Mathematics, 27.09.2019 21:40 rayastransformers

Which of the following tangent points on g(x)=36/(x - 1) has an instantaneous rate of change of -9?
a) (-3,-9)
b) (4,12)
c) (3,18)
d) (-5,-6)

Answers: 2

Show answers

Answers

Answer from: drcarver

$\bf g(x)=\cfrac{36}{x-1}\implies g(x)=36(x-1)^{-1}\qquad thus
\\\\\\
\cfrac{dg}{dx}=36\cdot -1(x-1)^{-2}\implies \cfrac{dg}{dx}=-\cfrac{36}{(x-1)^2}\\\\
-------------------------------\\\\
\textit{now, if the instantaneous rate of change is -9, then}
\\\\\\
-9-\cfrac{36}{(x-1)^2}\implies (x-1)^2=\cfrac{-36}{-9}\implies (x-1)^2=4
\\\\\\
x-1=\pm\sqrt{4}\implies x-1=\pm 2\quad x=
\begin{cases}
3\\
-1
\end{cases}$

well, then we know when x = 3 or -1, the slope is -9, what's "y"?

$\bf x=3\qquad g(x)=\cfrac{36}{(3)-1}\implies g(x)=18\qquad \boxed{(3,18)}
\\\\\\
x=-1\qquad g(x)=\cfrac{36}{(-1)-1}\implies g(x)=-18\qquad (3,-18)$

Answer from: Quest

answer: your correct answer is b. d.

step-by-step explanation:

Answer from: Quest

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder: $652=5q+r$

here $q$ ("q" for quotient) is the number of brownies each of your friends get, and $r$ is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so $q=130$ and $r=2$ .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.

Other questions on the subject: Mathematics

Mathematics, 21.06.2019 16:20, kingalex7575

Browning labs is testing a new growth inhibitor for a certain type of bacteria. the bacteria naturally grows exponentially each hour at a rate of 6.2%. the researchers know that the inhibitor will make the growth rate of the bacteria less than or equal to its natural growth rate. the sample currently contains 100 bacteria. the container holding the sample can hold only 300 bacteria, after which the sample will no longer grow. however, the researchers are increasing the size of the container at a constant rate allowing the container to hold 100 more bacteria each hour. they would like to determine the possible number of bacteria in the container over time. create a system of inequalities to model the situation above, and use it to determine how many of the solutions are viable.

Answers: 1

continue

Mathematics, 21.06.2019 18:20, katlynnschmolke

What is the solution set of the quadratic inequality x2- 5< 0? o {xl-55x55{x- 155x55){xl -55x5 15){x1 - 15 sx5/5)

Answers: 2

continue

Mathematics, 21.06.2019 19:00, keymariahgrace85

How much orange juice do you need to make 2 servings of lemony orange slush?

Answers: 1

continue

Mathematics, 21.06.2019 22:30, zacksoccer8279

Assume that y varies inversely with x. if y=1.6 when x=0.5 find x when y=3.2 acellus answer