given variables is 12.
The first variable + the second variable = 12,

The difference between the two variables is 4.
The first variable - the second variable = 4.

Step 3:
If we add both the equations we get,
and 
x = 8 and y = 4.
The first one is 12,and the second 24....dont worry about marking me as brainliest just thank me lol
XY = 17.
Because YW is a perpendicular bisector, we can say that TW and WZ are both equal to 3. It tells us that XZ is 12, so that means that XW must be 12+3 which equals 15.
It also tells us that YW is 8. So we can use the Pythagorean Theorem to find the hypotenuse of Triangle XWY. Thus,

To solve this equation, square and add both of the terms on the right like this:

And then take the square root of both sides. Your final answer should be:
XY = 17.