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 PV = C, where C is a constant. Suppose that at a certain instant the volume is 700 cm3, the pressure is 200 kPa, and the pressure is increasing at a rate of 30 kPa/min. At what rate is the volume decreasing at this instant?

Q: A dealer's profit, in units of $1000, on a new automobile is a random variable X having density func...

A:

Q: For the graph of the equation, identify the amplitude, period, phase shift, and vertical shift. Do n...

A: Given,            y=-4sinπx-1+5To find : The amplitude, period, phase shift and vertical shift

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

A:

Q: 8 sin 2x Find the value of lim z 20 7 sin (2x2 + x) 16 7 8 25

A:

Q: Match the graph with the first order differential

A: In this question we will use basic concepts of calculus i.e graphing of differential equation. Solut...

Q: Use synthetic division to show that x is a solution of the third-degree polynomial equation, and use...

A:

Q: 22. (MULTIPLE CHOICE) Which of the following statements is(are) true? (A) y = e is a solution of the...

A:

Q: Consider the following. 4x6 + y7 = 9x (a) Find  y ′  by implicit differentiation. y ′ =

A:

Q: Inverse Laplace Transform; f(s)= 1/s-3

A: Laplace Inverse Transform of 1s-3

Q: Find the area of the region bounded by y = la, y = 0, x = 0, x = 2 %3D Give your answer to the neare...

A:

Q: 3(sin y- cos y) chy cos y

A: First we use (siny - cosy) 2 =sin2 y + cos2 y -2sinycosy Then using u substitution let u =sexy + tan...

Q: Evaluate the integral using the indicated trigonometric substitution. (Use C for the constant of int...

A: Topic -Integration 

Q: Use the graph of the function f shown to estimate the following limits and the function value. Compl...

A:

Q: Please only solve 9,12 by partial fraction

A: We need to solve integrals by using partial fraction method.

Q: Find the lines that are tangent and normal to the curve at the given point. x²y? = 36, (1,6) %3D

A: We will find first slope of tangent and then from the slop and tangent and point will find a equatio...

Q: Зх +7 -dx = (х—1)(х-9)

A: Fully evaluate the integral.

Q: n

A:

Q: Find the Laplace transform of the following: f(t) = sin(5t) cos(5t)

A:

Q: du Formula Answer 7. S 4-5x+1 dx

A: Given: I=∫5x4-5x+1dx   .....(1)   We know that; The chain rule: fgx'=f'gx·g'x The derivative of ax i...

Q: For the next five questions, consider the following differential equation: (y? + cy°)dx + (5y² – xy+...

A: Given differential equation is y2+xy3 dx + ( 5y2-xy+y3siny) dy =0 Also, given that M is coefficient ...

Q: Let ƒ be differentiable on R. Suppose that f'(x) # 0 for every r. Prove that f has at most one real ...

A:

Q: A pair of dice is rolled. let X be the sum of the number of dots onthe top faces. The table below sh...

A:

Q: 3. lim f(x) lim f(x) 4. lim f(x) lim f(x) = -2, = +0, x+3- = 2 and f(2) = 0 = -0O x-2+ x+3+

A: Let's find. 

Q: What are the quartiles of a distribution? O A. The quartiles consist of the lowest value, the median...

A:

Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)

A: The objective is to verify the conclusion of clairaut's theorm.

Q: Find the value of lim sec 3. 2 Select your answer. 2/3 3 3 2/3 +3 3 2/3 – 3 3. 2/3 3 3

A:

Q: Tangent Line Approximation AP Calculus AB Tangent Line Approximation Discovery Let /(x) = 2x - 3x. (...

A:

Q: 5. Verify that, for any constant C, y = t+4vt +C satisfies the differential equation (y-t)y' = y-t+8...

A: Given differential equation 

Q: 8. A function f has the form f(x) = a+b ln x. If f(1) = 5 and f (e) = 7, find the values of a and b....

A:

Q: *Introduction to Derivatives (x²+2x-3 Using the 3 conditions, show that f(x) = if x 1 X-1 is both co...

A: If limxtends to 1f(x) =f(1) then f(x) is continuous at x=1 .  And if f'(1)  exists then f is differe...

Q: QUESTION 7 Write the form of the following argument, and prove that following is a vali If 91 is a p...

A: Given: Statement:  prove that following is a vali If 91 is a prime number, then 13 is not a divisor ...

Q: Evaluate the integral by applying the following theorems and the power rule appropriately. Suppose t...

A: ∫xr dx = xr+1r+1+C

Q: (7) Determine if the improper integral converges or diverges. Justify your answer. If it converges, ...

A:

Q: 8. Find the limit, if it exists, or show that it does not exist: 2x-y a) lim (xy)(1,2) 4x2-y2

A:

Q: Find csc (-270°). Select the correct choice below and, if necessary, fill in the answer box to compl...

A:

Q: , Which of the following processes is stationary? A) An MA(1) process with 0 = -1.6 B) Y, = 58.46 + ...

A: The stationary process is 

Q: Let f(x) = (6 + 5æ) f(x) has one critical value at A = For x A, f(x) is Select an answer

A: f(x)= (6+5x)2  Find the critical points of f. 

Q: (e^x+lny+(y/x))dx+(x/y+lnx+siny)dy=0 solve using exact equation (diff eq)

A:

Q: 25 and sec 0= 24 25 Determine the values of the trigonometric functions of 0, where csc 0= 7 sin 0 =...

A:

Q: The production function for a firm is p(x, y) = 96x*y"4, where x and y are the number of units of la...

A:

Q: 2. In(x + iy) = A. cos(x) cosh(y) - i sin(x) sinh(y) B. sin(x) cosh(V) + i cos(x) sinh(y) C. cos(x) ...

A: solution

Q: nt line of y = f(x)

A:

Q: n is bounded and monotonic for all n. n +1 6. Show that the sequence An

A: The objective is to solve the above question.

Q: Find the volume of the solid generated by revolving the region bounded by the graphs of the equation...

A: NOTE: Refresh your page if you can't see any equations. .

Q: Graph f, locate all points of discontinuity, and discuss the behavior of f at these points. 2+x if x...

A: The objective is to solve the above question.

Q: 5. Calculate the derivative of f(x) = Use this result to determine whether the sequence x2 + 1 An = ...

A:

Q: If F(x) = f(g(x)), where f(5) = 7, f '(5) = 2, f '(2) = 3, g(2) = 5, and g'(2) = 3, find F '(2). F '...

A:

Q: Exercise (2) If A and B are any (2x2) matrices. 1. C=A'+B

A: Note: - Since you have asked multiple questions, we will solve the first question for you. If you wa...

Q: With partial fraction decomposition the following rational expression can be expressed in the form x...

A: