It is determined that the temperature​ (in degrees​ Fahrenheit) on a particular summer day between​ 9:00a.m. and​ 10:00p.m. is modeled by the function f(t)=−t2+5.9t+88​, where t represents hours after noon.   What is the maximum temperature​ reached?

Q: 1. Evaluate the line integral I = = [v¢4x° + y*) dx + x(2x° + 3y*) dy] around the ellipse x/a? + y/b...

A:

Q: ly Find tue indefinive intgrel by making ful frebstitution x = 4sin O. de (16-x²) %

A:

Q: 2) Let r(t) = (t, t² , e'). Find an equation for the unit tangent vector T(t).

A:

Q: dy + 4y = 8 dy d. x- dx = (x – y)² %3D a. dr dy e. da dy + 4y = x? %3D b. = V1+x2 %3D dx dy dy c. dr...

A: This can be solved as follows:

Q: A container with square base, vertical sides, and open top is to be made from 1000 ft2 of material....

A: Let the container has a base side "x" and height "y"

Q: 6. S Ve3x + e4x dx

A: 6.∫e3x+e4x3 dx∫e3x+e4x13dx

Q: 2 V = 5500 find (1- 50 0<t< 50 the cate which water drains at tme (rate must be nesative).

A:

Q: 5/ 2 Vx 4. f (x) 4-3x ||

A:

Q: 8. y = In(x + Vx² +1)

A: According to given, only 8 is solved  

Q: TT(e-1) В. 2.

A:

Q: Find the goneral Solution: HW auswr メピー=C

A:

Q: Find the local maxima, local minima, and saddle points of z = f (x, y) = x2 + y* + 2xy Identify a,y,...

A:

Q: Consider

A: Please refer to the image below

Q: You record the temperature every hour from midnight until​ 8:00a.m. You see that the temperatures​ (...

A:

Q: Consider a particle moving along the x-axis where x(t) is the position of the particle at time t, x'...

A: According to the problem, we have

Q: Use an appropriate test to determine whether the series given below converges or diverges. 00 2n Σ 7...

A: We can test the convergence as below.

Q: / V16 – x² dx, we use Select one: O x = 4 sec 0 O x = 4 sin 0 O x = 3 sin 0 O x = 3 tan 0 O None of ...

A: The integration of the integral is√(16-x2).

Q: 2. Matching type: Match the functions in Column A with their corresponding antideriva- tives in Colu...

A: so in column A is given the derivative of column B so we derivate the column B a F(x) = 3x3 - x now ...

Q: show, by direct substitution, that the given functions y1(t) and y2(t) are solutions of the given di...

A: Given differential equation y''+4y=0  y1(t)=cos(2t)     , y2(t)=sin(2t)

Q: I ind the second derivative(y") of the following functions and simplify the final results. 1. y = x3...

A: Given y=tan-12+x1-2x To find y'':

Q: Find the centroid (a, j) of the region bounded by: 7а? + 5a, у — 0, г %3D 0, and x = 9

A:

Q: +o0 ΣΗ 1 -3 -1-n n=1

A:

Q: Let S be the sphere of radius 3, centered at the origin, oriented outward. [x³ + 2 sin(z)] y3 – 10xz...

A:

Q: Find the area of the triangle with the given vertices.     (−1,−1), (5,−1), (2,5)   The area of the ...

A: Area of triangle = 12x1y11x2y21x3y31 x1,y1=(-1,-1)x2,y2=(5,-1)x3,y3=(2,5)  

Q: 2+x 9 y = Arctan(- 1-2x

A:

Q: Use an appropriate test to determine whether the series given below converges or diverges. 00 In (n ...

A: We have to find if the given series converges or diverges.

Q: sinh (5) = %3D (A) 5+ v26 (B) In(5 + v24) (C) In(5 + v26) (D) 은 (E) 5

A: We can find the correct option from the answer as below.

Q: Write an equation for the line through center a circle (x2 + y2 + 4x+6y = 3) which make an angle) wi...

A:

Q: sinh (5) = %3D (A) 5 + V26 (B) In(5 + /24) (C) In(5 + v26) (D) 8. (E) 5

A: Use the definition of hyperbolic of sine function. 

Q: Find tue indefinike insegred. Jcostex) sin'ces) de 3 6 (os (2x) Sin

A:

Q: Let g(x,y) = x³ – 6x² – y* + 5. Find and classify the critical point(s) of g.

A:

Q: Find a power series representation for the function. (Center your power series representation at x =...

A:

Q: 4x 1. Зу': y? %3D

A:

Q: ( 2 + x², -2 <x< 0 4 f(x)dx; f(x) = 1 ·x + 2, 1. 0<x< 4 -2

A: ∫ xn dx = xn+1n+1 +C ∫ab f(x) dx = ∫ac f(x) dx + ∫cb f(x) dx , where , a&lt;c&lt;b.

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by ...

A:

Q: Ge Given revenue and cost functions R(q) = 70q - 0.4q and C(g) = 14q + 550, find the maximum revenue...

A: Given problem:- Given revenue and cost functions R(q) = 70q -0.4q² and C(q)= 14q+550, find the maxim...

Q: f(x) = x* – 72x2 Enter the critical points in increasing order. (a) Use the derivative to find all c...

A:

Q: Evaluate the given integrals. ex dx 7. e 2x+2ex+1

A:

Q: (1) Use the divergence theorem to evaluate F-S. where F (z, y, 2) = zzi – j+4:k and S is the surface...

A: we use divergence theorem for finding the surface integral.

Q: 7. Find the volume of the solid formed when the graph of the region bounded by y = e, x = 0, x 2, an...

A:

Q: Simplify the expression sin(-0) cos(0) csc(-0) to a single trigonometric function.

A:

Q: Suppose the temperature of a metal plate is given by f (x, y) = the temperature of the metal plate i...

A:

Q: B Graph the follo wing y, = 2sec2x %3D Yz = 1-25in (x+ ) Y3=2 cotx

A: We know, sin(x+π/2)= cosx Given functions, y1 = 2sec2x y2= 1-2sin(x+π/2) y3= 2cotx

Q: Find the first derivative of the given functions: 1.)  x=(Arcsinh(1-b))2   2.) y=e-xcosh ln(x)

A:

Q: e. Find the area under the curve y = vx + 8 from x = -8 to x = 4. Give exact answer.

A:

Q: Solve the differential equation y - X) - + sin + sin (* y'

A:

Q: By substitution u = x² + 5x, the definite integral (2x + 5) ln (x² + 5x) dx becomes Select one: O No...

A:

Q: True or False; In the partial fraction decomposition, x + 8 A В D + x(x – 1)(x + 3) х — 1 x + 3 - we...

A:

Q: - y = (2x² – 4x + 1)60

A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 5. y- Br*-+습

A: