Find the displacement of an object on the interval 1 ≤ t ≤ 6 if its velocity is shown. 8.5 O 10.5 14.5 V(t) VCD t 9 10

Q: Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). What is the period of the…

A: Let's draw the graph of trigonometric function.

Q: Use the Laplace transform to solve the given system of differential equations. dx dt dy = 5x - y dt…

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Q: 14. Prove that AC B if and only if An BC= 0.

A: The objective is to prove the above question.

Q: f Find f+g, f-g, fg and - Determine the domain for each function. g . f(x) = 3x² - 17x + 10,…

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Q: . After one​ year,    ________​% of the information is remembered. ​(Round to one decimal place…

A: The function fx=80e-0.3x+20 describes the percentage of information, a particular person remembers x…

Q: Graph the function by setting the x-intercept and the asymptote. Provide your answer below: f(x) z 4…

A: We need to graph the function.

Q: In the following exercises, use direct substitution to show that each limit leads to the…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = -4t² + 8t + 5…

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Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 2n +4n in (2n) X

A: Follow the procedure given below.

Q: Consider the function f(x) = ($) ². a. Find the inverse of f(x). b. Explain why the inverse is not a…

A: Solution is given below:

Q: Write a recursive formula for an, the nth term of the sequence 3, 4, 11, -18, .... a1 an = Submit…

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Q: Consider the following initial-value problem. y" 5y' = 8e4t4e-t, y(0) = 1, y'(0) = -1 Find L{f(t)},…

A: We need to fill in the blanks

Q: Find the area between the curve of X = 5 4 3 2 1 1 2 3 O 2.749 O 3.296 4.159 4.957 4 5 33 and the…

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Q: 2. Which equation models a quadratic relation? Oy = 2x²+1 Oy: O y = x -3z y = 3x+1

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: We have to find  the volume of the solid that results when the shaded region is revolved about the…

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the…

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Q: In (x) Find the area of the region enclosed by the graphs of y = 2x (Use symbolic notation and…

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Q: Find the average value have of the function h on the given interval. h(u) = (9 — 6u)−¹, [−1,1]

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Q: Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

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Q: The equation of the tangent plane of the graph of function z = xy + 2x² - y3 at point (2, -1) is

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Q: (B) x = -and x = -3 14. On which interval(s) is the graph of f(x) increasing? (A) (-∞0,00) (B) (-∞,…

A: Note : as per guidelines we support only three subparts of the questions.kindly repost next…

Q: cote √3)2sin0 + √2) = 0 - The solution set is {60°, 240, 225°, 315°} (30°, 210, 225°, 315°} O{45°,…

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Q: A spring whose natural length is 14cm exerts a force of 53N when stretched to a length of 18cm. (a)…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = 2t² - 5 sin(4t)…

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Q: The graph shown is f(x) = In (x + 2). What is the integral function g(t) that defines the area under…

A: Given that, the function is fx=lnx+2. Note that, the area under the curve fx between a and b is…

Q: Use two methods to find the area bounded by y=e-1, y = 2e-1 and the y-axis y = x-x 1

A: The area is bounded by y = x/(1-x) , y = e-1, y = 2e-1and y -axis. The region bounded by curves is…

Q: Consider the vector-field F = (2 — ysinr − 1) + (cos x − y ). – - (a) Show that this vector-field is…

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Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

A: ft=t,0≤t<70,t≥7

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Recall: L-1s2s2+a2=cosat Given, L-116s16s2+1

Q: 2) (a) Differentiate the function by using rules. f(x)=7-3x² + 4x (b) 1 f(x) = √x + ¹ X

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Q: How is the series 5 + 8 + 11 + ... +77 represented in summation notation? 25 ΟΣ(3q + 5) q=0 17 ΟΣ(4q…

A: Given Series is  5+8+11+........+77

Q: Find the area of the surface generated by revolving the given curve about the y-axis. 8xy² = 2y + 1,…

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Q: Let E be the solid region which lies above the region in the xy-plane bounded the curves y = √x and…

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Q: - Problem 2: x³y"" − 3x²y" + 6xy' - 12y = 2x¹ + lnx

A: The given differential equation is;  x3y'''-3x2y''+6xy'-12y=2x4+lnx.

Q: Q10. Evaluate the following Integrals. b) /V+³ de sin (1/2) C) de

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Q: What are the values of x where tangent line of graph of f(x)=1/x is parallel to the line y=−5x+4.…

A: Follow the procedure given below.

Q: Which of the following formulas would be used to calculate the trapezoid approximation of 0.2 3 0 T₁…

A: Here we using trapezoidal rule.

Q: Find the area of the region bounded above by y AY -x² + 8 and below by y = x². ==

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Q: a) A population of insects at a rate of 200+10t+0.25t² insects per day (t in days). Find the insect…

A: Hence,  the population of insects after 3 days will be 682.25 => i.e. approximately 682 insects…

Q: 2-if y³ = ln xx

A: Please refer to the image below

Q: a. Find the nth-order Taylor polynomials of the given function centered at 0 for n = 0, 1, and 2. b.…

A: a. Given that, the function is fx=e-10x. Note that, the Taylor series expansion for the function fx…

Q: The first three terms of a sequence are given. Round to the nearest thousandth (if necessary). 6, 12…

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Q: T Sin ³ de 3 1-cose

A: I have stated the used formulas in the solution

Q: A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if…

A: Disclaimer:  “Since you have asked multiple questions, we will solve the first question for you. If…

Q: S² (4-x²)³2x² dx

A: I am attaching image so that you understand each and every step.

Q: Let f(x, y) O a) 64 / 27 Ob) 64 / 125 Oc) 27/125 d) 27/64 =X x√√x² - y². Then f(5, 4) = Oe) 125 / 64…

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Q: A 390-unit hotel is trying to determine their daily rates. From experience, the hotel manager knows…

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Q: The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula…

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Q: Find the total area enclosed between y = x³ and y = x over the interval [-1,9]. NOTE: Enter the…

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