What is the distance between the points (12 , -17) and (-12 , -17) in the coordinate plane?

Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = e−4x, [0, 2] Yes, it does not m

Zigmanuir [339]

Answer:

(a) Yes, it does not matter if f is continuous or differentiable; every function satisfies the Mean Value Theorem.

(b) $c =0.51995$

Step-by-step explanation:

Given

$f(x) = e^{-4x};\ [0,2]$

Solving (a); Does the function satisfy M.V.T on the given interval

We have:

$f(x) = e^{-4x};\ [0,2]$

The above function is an exponential function, and it is differentiable and continuous everywhere

Solving (b): The value of c

To do this, we use:

$f'(c) = \frac{f(b) - f(a)}{b - a}$

In this case:

$[a,b] = [0,2]$

So, we have:

$f'(c) = \frac{f(2) - f(0)}{2 - 0}$

$f'(c) = \frac{f(2) - f(0)}{2}$

Calculate f(2) and f(0)

$f(x) = e^{-4x}$

So:

$f(2) = e^{-4*2} = e^{-8} = 0.00033546262$

$f(0) = e^{-4*0} = e^{0} = 1$

This gives:

$f'(c) = \frac{0.00033546262 - 1}{2}$

$f'(c) = \frac{-0.99966453738}{2}$

$f'(c) = -0.4998$

Note that:

$f'(x) = (e^{-4x})'$

$f'(x) = -4e^{-4x}$

This implies that:

$f'(c) = -4e^{-4c}$

So, we have:

$f'(c) = -0.4998$

$-4e^{-4c} =-0.4998$

Divide both sides by -4

$e^{-4c} =\frac{-0.4998}{-4}$

$e^{-4c} =0.12495$

Take natural logarithm of both sides

$\ln(e^{-4c}) =\ln(0.12495)$

$\ln(e^{-4c}) =-2.0798$

Apply law of natural logarithm

$\ln(e^{ax}) =ax$

So:

$-4c =-2.0798$

Solve for c

$c =\frac{-2.0798}{-4}$

$c =0.51995$

3 0

3 years ago

Lynn is making custom bricks. She combines 39 pounds of water and 48 pounds of brick dust in a mixing bucket. She spills 13 poun

ehidna [41]

Lynn mixes 39 pounds of water with 48 pounds of brick dust, so the mixture has a total weight of 39 + 48 = 87 pounds.

13 pounds are spilled during mixing, so she's left with 87 - 13 = 74 pounds to turn into bricks.

7 pounds are needed for 1 brick, so she can make 10 bricks because 7 • 10 = 70 and 7 • 11 = 77, and 70 < 74 < 77.

If she uses the mixture to make 10 bricks, she uses up 70 pounds of it, which leaves 4 pounds to be washed out.

5 0

3 years ago

Yo someone hellp me and if you see this please click!

Vinvika [58]

Answer:

3/4

Step-by-step explanation:

4 0

3 years ago

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Y=-x+8 what is this can you tell me

GREYUIT [131]

Answer:

algebra

Step-by-step explanation:- x - 8.

brainliest plzzz

4 0

3 years ago

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4 cups servers 12 people how many cups server 4 people

zloy xaker [14]

Your answer should be 3/4 a cup

7 0

3 years ago