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.
Answer:
The probability that Jones is lying is 6/7
Step-by-step explanation:
First we will list out 2 different cases when the outcome is a lie
1.probability that Jones tells lies is = 0.6 and probability that dalgiliesh analyses it correctly is 0.8
So the probability that dagliesh correctly analyses that he is telling lies is 0.8*0.6=0.48
2.Probability that Jones tells truth is 0.4 and if dagliesh analyses it incorrectly (which has a probability of 0.2) the outcome(as analysed by dagiliesh) is a lie
So probability that dagliesh analyses Jones truth as a lie is 0.2*.0.4=0.08
Total probability of outcome being a lie is 0.48+0.08=0.56
But we need the probability of Jones actually saying a lie which is nothing but 0.48/0.56= 6/7
Answer:
1.2 meters.
Step-by-step explanation:
Length of pen = 2x meters
width of pen = x meters
shape of pen is rectangular
we know that area of rectangle is given by length * width
Thus, area of the pen is x*2x = 
It is also given that area of pen is 2.8 square meters.
Equating numerical value of area with area in terms of x, we have
Thus value of x is 1.2 meters.
Answer:
Please see the attached file for the complete answer.
Step-by-step explanation:
