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3 years ago

Simplify the ratio: 2 days: 2 weeks [Write the answer without any units of measurement.]

Mathematics

1 answer:

Marysya12 [62]3 years ago

8 0

Answer:

1:7

Step-by-step explanation:

2 days = 2, 2 weeks = 14 days

2:14

u can divide it by 2

becomes 1:7

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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

Help me please! Will give brainly to correct answer.

marusya05 [52]

Sin(Angle) = Opposite Leg / Hypotenuse

Sin (Angle B) = 2 / 3

Angle B = Arcsin(2/3)

Angle B = 41.81 degrees.

5 0

3 years ago

Find the volume of a right circular cone that has a height of 17.5 ft and a base with a diameter of 6.1 ft. Round your answer to

julia-pushkina [17]

Answer:
volume of cone = 170.5 ft³

Explanation:
The volume of the right circular cone can be calculated as follows:
volume = $\frac{1}{3} * \pi *r^2 *h$

We are given that:
diameter = 6.1 ft.......> This means that: radius (r) = 6.1 / 2 = 3.05 ft
height (h) = 17.5 ft

Substitute with the givens in the above equation to get the volume as follows:
volume = $\frac{1}{3} * \pi *(3.05)^2*17.5$

volume = 170.477 which is approximately 170.5 ft³

Hope this helps :)

6 0

3 years ago

Find the radius r of the sphere.

AleksandrR [38]

Given:

The volume of the sphere = 12348π in³

To find the radius of the sphere.

Formula

The volume of a sphere of radius r is

$V = \frac{4}{3} \pi r^{3}$