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3 years ago

Please help me with this!

Mathematics

2 answers:

dezoksy [38]3 years ago

8 0

Answer:

x = 27

Step-by-step explanation:

Use the ratio and proportion:

x + 8 2x - 5

just X multiply:

14 ( x + 8 ) = 10 ( 2x - 5 )

-6x = -162

x = -162 / -6

x = 27

iragen [17]3 years ago

3 0

10/14 = x+8/ 2x-5, so 10*2x-5= 14*x+8(cross multiplication)
So 20x-50= 14x+112(simplification), so subtract 14x: 6x-50=112, then add 50 to both sides: 6x=162, divide by 6: x=27

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Step-by-step explanation:

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2 years ago

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]

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

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Step-by-step explanation:

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

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:

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

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

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

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

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

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

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

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

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

Apply law of natural logarithm

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So:

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Solve for c

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

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