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2 years ago

Which set(s) of numbers does 81−−√ belong to? Choose all that apply Natural numbers

Mathematics

1 answer:

prohojiy [21]2 years ago

6 0

Answer:

All of the above

Step-by-step explanation:

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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

2 years ago

What is 3/4 + 1/3? answer please

tatiyna

Answer:

13/12

Alternate form: 1.084 or 1, 1/12

Step-by-step explanation:

3/4+1/4

9/13+4/13

13/12 Solution.....

Sadanavam1979 GREETINGS

3 0

2 years ago

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A swimming pool is a rectangular prism. The pool is 36 feet long and 20 feet wide. What is the total amount of water, in cubic f

Sliva [168]

Answer:

$2880\ ft^{3}$

Step-by-step explanation:

The computation of the total amount of water needed could be determined by using the volume formula which is shown below:

$Volume = L \times W \times D$

where

L = length,

W = width,

and D = depth.

Now putting the values to the above formula

$Volume = (36\ ft) \times (20\ ft) \times (4\ ft) \\\\= 2880\ ft^{3}$

Therefore, the total amount of water needed is $2880\ ft^{3}$

We simply applied the above formula

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2 years ago

A graphic designer wants to translate rectangle DEFG using T–1, 2(x, y). The pre-image has coordinates D(–1, 3),

Lesechka [4]

Answer:The answer is B !

Step-by-step explanation:

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2 years ago

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What is 3.1666666667 as a fraction

never [62]

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2 years ago