1. A block of wood 10 ft from the bottom of a long, very smooth inclined board slides downward (from rest) under the action of gravity only. Find how long will it take the block of wood to reach the bottom of the board. Also, determine its terminal speed. The angle of inclination of the board is 10° with the horizontal.

Q: Find aw/as and aw/at using the appropriate Chain Rule. Function Values w = y³ - 5x²y x = es, y = et…

A: Given query is to find indicated partial derivatives.

Q: 1. Consider the DE d'y dx2 - 2 dy − 3y = −9x − 3, y(0) : (0) = ² – 1. - dr Verify that y =…

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Q: The area of the region bounded by the two curves y = x² and y = 16 is Square Units

A: To determine the area of the region bounded by the two curves y=x2 and y=16.

Q: Find the curvature of the curve r(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 Give your…

A: The given curve is  r(t)→=4cos(2t), 4sin(2t), 2t

Q: A 6 foot tall person walks away from a 14 foot tall lamppost at a constant rate of 2 feet per…

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Q: Set up but do not evaluate an integral for the volume of the solid obtained by rotating the region…

A: Topic = Volume

Q: Find the volume of the parallep lapiped with adjacents edges PQ, QPR, PS where PLO, -4,₁-4), Q (²-1,…

A: Concept: The volume of a parallelepiped with adjacent sides PQ, PR and PS is given by,…

Q: c. ( - 1 - 2 - 2 ) : ( - 1 - ₁ ) × (1 - 1) = C. 5 3 16 2

A: Concept: A situation is represented using mathematical symbols, variables, and arithmetic operations…

Q: Let 2 sinx+7cos y = 6. dr

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Q: For a given commodity and pure competition, the number of units produced and the price per unit are…

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Q: The reproduction function for a whale is estimated to be f(p) = -0.0005p² +1.02p, where p…

A: Given,          The reproduction function for a whale is estimated to be                     f(p) =…

Q: Find the unit tangent vector to the curve at the specified value of the parameter ()+8², ti T(1) -

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Q: Find the values of the following limit. If a limit does not exist, type DNE in the entry box. limx→9…

A: Given; Limx-9(x-9)/[sqrt(x)-3].

Q: 1. Compute the length of r(t) = (cos(t), sin(t), In(cos(t))) over the interval 0 ≤ t ≤ 4.

A: As we know that; The length of the curve of a vector-valued function rt=xt,yt,zt is given by:…

Q: Find the limit. 5) lim 3x²+7x-2 x- 3x² - 4x-2

A: We will find the required limit.

Q: Solve the DE. (1 + y²) dx + (1+x²) dy = 0 O tan x + tan y = C e + ey = C O lnx + lny = In C arctan x…

A: Topic = Differential equation

Q: Please

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Q: What is one solution to the trigonometric equation 3cosx - sinx + 3 = 0 in the interval [0, 2m]? 0 O…

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Q: A rectangular box is to have a square base and a volume of 81 ft3. If the material for the base…

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Q: Let f(x, y) = x² + 2y² List the critical points: 24xy. The critical point at the origin is a saddle…

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Q: Consider the following equations. f(x) √x + 3 1 g(x) +3 Sketch the region bounded by the graphs of…

A: Let's sketch the graph of functions and find area.

Q: Consider the following infinite series. Complete parts (a) through (c) below. IM8 Σ -|~ k=12 a. Find…

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Q: Provide the complete sign analysis using a table to clearly indicate the behavior of the function…

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Q: 5 Thass [[1(², 3)dA = [² [² fff(x, 0 1 drdo

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Q: HOMEWORK NO. 1 (A) Eliminate the arbitrary constants. 1. xsiny + x²y = c 2. ax² + x + y² = 0 3. y =…

A: We have to eliminate the arbitrary constant from the given expressions

Q: The area under the curve y = 3x bounded by the lines x = 2 and x = 14 above the x-axis is = Square…

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Q: A particle moves along the x-axis so that its position at time 0 < t < 18 is given by x(t), whose…

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Q: Given the vector-valued functions u(t)= esti+e-¹ + 2tk v(t) = 2ti - 3t² + 3k d find (u(t) v(t)) when…

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Q: Find a unit normal vector for the following function at the point P(1,−3,1): f(x,y)=x3 (Please show…

A: See the answer below

Q: lim x3 x²+2x+3 x+3

A: Given query is to find the limit of the expression.

Q: If f(4) = 13 and f '(x) ≥ 1 for 4 ≤ x ≤ 7, how small can f(7) possibly be? Need Help? Read It Watch…

A: See this solution in below.

Q: S Using the integration by parts method, 10x ex dx =

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Q: S* S* S*4cos(y) dydzdx 0 O 4r

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Q: Find the area of the region that is bounded by the given curve and lies in the spect r-eº, 37 ≤0≤ 31…

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Q: Suppose that the length 7, width w, and perimeter P of a rectangle are differentiable functions of…

A: Topic = Derivative

Q: 2. Find the speed of the object traveling along the curve r(t) = (t², sin(3t), cos(3t)) time t = 3.…

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Q: Find the following using the table below. 1 2 3 4 12 x f(x) 3 4 f'(x) 2 3 1 g(x) 2 1 3 g'(x) 2 3 1…

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Q: The area under the curve y= 7x bounded by the lines x = 8 and x = 17 above the x-axis is = Square…

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Q: The following table shows retail sales in drug stores in billions of dollars in the U.S. for years…

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Q: What are the zeros of the function f(x) = 2 - 4sinx? Ox-+2rn and x- Ox-7+ O 5x 6 Ox-+2rn and x- 3…

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Q: Find the area of the region included between the parabola py2 = x and the line x + y = p.

A: The solution is given below

Q: Evaluate

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Q: Use the Ratio Test to determine whether the series converges absolutely or diverges. 3(k!)² 5(2k)! 8…

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Q: x³ Find the absolute maximum and absolute minimum of the function f(x) = - 4x² + 12x - 5 over the…

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Q: 1. At all times, the length of the long leg of a right triangle is 3 times the length x of the short…

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Q: 1. Estimate y(1.4) with a step size h = 0.2. Answer: y(1.4)~ 2. Estimate y(1.4) with a step size h =…

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Q: D(x) = (x-8)², S(x) = x²

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Q: O Add and simplify. Ei (-8p'+4p5-8p+9)+(-6p² + 8p³ + p²) Check Answer X Ⓒ2022 Mc

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Q: Prove that the following differential equation: (1 + x2)y'' + 2xy' - 2y = 0 has the following…

A: To prove that y is solution of a differential equation then we just substitute the value of y' and…

Q: Find the area of the parallelogram with vertices P C0, 0, 0) QC 31-374) R(3₁-1₁ ~51 5C6₁ -4,-97

A: Concept: The area of the parallelogram ABCD is  Area=AB→×AC→