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3 years ago

The figure is reflected across line m and the reflected across line n. What type of transformation is the result?

Mathematics

1 answer:

slega [8]3 years ago

6 0

It's a translation.

A reflection across a line is like flipping that object like a pancake over the line. It gets turned upside-down.

When you flip the pancake again, now across a parallel line, it gets turned right-side up again, just in a new location.

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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!

6 0

3 years ago

A train travels at a speed of 90 miles per hour. How far will it have traveled<br> in 3 hour

DiKsa [7]

270 miles be 90+90+90 equals 270 and thats the answer

5 0

3 years ago

Read 2 more answers

Part D<br> What is the measurement of angle C?

NeX [460]

Step-by-step explanation:

I think we are missing some information (angle F or B or a side length would be great).

but just the right angles are not enough to calculate specific numbers. they would depend on the angle F or e.g. the side length of AB.

without any further information F and AB can be freely changed without changing the known facts, but it changes also C, B, G

so, all I can say is C = 180 - B.

and that G = B.

5 0

2 years ago

Round this number to the nearest thousand 7,433,654

Aliun [14]

The answer is going to be 7,434,000. hope that helped

5 0

3 years ago

Read 2 more answers

Can someone help me with this question?

Nikitich [7]

D. 5 5/6

Volume = l * b * h
= 2 1/2 * 3 1/2 * 2/3
= 5/2 * 7/2 * 2/3
= 35/6
= 5 5/6

4 0

3 years ago