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Novosadov [1.4K]
3 years ago
5

Floyd is an aspiring music artist. He has a record contract that pays him a base rate of \$200$200dollar sign, 200 a month and a

n additional \$12$12dollar sign, 12 for each album that he sells. Last month he earned a total of \$644$644dollar sign, 644.
Write an equation to determine the number of albums (a)(a)left parenthesis, a, right parenthesis Floyd sold last month.
Find the number of albums Floyd sold last month.
Mathematics
1 answer:
Thepotemich [5.8K]3 years ago
5 0
Floyd's contract consists of
(i) $200 per month fixed.
(i) $12 per album sold.

Let x =  number of albums sold last month.
Because total earnings is $644, therefore
200 + 12x = 644

To find x, do the following:
Subtract 200 from each side.
12x = 644 - 200 = 444
Divide each side by 12.
x = 444/12 = 37

Answer:
The equation is 12x + 200 = 644.
The solution for x (number of albums sold) is 37.

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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
Lisa is 53 3 4 inches tall. Joey is 1 1 2 inches shorter than Lisa and Jane is 1 1 5 inches shorter than Joey. How tall is Jane?
tester [92]

Answer: Jane's height =  51\dfrac{1}{20}\text{ inches}

Step-by-step explanation:

Given: Lisa's height = 53\dfrac34\text{ inches}=\dfrac{4\times53+3}{4}\text{ inches}

=\dfrac{215}{4}\text{ inches}

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=\dfrac{215}4-\dfrac32\\\\=\dfrac{215-6}{4}\\\\=\dfrac{209}{4}\text{ inches}

Jane's height = \dfrac{209}{4}-1\dfrac15 inches

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Hence, Jane's height = 51\dfrac{1}{20}\text{ inches}

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