3х – 10 y = 14 3х

Please help me answer this question

stealth61 [152]

The value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

<h3>Differentiation</h3>

From the question, we are to determine dy/dx for the given functions

(i) $x^{2} sin^{2}2x$

Let $u = x^{2}$

and

$v = sin^{2} 2x$

Also,

Let $w= sin2x$

∴ $v = w^{2}$

First, we will determine $\frac{dv}{dx}$

Using the Chain rule
$\frac{dv}{dx} = \frac{dv}{dw}.\frac{dw}{dx}$

$v = w^{2}$

∴ $\frac{dv}{dw} =2w$

Also,

$w= sin2x$

∴ $\frac{dw}{dx} =2cos2x$

Thus,

$\frac{dv}{dx} = 2w \times 2cos2x$

$\frac{dv}{dx} = 2sin2x \times 2cos2x$

$\frac{dv}{dx} = 4sin2x . cos2x$

Now, using the product rule

$\frac{dy}{dx} = u\frac{dv}{dx} + v\frac{du}{dx}$

From above

$u = x^{2}$

∴ $\frac{du}{dx}=2x$

Now,

$\frac{dy}{dx} = x^{2} (4sin2x.cos2x)+ sin^{2}2x (2x)$

$\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $xy^{2}+y^{2}x^{3} +2=0$

Then,

$x.2y\frac{dy}{dx}+ y^{2}(1)+y^{2}.3x^{2} + x^{3}.2y\frac{dy}{dx} +0=0$

$2xy\frac{dy}{dx}+ y^{2}+3x^{2}y^{2} + 2x^{3}y\frac{dy}{dx} =0$

$2xy\frac{dy}{dx}+2x^{3}y\frac{dy}{dx} =- y^{2}-3x^{2}y^{2}$

$\frac{dy}{dx} (2xy+2x^{3}y)=- y^{2}(1+3x^{2})$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy+2x^{3}y}$

$\frac{dy}{dx} =\frac{- y^{2}(1+3x^{2})}{2xy(1+x^{2}) }$

$\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Hence, the value of dy/dx for the functions are

(i) $\frac{dy}{dx} = 4x^{2}sin2x.cos2x+ 2x. sin^{2}2x$

(ii) $\frac{dy}{dx} =\frac{- y(1+3x^{2})}{2x(1+x^{2}) }$

Learn more on Differentiation here: brainly.com/question/24024883

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8 0

2 years ago

How many significant figures will there be in the answer to the following problem?<br> 7500×45.0879

Alchen [17]

Two significant Figures I believe because you want to go with the least amount of sig figs that are already in your problem which would be 2 in 7500 because the zeros are not significant

8 0

3 years ago

A parallelogram piece of paper 40cm by 25cm is cut into small parallelogram 8cm by5cm . How many pieces can be obtained. Step by

Bumek [7]

Step 1- multiply 40 by 25 to get 1000
step2- multiply 8 by 5 to get 40
step3- divide 1000 by 4 to get 250
answer. 250 pieces

5 0

3 years ago

PLZ help me!!! will mark brainlyest!!<br> what is the slope intercept form of a linear equation?

Greeley [361]

Answer:

y= mx+b

Step-by-step explanation:

m is the slope

b is the y intercept

5 0

3 years ago

A small garden measures 11 ft by 7 ft. A uniform border around the garden increases the total area to 140 ft2. What is the width

Leokris [45]

There are many ways to work a problem like this. You can write an equation for the area of the border and solve for its width; you can graph an equation for the border and find its solutions; or you can use a little number sense.

The difference in length and width of the garden area is 4 ft. If the border is uniform, the difference in length and width of the overall area will remain 4 ft. Thus you can look for factors of 140 (the area) that differ by 4.
.. 140 = 1*140 = 2*70 = 4*35 = 5*28 = 7*20 = 10*14
The last two factors listed differ by 4, so we take these as the overall dimensions of the bordered area.

Without the border, the garden area width is 7 ft. With a border on both sides, the garden area width is 10 ft. Then twice the border width is
.. 10 ft -7 ft = 3 ft . . . . twice the border width

The border width is 1.5 ft.

_____
The attached graph shows the solution to
.. (7 +2x)*(11 +2x) -140 = 0
The overall width with a border of width x will be 7 +2x. The overall length with a border of width x will be 11 +2x. The product of these dimensions is the overall area, 140 t^2. When we subtract that area from the product of dimensions, we want the result to be zero. The graphing program easily tells us the value of x that makes the result zero: 1.5 ft.

8 0

3 years ago

3х – 10 y = 14 3х - 9y = 15​

3х – 10 y = 14 3х - 9y = 15