A freshly brewed cup of coffee has temperature 95°C in a 20°C room. When its temperature is 65°C, it is cooling at a rate of 1°C per minute. After how many minutes does this occur? (Round your answer to two decimal plad 23 x min

Q: evaluate the differential equation y- 2y +1 =0 if y(0)= 3

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Q: Find the solution to the initial-value problem. y' = −8x tan(y), y(0) =  ? 2 y =

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Q: Match each graph type with its corresponding function. 1. y= Exponential Function 2. y= log 4x Logar...

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Q: Case 3: non-repeate quadratic factor (x²-x-21) Example 1: S 2x3-x2+8x-4

A: Given

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A: Function which is differentiable for every value of x is

Q: Please include solutions, for me to understand it more. Thank you

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Q: Find u•v, where tetha is the angle between u and v llull=4, llvll=16, tetha=2pi/3

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Q: Find the indefinite integral. X COS 9TX

A: Given,I=∫ xcos9πx2dxPut u=9πx2Differentiatedu=9π(2x)dxdu=18πxdxdu18π=xdxThereforeI=∫xcos9πx2dxI=∫cos...

Q: d) Describe the continuity of this function and make a sketch of the graph.

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Q: A fourth degree polynomial with constant coefficients may have (1) 4 distinct real roots. (1I) 3 dis...

A: Topic:- polynomial

Q: 3. Given the following piecewise function (x² – 4x – 5, x # -3 13 – x, x = -3 f(x) = Determine the v...

A: As per the company guidelines we are supposed to answer only the first three subparts.Kindly repost ...

Q: Find the derivative of the vector function below r(x ) = sin (secx 2)i +csc°(Vx² +1)j +8tan(x")k 1 A...

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Q: Directions: Evaluate the following. Show ALL necessary solutions. x³+2x²-1 1. lim x--2 5-3x 2. lim v...

A: In this question we have to find the limits. Note: As per our policy we are suppose to do only 1st t...

Q: Find the solution of the differential equation that satisfies the given initial condition. dy y(0) =...

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Q: a . Use separation of variables to find the general implicit solution to the differential equation. ...

A: Answer: As per guidelines we can do only 1 question at a time so post other question separately , th...

Q: Consider vectors u and v. u = 4i + 2j,  v = 2i + 3j a.) Find the vector projection w = projuv of vec...

A: Us vector and scalar projection formula

Q: Write the first five terms of the sequence with the given nth term. 6. 3 + - = 10 + - n2 %3D a2 %3D ...

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Q: The derivative of the function y=f(x) at the point x=c is characterized as the of the function at x=...

A: We have to tell what is derivative of function y=f(x) at x=c called ...  a. Slope  b. Point of infle...

Q: Example 52. x log x dx.

A: ∫ xlogxdx ∫f(x)g(x)dx = f(x)∫ g(x)dx - ∫ (f'(x))∫ g(x)dx)dx   ∫ xlogxdx =∫ (logx)(x)dx              ...

Q: ind the equation of the osculating circle at x=2 for y= 1/4x^2-x. Draw the circle

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Q: (a) If point A(2, 4, 3) is the opposite vertex to the origin, then find the coordinates of the other...

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Q: 3. f(x)=2cot(x-→+1 Period: f(x) Vertical Shift Horizontal Shift Start End: Increments:

A: According to question,Given function,fx = 2 cotx - π2+1

Q: The function has a relative maximum of 16 at x=| 46 (Use a comma to separate answers as needed.) 42 ...

A: Here we see that critical points of f(x) is -2,0,2  

Q: 00 Σ n2(n2 + 6) n = 1 1. n2(n2+6) =L>0 converges

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Q: 2.2.7 Exercise Let X be a nonempty set and S the smallest o-algebra in X which contains all singleto...

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Q: Find the indefinite integral. sin 66 V cos 60 d

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Q: Write the equation for the linear function. A = {(x, y): (-4, 2)(-1, ) (1.).) Oy= - 2 y= - +1 Oy= Oy...

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Q: piecewise

A: Please refer to the image below

Q: (-2) = –3, g'(-2) = 6, (f g)'(-2) = 15. Find g(-2) %3D

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Q: (a) Find the equation of the tangent line to the curvey = 2 sec x – 4 cos x at the point (, 2) %3D

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

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(−1, 5...

A: Given, Centre =C(-1,5,4) And Radius , R=4  

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A: We have to find rational function for the given condation.

Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d. ...

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to d...

Q: Find the Taylor polynomials of orders n = and then find the nth Taylor polynomial for the function i...

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Q: Let f(x) = 2x° + 20x + 3. a. Find the values of x for which the slope of the curve y=f(x) is 0. b. F...

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Q: Find the Maclaurin polynomials of orders n=0,1,2,3  and 4, and then find the nth Maclaurin polynomia...

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Q: 7. Your friend, Jimbo, asks you for help with a homework question about derivatives, The following s...

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Q: 11. What is the slope of the tangent line to the curve y = 3x² – 5 at point (-1,-2)? %3D a. -5 b. -6...

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Q: Find all functions f : R → R for which f(x + y) − 2f(x − y) + f(x) − 2f(y) = y − 2

A: We are given that f:ℝ→ℝ, which follows: fx+y-2fx-y+fx-2fy=y-2 for all x,y∈ℝ.  

Q: 1. If y = V6x + 1, then what is Y? dy? %3D dx dy a. 2(6x – 1) 3(6x + 1)7 2(6x + 1) dy С. dx %3D %3D ...

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Q: 9. A thermometer reading 34°F is brought into a room with a constant temperature of 80°F. If the the...

A: Given: Newton's Law of Cooling: u(t) = T+(u0-T)ekt Where u(t): Temperature after time t T: Temperatu...

Q: 14. What is the first derivative of f (x) = (x²- 4)(3x - 2)? %3D a. 9x2- 4x – 12 С. 6х d. (x + 2)(x ...

A: first derivative of f(x) = (x2 -4)(3x-2) f(x) = 3x3 -2x2-12x +8 now df(x)/dx = 9x2 -4x -12 so answer...

Q: B) Find the derivative of the foiiowing: 1) y = 2sin2(5x) ,2) y = x, 3) xsin-14y = y tan-14x 4) y = ...

A: As per the company  guidelines we have to solv first 3 subparts if suborats are not mentioned  So fo...

Q: A function y(t) satisfies the differential equation dy =y4-5y3+ 6y2. dt (a) What are the constant so...

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Q: In the quadratic equation Ax2+ Bx + C=0 describe the roots when 32 -4AC is negative. The roots are r...

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Q: An air traffic controller is monitoring two small planes flying at the same altitude. One is flying ...

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Q: Find the derivative of each function by using an appropriate differentiation rule. 1) F(x)= sin(3 l...

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Q: А. Σ 5n –1 n=1

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Q: A Ferris wheel with a radius of 5 m is rotating at a rate of one revolution every two minutes. Exact...

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Q: Given the below differential equation, solve for the value of y(t) att = 3.8 s. 2.5y" + 11.2y' + 5.4...

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