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san4es73 [151]
3 years ago
15

If f(x) = (4x-3)^2, then f(-2)=? A: -121 B: -22 C: 22 D: 25 E: 121

Mathematics
1 answer:
SOVA2 [1]3 years ago
7 0
The answer is E. 121.
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Pamela's boss rewards her hard work by telling her she is receiving a 12% raise. Pamela had been earning $15 per hour. After the
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It should be 16.8,
15 x (100% + 12%)
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Find the differential coefficient of <br><img src="https://tex.z-dn.net/?f=e%5E%7B2x%7D%281%2BLnx%29" id="TexFormula1" title="e^
Gemiola [76]

Answer:

\rm \displaystyle y' =   2 {e}^{2x}   +    \frac{1}{x}  {e}^{2x}  + 2 \ln(x) {e}^{2x}

Step-by-step explanation:

we would like to figure out the differential coefficient of e^{2x}(1+\ln(x))

remember that,

the differential coefficient of a function y is what is now called its derivative y', therefore let,

\displaystyle y =  {e}^{2x}  \cdot (1 +   \ln(x) )

to do so distribute:

\displaystyle y =  {e}^{2x}  +   \ln(x)  \cdot  {e}^{2x}

take derivative in both sides which yields:

\displaystyle y' =  \frac{d}{dx} ( {e}^{2x}  +   \ln(x)  \cdot  {e}^{2x} )

by sum derivation rule we acquire:

\rm \displaystyle y' =  \frac{d}{dx}  {e}^{2x}  +  \frac{d}{dx}   \ln(x)  \cdot  {e}^{2x}

Part-A: differentiating $e^{2x}$

\displaystyle \frac{d}{dx}  {e}^{2x}

the rule of composite function derivation is given by:

\rm\displaystyle  \frac{d}{dx} f(g(x)) =  \frac{d}{dg} f(g(x)) \times  \frac{d}{dx} g(x)

so let g(x) [2x] be u and transform it:

\displaystyle \frac{d}{du}  {e}^{u}  \cdot \frac{d}{dx} 2x

differentiate:

\displaystyle   {e}^{u}  \cdot 2

substitute back:

\displaystyle    \boxed{2{e}^{2x}  }

Part-B: differentiating ln(x)•e^2x

Product rule of differentiating is given by:

\displaystyle  \frac{d}{dx} f(x) \cdot g(x) = f'(x)g(x) + f(x)g'(x)

let

  • f(x) \implies   \ln(x)
  • g(x) \implies    {e}^{2x}

substitute

\rm\displaystyle  \frac{d}{dx}  \ln(x)  \cdot  {e}^{2x}  =  \frac{d}{dx}( \ln(x) ) {e}^{2x}  +  \ln(x) \frac{d}{dx}  {e}^{2x}

differentiate:

\rm\displaystyle  \frac{d}{dx}  \ln(x)  \cdot  {e}^{2x}  =   \boxed{\frac{1}{x} {e}^{2x}  +  2\ln(x)  {e}^{2x} }

Final part:

substitute what we got:

\rm \displaystyle y' =   \boxed{2 {e}^{2x}   +    \frac{1}{x}  {e}^{2x}  + 2 \ln(x) {e}^{2x} }

and we're done!

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3 years ago
A certain microprocessor requires either 2, 3, 4, 8, or 12 machine cycles to perform various operations. Twenty-five percent of
myrzilka [38]

Answer:

The average number of machine cycles per instruction for this microprocessor is 5.8.

Step-by-step explanation:

To find the average number of machine cycles per instruction for this microprocessor, we multiply each number of cycles for it's relative frequency.

We have that:

25% require 2 cycles.

20% require 3 cycles.

17.5% require 4 cycles.

12.5% require 8 cycles.

25% require 12 cycles.

So the average number is:

M = 0.25*2 + 0.2*3 + 0.175*4 + 0.125*8 + 0.25*12 = 5.8

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Choose the inequality that represents the following graph.
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\frac{29}{3}
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