Rewrite the Cartesian equation r(0) = Enter theta for if needed. = 3 as a polar equation.

Q: (d) Given r(t) = (ln(t+1), t cos 2t, 2¹). (i) Find r'(t). (ii) Find parametric equations for the…

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Q: 11. y = tan e³x + etan3x

A: We can find y' as below.

Q: Find the determinant of the matrix, O2²-12-13 O22-12+13 O²+12+13 Oλ-13 2-11 4 6 2-1

A: Determinant , λ-11λ-1-24 λ2-11λ-λ+11-24 λ2-12λ-13

Q: Basic Ca Derivatives Water is being poured at a rate of 5m^3/s into an inverted conical tank of…

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Q: Question Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 2), and (3,…

A: Given problem:- Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 2),…

Q: -1 2 (x² +1) dx

A: To evaluate: ∫x6-1x2+1dx Let I = ∫x6-1x2+1dx Using polynomial division we get  I = ∫x4-x2+1-2x2+1dx

Q: and A solid is generated by rotating a plane region that is bounded by the curves y = 2² = y about…

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Q: Find the area of the surface obtained by revolving the graph of x = y³ on the interval [0,1] about…

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Q: A = 15-6 14 53 2, b= 22 12 9 -6

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Q: Find the area bounded by the curve r = 2-cos 8.

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Q: Problem 7 Ső S xvx² + 1 dx

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Q: 1. ²³(x³ + x) dx 3

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Q: B. In the diagram below, not drawn to scale, A, B, C and D are points on the circumference of a…

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Q: Calculate (31-2). 051 0142 743

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Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

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Q: Find the area bounded by y=-x²+1, y = − 2x+2, x=-2, and y=2 (A) 1/3 None of these B) 16/3 D) 4/3 E 5

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Q: a particle moves a long a straight line with equation motion s=t^2-3t+2. find the value of t at…

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Q: Evaluate the integral S (2x − 8)dx - x² - 6x + 18

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Q: What is the mass in both (a) slugs and (b) kilograms of a 4390-lb car? Answers: (a) m = slugs (b) m…

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Q: (e) Find the exact length of the curve. x = e cost, y = et sint, 0 ≤ t ≤n.

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Q: A 200 gallon tank initially contains 100 gallons of water with 20 pounds of salt. A salt solution…

A: We are given that in a 200 gallon tank , intially there was 100 gallon of water which contains 20…

Q: 21 The equation x2 + y2 = 5 has _______. a center at (5, 5) and a radius with a length of five…

A: We know that the equation of circle is: (x-h)2+(y-k)2=r2 where, (h,k)- centre of circler-radius of…

Q: Convert the point with polar coordinates 9, 3 The point is: C M 2 3 4 5 6 wend W е t 1 9 C $ % Oll y…

A: Given query is to convert polar to rectangular coordinates.

Q: the appropriate integral to be used to find the volume of the solid generated? 8 7 6 5 4 3 2 1 -1 O…

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Q: Q9- Find the turning points of the function f(x,y)=x^2+ 2xy and state whether the points are max,…

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Q: 1. Lim x-2 X x² - 4 x³ -x-6

A: Lets factor x3-x-6: x3-x-6=x3-2x2+2x2-4x+3x-6                =x2(x-2)+2x(x-2)+3(x-2)…

Q: Given the function F(x) = 2x 3 - 6, find the value F(-1). 10 -8 -4

A: Solution is done in step 2

Q: Points: A(2,1,-1), B(-3,0,1), and C(1,4,0) a.) find parametric equations of line that passes…

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Q: An elliptical plate, major axis 6 feet and minor axis 4 feet, is submerged vertically until its…

A: Follow the procedure given below.

Q: solve the following problems. Draw the necessary figures for each. The area bounded by the parabola…

A: The area bounded by the parabola y2+x-2y=1, the x‐axis, and the line x=2, revolves about the x‐axis.…

Q: Written Respons 1) A school's debate team consists of 9 students and must consist of at most 3 boys.…

A: team consist 9 student  maximum 3 boys it means 0 , 1,2,3 consider  total boy 12 total girl 9 so…

Q: Let f(x) = 2x³-9x² - 24x+2. a. Find all points on the graph of f(x) at which the tangent line is…

A: Topic = Derivative

Q: 1. Let f(x) be the cubic function graphed below and g(x) be the quadratic function graphed below.…

A: From the given graph of the region, we have to find its area

Q: Given: A R= 8√3 1 2 2√3 30° R 4√3 B

A: here right angle triangle is given  so here we apply sine rule to find the R   sinA = opposite…

Q: 8 Find the area bounded by y y = 2x, y=0 and x = 3. X Using vertical element, what is the integral…

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Q: A region in the first quadrant is bounded by the curve >= 1+ sin²x, the coordinate axes and the line…

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Q: Sketch the graph of each quadratic function and identify the vertex, direction of the opening of the…

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Q: Write the equation of a circle with a center at (2, -3) and a radius of 4. ( x - 2) 2 + ( y + 3) 2…

A: To write the equation of a circle with a center at (2, -3) and a radius of 4.

Q: H.w: Find LT-¹ of the following functions by using partial fraction method: 2- Find L-1 [s³ +S-1 Ls²…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: dy dx + y = 2xy-ex

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Q: ضوع الشرب Please prove it Sin Cos +1 = 1 + sin Sin + Cos - 1 Cos ##

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Q: (D² + 3D + 2)y= sin ex

A: The given differential equation is  (D2+3D+2)y=sinex

Q: Find the lower sum for f(x) = +4 on the interval [-4, 0] using 2 rectangles. 10 "F Submit your…

A: Here we have to find the left sum of given function.

Q: Q2:Expand using Maclourin series (1 - x 1-x² 2 ln(1 + x4) )? -

A: As per our guideline we are supposed to answer only one question of  multiple type of questions.…

Q: 7. Evaluate the volume generated by revolving the area bounded by the given curves using the hollow…

A: The given curves are x=4y-y2, y=x.   Now find the point of intersection between the curves…

Q: Given the function G(x)=√x² - 4, G(x - 1) = √x² 2x 3 x² 3 x²+2x-3 x²-3 O

A: Solution is done in step 2

Q: B. Graph each equation. 1. 2y² + x + 8y - 4 = 0 2. x² + y² + 6x + 8y = -9

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Q: The graph C of the equation y = gives the course taken by an oil tanker after leaving port, which is…

A: Here we have to find the arc length.

Q: (a) √738(t - 4)dt (b) 738(t + 2)dt (c) √²38(t+4)dt (d) f²3x²8(t-4)dt (e) ¹3x²8 (t+2)dt -3 (f) ²3x²8…

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