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3 years ago

Simplify expressions and combine like terms. 4y squared - 4y cubed -6y squared +6y cubed

Mathematics

1 answer:

choli [55]3 years ago

7 0

That will be -2² + 2³

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A fence must be built to enclose a rectangular area of ft. Fencing material costs per foot for the two sides facing north and so

avanturin [10]

The complete question is

A fence must be built to enclose a rectangular area of 5000ft^2. Fencing material costs $1 per foot for the two sides facing north and south and 2$ per foot for the other two sides. Find the cost of the least expensive fence.

Answer:

Total cost will be $400

Step-by-step explanation:

Let x = be other side

y = north and south side

Area = x*y = 5000

Perimeter of the rectangle = 2x + 2y

cost of fencing = 2(1)*5000/x + 2*2x

= 10000/x + 4x

now to get the least we will take the derivative of this

C'(x) = 10000(-1/x^2) + 4 =0

x^2 = 2500

x= 50ft cost = 2*$2*50 = $200

y= 100ft cost = 2*$1*100 = $200

Total cost = $400

3 0

3 years ago

Hi! Please help me find the slope of the line.

lana66690 [7]

Answer:

3/2

Step-by-step explanation:

We can use the slope formula to find the slope of the line

m = ( y2-y1)/(x2-x1)

Using the points (0,-4) and (2,-1)

m = ( -1 - -4)/( 2 - 0)

= (-1+4)/ (2 -0)

= 3/2

7 0

2 years ago

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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

#SPJ1

8 0

2 years ago

What is the equation of 3p – 7 + p = 13

forsale [732]

3p - 7 + p = 13

3p + p = 13 + 7
4p = 20
p = 20 : 4
p = 5

4 0

3 years ago

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I need help with this one

Reika [66]

Answer:

look it up

Step-by-step explanation:

8 0

3 years ago

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