Let the graph below represent an object's velocity as moves away from a sensor. At what time, in seconds, is the object furthest from the sensor? ↑v(2)

Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

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Q: Solve the linear differential equation dy y 2x2 dx

A: This ODE can be solved as follows:

Q: 5x-10 Find the area under the curve of f(x)=- 05 O-10In 2 O 5-10lm 2 0-5 from 1 to 2.

A: Solve the given

Q: Question 3 How much work is required to pump all the water from a right circular cylindrical tank,…

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Q: QI// Find the Area bounded by: x = -y2 and x =y-2

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Q: Find the equation of the final function after all the following transformations have been made on y…

A: The below image has all the steps

Q: Derivative of f(x) and derivative of g(x) are equal. Then f(x) = g(x). %3D Select one: O True False

A: Answer is given with example.

Q: 1. Jx cos 3x dx Sx² cos x dx 2.

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Q: 3 S(x) = 6x² + x – 7 Find the coordinates of the point of inflection on and prove that it is a point…

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Q: In a trend that scientists attribute, at least in part, to global warming, a certain floating cap of…

A: Given problem:- In a trend that scientists attribute, at least in part, to global warming, a certain…

Q: gra Ốf j at point (b) Find the directional derivative of f at the point (0,–2) in the direction of…

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Q: Find the Area bounded by: x = -y2 and x =y-2 %3D

A: This question can be solved using the concept of area bounded by two curves.

Q: 8. Determine if 2n-1 [5 -1 is cont 7n n=1

A: Given

Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

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Q: Which of the following is the Taylor series expansion of the function (x) =ex? with center at 0. 00…

A: Taylor Series representation of e-x about x=0 is given by, e-x=∑n=0∞-1nxnn!....(i)

Q: Suppose that , g(t) dt = v7 rg(x)] dx 1. g(r) dr 2.

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Q: Find the volume of a solid bounded by y=(x2 -4) and y=(2x - x2) about the axis y=-4.

A: formula : here

Q: 6. The initial population of a town was 12000. After 5 years the population increased to 38000…

A: Equation of population growth: P = P0 e^(at)

Q: A 16 cm x 10 cm open rectangular box is to be constructed by cutting square corners out of a piece…

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Q: 8. If the graph of h(x) goes thro following statements are true fc

A: 8) y=h(x)g =h(x)This transformation only affects y-value.A(-16, 4)y(x=-16)=4, g(x=-16)=4 =2A' (-16,…

Q: If å is a vector in the direction of S60°E, then draw its opposite vector and state the direction

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Q: x³+2x? -3x x²+4x+3 2) Evaluate lim -6-1. x→-3

A: Use l-hospital rule.

Q: >(6k – 4)(7k + 3) - k=1 Enter your answer as a number without any arithmetic symbols. Sum =

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Q: (4) Evaluate S SR e™y-2dA where R is the region enclosed by y = 4x, y = }, y = ± and y = 1.

A: Let's find.

Q: 2. Find the area of the region bounded by the curve r = 2 cos 30 .

A: Given problem:- Find the area of the region bounded by the curve r = 2cos(3θ)

Q: a) 2 B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (iv) a card…

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Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

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Q: TOPIC: OPTIMIZATION IN DERIVATIVES Directions: Read and analyze each problem carefully and solve for…

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Q: Let C be the parametric curve defined by x(t) = t2 – 2, y(t) = t³ – 3t + 1. Determine if C is…

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Q: Solve the following set of equations with LUdecomposition: 3x1 – 2x2 + x3 = -10 2x1 + 6х2 — 4хз — 44…

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Q: 44. V 3(-4V3. –2V3)

A: Given  Vector

Q: Evaluate y' of the given functions: 1. y = (x² – 2)(x + 3)

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Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: B: .A card is drawn from a well shuffled pack of 52 cards. Find the probability of: (iv) a card of…

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Q: A rectangle is bounded by the x- and y-axes and the graph of y = (6 - x)/2 (see figure). What length…

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Q: Find the focus of the parabola y = x 2 - 12x. (6, -35) (6.75, -36) (6, -35.75)

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Q: Consider the following rectangular box. F a) Give a pair of equal vectors. b) Give a pair of…

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Q: Solution

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Q: Find dy/dx: solution in handwritten 1. y = , Vu du

A: Note:- Here limit of integral 0 to t4  then in your question we need to find dy/dt instead of dy/dx…

Q: Find T(t) and N(t) at the given point. r(t) = (t² – 11)i + tj; t = 11 T(11) : N(11)

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Q: 10) Find T4(x), the degree 4 taylor polynomial of the function for f(x) = cos(5x) centred at c = 2n…

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Q: dr

A: To find integration.

Q: Without eliminating the parameter t, find a Cartesian equation for the line tangent to the curve C,…

A: Let's find.

Q: Find the four second partial derivatives. Observe that the second mixed partials are equal. z = 10xe…

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Q: 4. Find the volume of the solid that lies under the paraboloid z = x? + y² and above the region R in…

A: We want to find the volume.

Q: What is the area enclosed by the curve r = 2 cos 30? Answer is in square units. Use two (2) decimal…

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Q: 7x + 4 if x 1 |

A: Here, the given function is: f(x)=7x+4, if x<-2x2+1, if -2≤x<12-3x if x=11-x+x if x>1 where…

Q: dx = 4x +2y+e'+t dr Write the system in matrix form: dy - 2x - y+ 3e' di 4 A. X'= 1 4 B.X' = 2 -1 3…

A: We have to find the system in matrix form.

Q: 5. A line passes thru (3, 4) and cuts a right triangle with the coordinate axes in the second…

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Q: Analyze and sketch a graph of the function. Find any intercepts, relative extrema, points of…

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