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3 years ago

What is 44/12 in simplest form?

2 answers:

7 0

The numerator and denominator when both divided by 4 results in the fraction 11/3. To simplify this further, you can turn it into a mixed number which is 3 2/3

vekshin13 years ago

5 0

The answer is 3and 2/3

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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

Rewrite the product (x-3)^2 in standard form.

Schach [20]

Answer:

x² - 6x + 9

Step-by-step explanation:

5 0

3 years ago

Write a function g whose graph is a horizontal shrink by a factor of 1/3

mote1985 [20]

Answer:

g(x) = 6|x + 1| - 2

-----------------------------------------

Given:

Function f(x) = 2|x + 3| - 2

Find a function g which is a horizontal shrink by a factor of 1/3 of f(x).

Horizontal shrink by a factor of k is:

g(x) = f(x/k)

Apply this to the given function:

g(x) = f(x : 1/3) = f(3x) = 2|3x + 3| - 2 = 6|x + 1| - 2

7 0

1 year ago

Determine whether the graph of the quadratic function y = –x^2 – 10x + 1 opens upward or downward. Explain.

REY [17]

C. If the first coefficient is negative, then the graph opens downwards

3 0

3 years ago

Using identities, find a)(2 + 3) 2 b) (x+2y) (x-2y)

shutvik [7]

Pop ok you see so the answer here would be frantically elastic

5 0

2 years ago