Convert the rectangular equation x2 + y2 = 45 to an equation in (a) cylindrical coordinates and (b) spherical coordinates.

Q: Find the Arc Length. y=sin(x), [0,π]

A: Given: y=sinx, x∈0,π To Find: Arc length Concept: Arc length of  f on interval a, b is:L=∫ab1+f'x2dx

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Q: Can you help me solve the questions (A) through (G) based on the equation at the top of the photo?

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Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

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Q: One side of a right triangle is known to be 20 cm long and the opposite angle is measured as 30°, wi...

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Q: Eliminate the parameter 0 in the following parametric equations. (This curve is called a hyperbola.)...

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Q: What are the first 5 terms of this sequence of partial sums?

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Q: Show that if acceleration is constant, then the change in velocity isproportional to the length of t...

A: Show that if acceleration is constant, then the change in velocity is proportional to the length of ...

Q: Consider the following function. f(x) = 16 − x2/3 Find  f(−64) and f(64).   f(−64)  =       ...

A: Given function f(x)     We have to find f(-64) and f(64)

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Q: The functionf(x) is Find the first derivative in fa Set up a number line with t increasing, decreasi...

A: The given function is fx=3x5-5x4. Find the first derivative of the function by the power rule of dif...

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Q: Consider z = Ax + By + D be the tangent plane to f (x, y) = 5x² + 10y³ + 6xy + 8x + 7y at (-0, 4). W...

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Q: Find the derivative: f(x) = cos 1 + e8x 1- e6x – ebz f'(x) =

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Q: Evaluate

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

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Q: The graph of the derivative f' of a continuous function f is shown below. (Assume f' continues to o....

A: ACCORDING TO BARTLEBY GUIDELINES, SOLUTION WILL BE PROVIDED FOR FIRST THREE SUBPARTS.

Q: What is the equation of the tangent line to xy – 3y = 1 at the point (4, 1)? (Express numbers in exa...

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Q: how to solve this problem?

A: We have to describe the triangular region whose vertices are 0,0,2,2 and -2,2

Q: Use a system of linear equations with two variables and two equations to solve.   210 students enrol...

A: As the question has only one condition in which 5 times the number of students passed as failed. so,...

Q: The bearing from point O to point P is the acute angle, measured in degrees, between ray OP and a___...

A: To fill in the blank: The bearing from point O to point P is the acute angle, measured in degrees, b...

Q: Q4

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Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Th...

A: Given polynomial function f(x)= 2x²-4x+3 Which is continuous and differentiable on [-1,3]

Q: Solve the equation. (List your answers counterclockwise about the origin starting at the positive re...

A: Consider the equation: z3+2=−2i To solve the equation:zk=r1ncosθn+2kπn+isinθn+2kπnwhere, k=0,1,2,3,…...

Q: 1 [3] b) Determine whether dx converges or diverges. Justify your answer 1+x?

A: According to the question, we have to determine whether ∫0∞11+x2 dx converges or diverges. If the in...

Q: Find the integral of t cos ti + t sin(t )j – te" k) dt 1 (t sint + cos t)i – cos(t² )j – e k + C | 2...

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Q: Theo and Sasha start at the same place on a straight road riding bikes with the following velocities...

A: (a) The velocity of Theo is vTt=10 for t≥0. Note that the velocity function dos not depend on the ti...

Q: Q9)The curvature of the circle * x^2+ y^2=9 is equal to 1/2 F O

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Q: -f(x) = x* – 6x³ –+ Vz7 %3D f'(x) = %3D id x5

A: Given,            f(x) =72x4 - 6x3 -2x5+x73

Q: Write z1 and z2 in polar form. z1 = 6V3 - 6i, z2 = 12i 21 = and 1 2 Find the product z1z2 and the qu...

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Q: Please help explain D and its subsections

A: Solving part D as requested. Given: A'10=A'20=0Bt=0.5At+t2-10t-100 The graph of A''(t) is given as:

Q: A 200-foot cliff drops vertically into the ocean. If the angle of elevation from a ship to the top o...

A: Given that: A 200 - foot cliff drops vertically into the ocean. Angle of elevation from a ship to th...

Q: In a large on-the-job training program, half of the participants are female and half are male. In a ...

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Q: Find the integral t5sin

A: let  I=∫t5sin(t6)dtsubstitutet6=udifferentiate6t5dt=duort5dt=16du

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Q: 6) a) show that Sx dx is divergent b) Show that Lim = 0. This shows we canuat xdx -- define = im f(x...

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Q: Let f(r) = -4(x – 2)³ + 1. Find a formula for f-1.

A: We plug f(x)=y, then switch x and y f(x)=-4(x-2)3+1 y=-4(x-2)3+1x=-4(y-2)3+1

Q: The position of an object in circular motion is modeled by the given parametric equations. Describe ...

A: x=7sint, y=7cost. Now, x2+y2=49sin2t+49cos2t⇒x2+y2=49sin2t+cos2t⇒x2+y2=491⇒x2+y2=49⇒x2+y2=72 Compari...

Q: Convert the polar equation to rectangular coordinates. (Use variables x and y as needed.) θ = 4π

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Q: Let f(x)=x2−10x+6f(x)=x2−10x+6. Find the critical point cc of f(x)f(x) and compute f(c)f(c). The cri...

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Q: Calculus is a powerful tool used in economics. One of the initial applications areas is the study of...

A: Given,           C(x) =20x - 10x - 5

Q: Find the surface area of revolution about the x-axis of y=3sin(7x) over the interval 0≤x≤π

A: To find the surface area of revolution about the x-axis of y=3sin(7x) over the interval 0≤x≤π.

Q: Let g(x) = 5x - 2 + |x + 4|. Find all values of a which satisfy the equation g(a) = 4a + 6. The answ...

A: g(x) = 5x-2+|x+4| Case 1 When x>-4 gx=5x-2+x+4      =6x+2ga=6a+2 Given g(a)=4a+6 ga=6a+2=4a+62a=4...

Cylindrical Coordinate System

The distance from a selected reference axis, the direction from the axis relative to a selected reference direction, and also the distance from a selected reference plane perpendicular to the axis area unit, all accustom outline purpose positions in a cylindrical reference frame. Counting that the aspect of the reference plane faces the purpose, the latter distance is expressed as a positive or negative variety.