Evaluate the integral. √²-144 y -dy, y> 12 ... Which substitution transforms the given integral into one that can be evaluated directly in terms of 0? O A. y = 12 sec 0 B. y = 12 sin 0 O C. y = 12 tan 0

Q: 33.y = cos²x

A:

Q: A baseball diamond has the shape of a square with sides 90 feet long (see figure). A player running…

A: A baseball diamond has the shape of a square with sides 90 feet long.A player running from second…

Q: Write the standard form of the quadratic function whose graph is a parabola with the given vertex…

A:

Q: Find the general solution of the differential equation, y" + 2y' + y = e 2x for x > 0.

A: The general solution to a(x)y'' +b(x)y' +c(x)y=g(x) can be written as

Q: Use a graphing utility to graph the quadratic function. f(x) = 2x² + 16x - 32 O -10 -10 -5 f(x) 10 5…

A: Standard form of quadratic equations f(x) = a(x-h) 2 + kWhere vertex: (h, k) Axis of symmetry x=h

Q: dz дz Find the values of and at the given point. дх ду 2z³-4xy + 5yz + 2y³ - 35= 0, (3,3,1)

A:

Q: For questions 3.11 to 3.14, you must use the definition of the derivative as a limit. Either use the…

A: The equation of a line passing through the point and slope m is

Q: Find the derivative of the function at Po in the direction of u. x-y xy +3' g(x,y) = Po(2,-2), u =…

A:

Q: Use the trapezoidal rule, the midpoint rule, and Simpson's rule to approximate the given integral…

A:

Q: The temperature T = T(x,y) in °C at point (x,y) satisfies Tx(1,8) = 2 and Ty(1,8)= -4. If x=e4t-4 cm…

A: The Rate of change of temperature is given as follows

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 20. dx (1 + 2x tan y)…

A: Differential equation:

Q: Ex 3.7.3: Differentiate each equation. 2x a) y = e²x (2x - 7)5

A: Given Function for differentiation is given as follows Chain Rule formula is given as follows

Q: USE INTEGRATING FACTORS 1. Find the General Solution: Answer is already given. 4. (y + 1) dx +…

A:

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 7. y'= x 4xy Solve by…

A:

Q: Consider the function y = 2e4. Which of the following statements is true for y? O y'=y Oy = /v O…

A: given,

Q: for g(x) = ln(1-x^2) and f(x) = sqrt(x + 3), determine the subset of the domain of g on which the…

A: To determine the subset of the domain of g(x)=ln(1−x^2) on which the composition f∘g is…

Q: identify whether it's a VSDE (Variable Separable DE), HDE (Homogenous DE), or EDE (Exact DE). 1.…

A:

Q: Solve the inequality to two decimal places where 0 ≤ x ≤ 2ñ, 4 cos(x) + 2 > T

A:

Q: g(x) = (5+3x)/(x−3) (a) What is the domain of g(x)? (b) Verify (with a sketch and/or short argument)…

A: The given function is

Q: An object travels with velocity function given by v (t) = 3t + 5. The next three questions refer to…

A:

Q: If x = 3 cot θ, use trigonometric substitution to write (sqrroot of 9) + x^2  as a trigonometric…

A:

Q: Find the area under the curve Y=2x-3 from x = 8 to = t and evaluate it for t=10, t = 100. Then find…

A:

Q: Find the general solution to y" – 14y' + 49y = 0.

A:

Q: Use the Second Fundamental Theorem of Calculus to find F'(x). • L₁ VE 4 + 4 dt Vt Step 1 F(x) = Note…

A:

Q: 1. Let a=⟨0,1,−5⟩ and b=⟨4,0,1⟩. Compute: a+b=⟨____,_____ ,_____ ⟩ a-b=⟨____,_____ ,_____ ⟩…

A: According to Bartleby guidelines we are supposed to do the first three sub parts of multiple sub…

Q: Determine whether the equation is exact. If it is, then solve it. 2e¹ (3y - 4t)dt + (7 + 6e¹) dy = 0…

A: The given differential equation is 2et(3y-4t) dt+(7+6et)dy=0

Q: Use a graphing utility to graph the quadratic function. f(x) = x² - 4x -10 O -10 -5 (x, f(x)) = S…

A: x intercept is the point where the curve crosses the X axis.

Q: Determine the following limits: (a) 42³-19z²+12z lim x 0 7x³-23x2-20x Number (b) 423-192²+12x lim x…

A:

Q: USE INTEGRATING FACTORS I. Find the General Solution: Answer is already given. 2.2(2xy +4y - 3) dx +…

A:

Q: 3. Let a=⟨4,5⟩ and b=⟨3,−4⟩. Show that there are scalars s and t so that ?a+?b=⟨−10,−28⟩

A: Note:-Since you asked multiple questions, according to our policy we can answer only first the…

Q: Let f(x)=2x²-16x + 9. a. Find the values of x for which the slope of the curve y = f(x) is b. Find…

A:

Q: Differentiate the following function with respect to x: f'(x) = f(x) = √5+x² 2x

A:

Q: Find the derivative of the function y defined implicitly in terms of x. 7xy³ + 2x³y: 2x³y = 1 dy dx…

A:

Q: Find a formula for the derivative of the function g(x)=3x2-1 using difference quotients:…

A: g(x)=3x2-1

Q: Find the limit. Use l'Hopital's Rule where appropriate. If there is a simpler method, consider using…

A:

Q: Determine whether the equation is exact. If it is, then solve it. e'(7y - 4t)dt +(3+7e¹) dy = 0 A.…

A:

Q: Consider the function f(x) = 2x³ + 3x² + z-4 Find the average rate of change of this function on the…

A:

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

A:

Q: 8. H(x)=4x7 - 6x² + 3x - 12 9. g(x)=6√x-2 10. -2-8 h(x) = 2x5+7x 2X

A:

Q: Evaluate the integral using the following values. 6 6 ["x³ dx = 320, [°x dx = 16, ["dx = 4 b [kf 6…

A:

Q: Find the derivative of the following function. y = 9x 5 2 + 2x 1 2 + x -2

A:

Q: ·N 2 v(t) @. 3 An object moves with velocity function v (t) = sin(t) during the time interval [0;…

A: The given velocity function  during the time interval

Q: 2. Let z= x²sin2y дz Compute (a) дх (b) дz ду

A:

Q: (1) Evaluate solution= Hint: Express cos a in terms of sin a. Then use the substitution usinx. Back…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies.…

A: Given that  where G,u and v are differentialblle functions

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,…

A:

Q: (a) (c)= dx (c) & √(x²). (e) d [ƒ(g(x))]= (g) (sin x)= dx (i) --(tan x) = dx d (k) (sec x) = dx (m)…

A:

Q: Solve the given initial value problem. O x²y² + xy³ = -18 Ox³y² +xy³ = 18 O x³y²+y³ = 45 Ox³y² - xy³…

A: The given differential equation is; dy/dx = - (3x2y+y2)/(2x3+3xy), y(2)=-3.

Q: y-values y-values 9- 8 7 6- 5 3 2 1 5 4 1 If f(x) = = f'(4) = g(x) h(x) 1 1 g(x) h(x)' then 2 3…

A:

Q: dx Assume that x= x(t) and y = y(t). Let y = x² + 3 and dt Find dy dt || dy dt when x = 3. (Simplify…

A: Given.