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:
x = 23 degrees
Step-by-step explanation:
sin theta = opposite side/ hypotenuse
sin x= 9/23
Take the arcsin of each side
arcsin( sinx) = arcsin (9/23)
x = arcsin (9/23)
x=23.03568411
Rounding to the nearest degree
x = 23 degrees
X±49
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Cubed square root of 7 or decimal form of ±25.615140
Greetings from Brasil...
According to the statement of the question, we can assemble the following system of equation
X = 7 + 3Y i
X + Y = 75 ii
So, multiplying ii by -1 and adding with i
X = 7 + 3Y
- X - Y = - 75
- Y = 7 + 3Y - 75
4Y = 68
Y = 17
for X we will use ii:
X + Y = 75
X + 17 = 75
X = 58
The smaller number is: 17
7 squared = 49 and 9 squared= 81 add up 49 and 81 and you get 130
