Mathematics, 24.03.2020 21:41 blondie02

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation P V = C , where C is a constant. Suppose that at a certain instant the volume is 800 cm 3 , the pressure is 160 kPa , and the pressure is increasing at a rate of 40 kPa/min . At what rate is the volume decreasing at this instant?

Answers: 1

Show answers

Answers

Answer from: yhbgvfcd6677

The volume decreasing at the rate of $200\:\frac{cm^3}{min}$ .

Step-by-step explanation:

We need to find at what rate is the volume decreasing $\frac{dV}{dt}$ , when $V=800\:cm^3$ , $P=160\:kPa$ , and $\frac{dP}{dt} =40 \:\frac{kPa}{min}$ .

We know that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation P V = C , where C is a constant.

So, we can differentiate this equation with respect the time. For this we use the Chain Rule

$\frac{d}{{dx}}\left[ {f\left( u \right)} \right] = \frac{d}{{du}}\left[ {f\left( u \right)} \right]\frac{{du}}{{dx}}$

and the Product rule

$\frac{d}{{dx}}\left( {f\left( x \right)g\left( x \right)} \right) = f\left( x \right)\frac{d}{{dx}}g\left( x \right) + \frac{d}{{dx}}f\left( x \right)g\left( x \right)$

to differentiate both sides with respect to time.

$V\frac{dP}{dt} +P\frac{dV}{dt} =\frac{d}{dt} C\\\\V\frac{dP}{dt} +P\frac{dV}{dt} =0$

Next, we substitute the given values

$800\cdot 40+160\cdot\frac{dV}{dt} =0$

and we solve for $\frac{dV}{dt}$

$800\cdot 40+160\cdot\frac{dV}{dt} =0\\\\160\cdot\frac{dV}{dt} =-800\cdot 40\\\\\frac{dV}{dt} =\frac{-800\cdot 40}{160} =-200\:\frac{cm^3}{min}$

Answer from: Quest

the most boring ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Answer from: Quest

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula

Another question on Mathematics

Mathematics, 21.06.2019 16:20

Taking algebra two apex courses and need with these questions

Answers: 1

Answer

Mathematics, 21.06.2019 20:00

Aclothing store has the sign shown in the shop window. pani sees the sign and wants to buy 3 shirts and 2 pairs of jeans. the cost of each shirt before the discount is $12, and the cost of each pair of jeans is $19 before the discount. write and simplify an expression to find the amount pani pays if a $3 discount is applied to her total

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Tom is the deli manager at a grocery store. he needs to schedule employee to staff the deli department for no more that 260 person-hours per week. tom has one part-time employee who works 20 person-hours per week. each full-time employee works 40 person-hours per week. write and inequality to determine n, the number of full-time employees tom may schedule, so that his employees work on more than 260 person-hours per week. graph the solution set to this inequality.

Answers: 1

Answer

Mathematics, 21.06.2019 23:00

Describe the end behavior of the function below. f(x)=(2/3)^x-2 a. as x increases, f(x) approaches infinity. b. as x decreases, f(x) approaches 2. c. as x increases, f(x) approaches -2. d. as x decreases, f(x) approaches negative infinity.

Answers: 1

Answer

You know the right answer?

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P...

Questions

Mathematics, 27.03.2020 02:23

MGSE9-12.G. GPE.5 3) Explain how to prove EACH of the following with coordinate: a. Two lines are perpendicular. b. Two lines are pa...