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Harman [31]
1 year ago
10

The perimeter of a rectangle is 36 units. the width, w, of the rectangle is 8 units.which equation correctly relates the given i

nformation and the length
Mathematics
1 answer:
pychu [463]1 year ago
6 0

The length of the given rectangle is 10 units.

Here, we are given that the perimeter of a rectangle is 36 units.

A rectangle is a figure with 4 sides and opposite sides equal. The perimeter of a rectangle is calculated using the given formula-

Perimeter = 2 ( length + breadth )

Here, the breadth (width) is given to be 8 units.

Let the length be x units.

Then, we can form the following equation-

Perimeter = 2( x + 8 )

36 = 2x + 16

36 - 16 = 2x

20 = 2x

2x = 20

x = 20/2

x = 10

Thus, the length of the given rectangle is 10 units.

Learn more about perimeter here-

brainly.com/question/19819849

#SPJ4

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Suppose that x and y are both differentiable functions of t and are related by the given equation. Use implicit differentiation
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Example:- \frac{dy}{dx}  = \frac{-(y+2x)}{(x+2y)}

Step-by-step explanation:

<u>Partial differentiation</u>:-

  • Let Z = f(x ,y) be a function of two variables x and y. Then

\lim_{x \to 0} \frac{f(x+dx,y)-f(x,y)}{dx}    Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to x.

It is denoted by δ z / δ x or δ f / δ x

  • Let Z = f(x ,y) be a function of two variables x and y. Then

\lim_{x \to 0} \frac{f(x,y+dy)-f(x,y)}{dy}    Exists , is said to be partial derivative or Partial differentiational co-efficient of Z or f(x, y)with respective to y

It is denoted by δ z / δ y or δ f / δ y

<u>Implicit function</u>:-

Let z = f(x, y) where f(x, y) =0 then the implicit function is

\frac{dy}{dx} =\frac{-δ f/ δ x }{δ f/δ y }

The total differential co-efficient

d z = δ z/δ x +  \frac{dy}{dx} δ z/δ y

<u>Implicit differentiation process</u>

  • differentiate both sides of the equation with respective to 'x'
  • move all d y/dx terms to the left side, and all other terms to the right side
  • factor out d y / dx from the left side
  • Solve for d y/dx , by dividing

Example :  x^2 + x y +y^2 =1

solution:-

differentiate both sides of the equation with respective to 'x'

2x + x \frac{dy}{dx} + y (1) + 2y\frac{dy}{dx} = 0

move all d y/dx terms to the left side, and all other terms to the right side

x \frac{dy}{dx}  + 2y\frac{dy}{dx} =  - (y+2x)

Taking common d y/dx

\frac{dy}{dx} (x+2y) = -(y+2x)

\frac{dy}{dx}  = \frac{-(y+2x)}{(x+2y)}

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