1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

Q: The current population of a small town is 2104 people. It is believed that town's population is…

A:

Q: Determine the singular points of the given differential equation. Classify each singular point as…

A: Concept: The general homogeneous second order differential equation: y''+P(x)y'+Q(x)y=0 Regular and…

Q: Evaluate the following integral. JJ. xyz dV if S is the region bounded by the cylinders x² + y² =…

A:

Q: For a particular financial methodology, the risk-reward function was defined as y=x(Inx-2), where y…

A: The risk-reward function,    y=xlnx-2y=units of reward, x=units of risk

Q: - Solve the linear ODE using an Integrating Factor. x². dy dx + 2xy = 3sin(8x)

A: solution is given below

Q: Use triple integration in Cartesian coordinates to find the volume of the region in the first octant…

A:

Q: 2 Find the area bounded by the parabola y = 4x and the line y = 2x - 4.

A:

Q: 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258 (c) 82 (d) 734…

A: Given problem:- 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258…

Q: Evaluate the following: fo(5x²y³ + 3x) dydx a. b. ff ex+ydA where R = {(x,y)|-x≤ y ≤x, 0≤x≤ 2}

A: To find the value of given double integrals.

Q: 1) If y = (x − a)√/2ax - x² + a² sin a is constant. sin-¹(*), then y' = 2√/2ax - x² a

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

A: follow next step

Q: S eln (1-t) 1-t - dt ed to you in any form

A:

Q: Activity #3: Present Value Max was injured and can no longer work. As a result of a lawsuit, he is…

A: We need to find Present value.

Q: 11. Given f(x, y) = 6r² - 2r³ + 3y² + 6ry. Determine any local maxima, local minima, and saddle…

A: To find out the local maxima, local minima and saddle points.

Q: Solve for y at x=2: (x5 + 3y) dx - x dy = 0; x=1, y=2

A: We need to s0olve D.E.

Q: Find the area of the region bounded by y = 3x - x² and the x- axis. 9/4 9/7 9/2 9/5

A:

Q: 6. I. Evaluate each determinant. тут 3-3 4 1 -5 0 -1 -4

A:

Q: what substitution formula is used here ?

A: the substitution formula used here is-

Q: Evaluate csc(π/6)   Enter the exact answer.

A: Solution ) csc(π/6)  Angle in first quadrant  We know that  Sin x = 1/ csc x  x = π/6 Sin (π/6)  =…

Q: Find the length of the shortest ladder that can extend from a vertical wall, over a fence 2 m high…

A:

Q: A poster of area 960 cm² has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

A:

Q: 1/2 x3 1-x4 1/2 √3 - 2/2 √2/560 16 Option 1 1/11 Option 3 1 15 2 16 dx 1 Option 2 Option 4 15 8 √15…

A: Given, ∫012x31-x4dx

Q: The position of an object at time t is given by the parametric equations x = 3t² + 1t y = 3t² + 3…

A:

Q: a. y = 3et-2 et +1

A:

Q: Which of the following are parametric equations for the entire line y = x + 1? Choose all that…

A:

Q: the polar coordinates to find the volume of a sphere of radius 1. -

A: Given;  Sphere of radius 1.

Q: Exercise 25.7.1. Give the Taylor series of the function 1 f(x):= 3x² around the point c = 1 and give…

A: The function is given by, f(x)=13x2 = 13x-2    ⇒f(1)= 13Differentiating the function 1, 2 , 3 ...…

Q: Question 10 The parametrization describes a cone. O True O False r(u, v) = (u, sin v, cos v)

A:

Q: nd the reference angle, the quadrant of the terminal side, and the sine and cosine of 225°   Enter…

A: Find the reference angle, the quadrant of the terminal side, and the sine and cosine of 225°

Q: 2. Create a graph of a function which satisfies all of the given conditions. D = {x € R|x = -2} •…

A: The function satisfies the…

Q: Evaluate the integral and it gives x x 2 sin+cos sin²x 2 dx 2 In | csc (1/2)x-cot (1/2) x | + 2 csc…

A: The given integral is ∫sinx2+cosx2sin2x2 dx=∫1sinx2+cosx2sin2x2 dx=∫cscx2+cscx2 cotx2…

Q: A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river…

A:

Q: Find the area of the region bounded by y = x³ - 8 the x-axis and the y axis. 1/3 3 1/9 9 None of the…

A:

Q: Find the local maximum and minimum values of the function f(x) = -x - 25 using the Second Derivative…

A: Given problem:- Find the local maximum and minimum values of the function f(x) = -x- 25/x using the…

Q: Consider the falling object of mass m = assume that the drag force is proportional to the 12 kg, and…

A: We need to choose correct option.

Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

A:

Q: 3. I. -1 2 Evaluate each determinant. 5 3

A: Given,-1523

Q: √ √tan tan x dx

A:

Q: The ellipse + 1 can be drawn with parametric equations where (t) is written in the form 4²2 r(t) = r…

A:

Q: Determine the area of the region bounded by x=3+y^2, x=2-y^2, y=1 and y=-2. *

A:

Q: Find the general solution of the following DE. xy(y')² + (x² + y²)y' + xy = 0

A:

Q: ered # tion Bi Q) choose one only 1. If (x + y)² = x² + y² prove that = - dx 2. If y = sin³ () cos³…

A: To find the differentiation of given functions.

Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y=√x,…

A:

Q: Suppose a state's income tax code states that tax liability is 18% on the first $19,500 of taxable…

A: The tax function,   T(x)=a+0.18xx≤19,500b+0.14x-19,500x>19,500

Q: Given the function y = x(x + 1)3. Determine the value of its second derivative at x = 1.

A: Given the function  y=xx+13. We have to find the value of its second derivative at x=1.

Q: USING CYLINDRICAL METHOD Find the volume of the solid obtained by rotating about the y-axis the…

A: Given that, Solid obtained by rotating about the y-axis the region bounded by y=2x2 - x3 and y = 0

Q: Properties Of The Dot Product (- 2-.. pesta ) n. v = 0 = i = 0 or D = 0or ii 1 v تريلية

A: We have to prove the given property.

Q: On the Illinois state tax form, numbers are to be rounded to the nearest dollar. If Heat earned…

A: If you have to round off to complete integer then we need to look the first number after decimal.

Q: Let r(t)=(3-2 cost)i + (2+2 sin t)j. Find the arc length parametrization in term of the arc length…

A:

Q: Let p(t) represent the population of a major city t years after 1950, as shown in the table and…

A: