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Gre4nikov [31]
3 years ago
10

1. On Tuesday, 12 Kittens at the shelter were adopted and 4 dogs also found new homes. What percentage of the newly adopted pets

at the shelter were dogs?
2. Gabe read 10 books over the summer. 4 were nonfiction. The rest were fiction. What percentage were fiction?
Mathematics
1 answer:
aleksley [76]3 years ago
5 0
1.  25% of the new dogs found new home

2.  60% of the book Gabe read are fiction
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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
stepan [7]

Answer:

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 }

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)}

7 0
3 years ago
Which expression is equivalent to: (5⁹ × 5⁻⁷)⁻² ?
lutik1710 [3]

Answer:

(6^4 x 2^-9)

Step-by-step explanation:

4 0
2 years ago
In right triangle abc shown below, AC=29 inches, AB=17 inches, and m
lapo4ka [179]
Need drawing not sure where m is
6 0
2 years ago
I only need help on the questions in Number 36.
lidiya [134]
A:12/3 = -4
b:-12/3 = -4
c:-12/-12 = 4
e:-5/5 = -1
f:5/-5 = -1
g:-5/-5 = 1
7 0
3 years ago
What is the value of c?
lara31 [8.8K]
You have to use the Pythagoreas theorem where you do 3 squared + 4 squared=25
Then you square root 25 which is 5 so
c is 5
5 0
3 years ago
Read 2 more answers
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