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melamori03 [73]
3 years ago
5

Determine whether each question below is a statistical question. Write "yes" or "no" in the spaces provided.

Mathematics
1 answer:
nikdorinn [45]3 years ago
7 0

Answer:

a yes

b no

c no

d yes

e yes

f no

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Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a)
Anna35 [415]

Rolle's Theorem does not apply to the function because there are points on the interval (a,b) where f is not differentiable.

Given the function is f(x)=\sqrt{(2-x^{\frac{2}{3}})^{3}}  and the Rolle's Theorem does not apply to the function.

Rolle's theorem is used to determine if a function is continuous and also differentiable.

The condition for Rolle's theorem to be true as:

  • f(a)=f(b)
  • f(x) must be continuous in [a,b].
  • f(x) must be differentiable in (a,b).

To apply the Rolle’s Theorem we need to have function that is differentiable on the given open interval.

If we look closely at the given function we can see that the first derivative of the given function is:

\begin{aligned}f(x)&=\sqrt{(2-x^{\frac{2}{3}})^3}\\ f(x)&=(2-x^{\frac{2}{3}})^{\frac{3}{2}}\\ f'(x)&=\frac{3}{2}(2-x^{\frac{2}{3}})^{\frac{1}{2}}\cdot \frac{2}{3}\cdot (-x)^{\frac{1}{3}}\\ f'(x)&=\frac{-\sqrt{2-x^{\frac{2}{3}}}}{\sqrt[3]{x}}\end

From this point of view we can see that the given function is not defined for x=0.

Hence, all the assumptions are not satisfied we can reach a conclusion that we cannot apply the Rolle's Theorem.

Learn more about Rolle's Theorem from here brainly.com/question/12279222

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8 0
2 years ago
Let 40 x 55 = n. Which of the choices shown is also equal to n?
labwork [276]
D) (10 x 55) + (10 x 55) + (10 x 55) + (10 x 55)

use distributive rule to factor out 55:
55 (10+10+10+10) = 55×40
5 0
3 years ago
Polar form of (x+6)^2 +y^2=36
Sindrei [870]

Answer:

  r = -12cos(θ)

Step-by-step explanation:

The usual translation can be used:

  • x = r·cos(θ)
  • y = r·sin(θ)

Putting these relationships into the formula, we have ...

  (r·cos(θ) +6)² +(r·sin(θ))² = 36

  r²·cos(θ)² +12r·cos(θ) +36 +r²·sin(θ)² = 36

  r² +12r·cos(θ) = 0 . . . . subtract 36, use the trig identity cos²+sin²=1

  r(r +12cos(θ)) = 0

This has two solutions for r:

  r = 0 . . . . . . . . a point at the origin

  r = -12cos(θ) . . . the circle of interest

4 0
3 years ago
List all prime numbers between 27 and 35.​
LiRa [457]

Answer:

29 and 31 are the only primes.

5 0
3 years ago
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What is the answer to the following <br>-1+8=​
GenaCL600 [577]

Answer:

Step-by-step explanation:

-1+8=7

8 0
2 years ago
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