Consider the following. 7 x + 7 y = 6 (a) find y' by implicit differentiation. y' = correct: your answer is correct. (b) solve the equation explicitly for y and differentiate to get y' in terms of x. y' = (c) check that your solutions to part (a) and (b) are consistent by substituting the expression for y into your solution for part (a). y' =

Answer with Step-by-step explanation:

We are given that an equation

[tex7x+7y=6[/tex]

a.We have to find y' by implicit differentiation.

Implicit function:That function which is consist of x and y.The value of y does not depend  x directly.

Differentiate w.r.t x

b.We have to solve the equation explicitly for y and differentiate to get y' in terms of x.

Explicit function:It is that function in which y is directly depend  on x.

Differentiate w.r.t x

c.We have to find solutions of part a and part b are consistent by substituting the expression of y into the solution of part a.

When substitute  in y' of part a.

Then,

Hence, solution of part a  and part b are consistent.

dd

step-by-step explanation:

dd

area of part 1:

a1=base*height/2=(8+2)*(8-2-2-1)/2=10*3/2=15 ft^2

area of part 2:

a2=length*width=(8+2)*1=10 ft2

area of part 3:

a3=length*width=8*2=16 ft2

total shaded area : a1+a2+a3=41 ft2

total area of the reactangle : a=16*8=128 ft2

total area of the nonshaded region : 128-41=87 ft2