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Diano4ka-milaya [45]
3 years ago
13

Consider the following.3x + 3y = 8(a) Find y' by implicit differentiation.(b) Solve the equation explicitly for y and differenti

ate to get y' in terms of x.(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' =
Mathematics
1 answer:
ludmilkaskok [199]3 years ago
8 0

Answer:

a.y'=-1

b.y'=-1

c.Yes

Step-by-step explanation:

We are given that consider a function

3x+3y=8

Implicit function: That function is a relation in which dependent variable can not be expressed in terms of independent variable

Explicit function: It is that function in which dependent variable can be expressed in terms of independent variable.

a.3x+3y=8

Differentiate w.r.t x then we get

3+3\frac{dy}{dx}=0

3\frac{dy}{dx}=-3

\frac{dy}[dx}=\frac{-3}{3}=-1

\frac{dy}{dx}=y'=-1

b.3x+3y=8

3y=8-3x

y=\frac{8-3x}{3}

Differentiate w.r.t x then we get

\frac{dy}{dx}=\frac{-3}{3}=-1

\frac{dy}{dx}=y'=-1

When we substituting the value of y obtained from part b into a solution of part a then we get

y'=-1

Hence, solutions are consistent.

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Step-by-step explanation:

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bacteria colonies can increase by 73% every 2 days. if you start with 150 bacteria microorganisms, how large would the colony be
slavikrds [6]

Using an exponential function, it is found that the colony will have 1344 bacteria after 8 days.

<h3>What is an exponential function?</h3>

An increasing exponential function is modeled by:

A(t) = A(0)(1 + r)^t

In which:

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Considering the initial amount of 150, and the growth rate of 73% each 2 days, the equation is given by:

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Hence, after 8 days, the amount of bacteria is given by:

A(8) = 150(1.73)^{\frac{8}{2}} = 1344

More can be learned about exponential functions at brainly.com/question/25537936

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