2) Find and of the following equation then simplify whenever possible. dx² x = Cos ß + Sin ß y = Sin ß – Cos ß

Q: A stone is thrown vertically upward from the ground with an initial velocity of 128 ft/sec. How long…

A: see below the answer and explanation

Q: Find the partial derivative. z = (x2 + 4x – 2y)° -

A:

Q: dx 2. x²V4-x?

A: Just use the trigonometrical substitution to make integral easy and then solved it.

Q: y = 3x - x² and y = 2x %3D

A: See the details solution in below

Q: Find the absolute extrema if they exist, as well as all values of x where they occur, for the…

A:

Q: y" + 9y = 9 sec² 3t, 0<t < T/6

A: To solve the following differential equation

Q: Find div F and curl F if F(x, y, z) = xz°i+ 5y*x²j +4z²yk. div F= curl F=

A: To find curl F and div F.

Q: Sn sin4xdx = 4 */3 1/12 Select one: O True O False

A:

Q: e the initial value problems with initial conditions y' = y – 1 @ yo = 0 b. у %3D et- 1 а. у%3 у?— 1…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3 dy – sin-! 3y -12+C %3D sin-1. 4- 9y 3

A:

Q: (3x? + у?)dx — 2хydy %3D 0

A:

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A:

Q: Evaluate the definite integral. NOTE: Enter the exact answer. ti +t dt

A:

Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

A:

Q: 21. Solve the equation y' = (x²+ 7) / 9 (2x / 9) + c b. y = (x / 18) + c 22. Solve the equation y' =…

A:

Q: Describe the graph of the equation. r = 15 sin 18t i + 15 cos 18t j O It is an ellipse in the…

A:

Q: Consider the parametric equations x = 4 cos(0) and y = 2 sin(0). (a) Create a table of x- and…

A: We know that   cos(-θ)=cosθ  and   sin(-θ)=-sinθ

Q: 5xdx 3. Find the integral (x-1)3 -5 a. 2(x-1)2 +C b. ++C -5 2(x-1)2 X-1 c. In () – in () + c )-In()…

A:

Q: S. dx 2. x²V4-x2

A:

Q: The differential equation (xy2 + y)dy = (x+1)dx is separable. %3D

A:

Q: cosxsin?xdx Solve using algebraic substitutionf V1+sinx

A: We have to find Integration using algebraic substitution.

Q: Evaluate the double integral using single applications of Simpson's 1/3 rule 2 (x2. 3y2 + xy³) dx dy…

A:

Q: Find div F and curl F if F(x, y, z) = 7e*Y i – 6 cos yj+ 10 sin? z k. - div F= curl F=

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx

A: see below the answer and calculation with steps

Q: 6. y = (x +3x + 2)(x2 +5x + 1)

A:

Q: The most conveneient way to evaluate xx2-4 by substitution is to let x2- A True B) False

A: We have to find out

Q: To earn an A in a course, a boy must have a final average of at least 84%. On the first four…

A:

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy? = 2y® +…

A: To Find: Surface area of the region

Q: Find the indefinite integral. (Use c for the constant of integration.) (4t³i + 12tj – 8Vik) dt Need…

A:

Q: d,x+7 3. dx 2x-3

A: To find: ddxx+72x-3

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwise.…

A:

Q: We have a piece of cardboard that is 14 inches by 10 inches and we're going to cut out the corners…

A: We need to determine height of the box.

Q: Solve for the derivative of the following composite functions. f(g(x)) = (x + 4)5 1.

A:

Q: A projectile fired downward from a height of 112 ft reaches the ground 2 seconds. What is the…

A:

Q: 3. Find the area of one of the sine curve.

A:

Q: Which of the following is an antiderivative of f (x) = 52x? O (In 5) 52z – 1 52z +3 In 5 52 - 2 In 5…

A: we have to find anti derivative.

Q: Find the arc length of the graph of r(t) = ev2'i + e-V24j+ 2tk, 0<t< v2 In 9 NOTE: Enter the exact…

A:

Q: A cylindrical can is being filled at the rate of at =3t" , h(t) describes the height of the…

A:

Q: Find the area bounded by the indicated curves. x = 2y2 - 1, x = y2 + 8 For visualization, input the…

A: Topic:- application of integration

Q: 20 u(x) = 0.3e(0.5(-x+ 275.1)) + 3.62 21 v(x) = -1.2 log, (0.3(x – 269.73))+4.4

A: We need to find derivative.

Q: 2. Evaluate f'(5) for y = v2x² – 1

A:

Q: Find the differential equation whose general solution is y = c,x + Cze* . A. (x – 1)y" – xy' + y = 0…

A: The simplest approach to do this question is to verify through options.

Q: 6. Evaluate - x4 dx by making a substitution and interpreting the resulting integral in terms of an…

A:

Q: L (7+ 4)(x + 3)dæ = 74/3 %3D Select one: O True O False

A: The given integral,       ∫-11x+4x+3dx=743

Q: Determine if the following functions are odd, even, or neither. Provide reason. (a) f(x) = x² (b)…

A:

Q: A tank contains 3 kg of salt dissolved in 430 L of water. A salt solution of 0.01 kg salt/L is…

A:

Q: Find r'(t), r"(t), r(t)•r"(t), and r'(t) × r'"(t). r(t)-흑러 - 26 + (a) r'(t) (b) r"(t) (c) r'(t) ·…

A:

Q: A differential equation is considered to be ordinary itit has one independent variable None of the…

A:

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

A: