What is the rectangular form of the polar equation: r = 4sin(θ)

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: given the differential equation (cos x + 2xcos²y) dx + (6y2 - x²sin 2y) dy

A: The given differential equation is:

Q: Down hill 109 cm / 4.42 sec = 24.66 cm/sec 63 cm/2.54 sec = 24.80 cm/sec

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Q: Find the area of the region in the first quadrant bounded above by y = √x + 2 and below by y = x.…

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Q: How would you express the equation of a sphere with a center at the origin (0, 0, 0) and a radius of…

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Q: If polynomial 4x^3 -12x^2 + kx + 4 = 0 has root at x=2. Calculate exact values of other two roots

A: As the given equation has a root x=2. Then, we need to put it, to find the value of k. , Now put x=2…

Q: 1) Consider the function z = x² sin(ny) +; xy² a. Find the partial derivatives. b. Find the tangent…

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Q: Draw a sketch of the graph of f(x) = 2√x + 1 − 1. Explain the trans- formations of the graph of…

A: Explaination of the answer is as follows

Q: 3. Find the equation of the line or plane ( c) The line that is perpendicular to the line 2x-3y +1=0…

A: Find The Equation of the Line or Plane :c.) The line that is perpendicular to the line 2x – 3y + 1 =…

Q: Find the volume of the solid obtained by rotating the region bounded by y = 4x², x = 1, x = 2 and y…

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Q: The base of a three-dimensional figure is bound by the line y = 2x + 3 on the interval [1, 3].…

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Q: 3 y=-andy=1 8 7 4

A: For horizontal asymptotes then compare the both numerator and denominator

Q: X J1 √x +3 da

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: In Exercises 23-38, either use the formula for the sum of a geometric series to find the sum, or…

A: The given series is? 1+1/6+1/62+1/63+...Find the sum and the series is converges or diverges.

Q: stance in between the point P

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Q: Consider the following cost function. a. Find the average cost and marginal cost functions. b.…

A: C(x) = 0.04x^3 +0.02x^2 +30x +90, 0< x < 1500, a = 1000The marginal cost function is the first…

Q: Given f(x) = 7x - 6; x < 6 x ≥ 6, 4x + 3 ; Find: lim x →6 f(x)

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Q: formula

A: Solving the problem

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: Evaluate f(3) for the function f(x) = -ex: 3 O -10.048 O 20.086 O -20.086 O 10.048

A: We are givenWe have to find

Q: 37. 78 - 49 343 + 64 512 25 5 - 3 2401 4096 9 + ... 27

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Q: determine convergence or divergence using any method covered so far.

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Q: 27. (u + 2)(n-3) du 29. f. 2+² dx 28. f*(4-1)√1 dt 30. f²₁ (3u-2)(u + 1) du

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Q: A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 7x+3y-4z+8=0, determine: 6. For the plane (a) its z-intercept. (b) one vector equation of the plane.

A: X/a + y/b + z/c = 1 is intercept form of plane

Q: Determine whether the alternating series converges. k + 1 9k + 1 Σ(-1)²+1, k=1

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Q: (1-x)y' + xy = x(x - 1)²

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Q: An? + 15η n=23n – 5n2 – 17 1= 75. Σ

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Q: Complete the square and find the indefinite integral. (Use C for the constant of integration.) x² √…

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Q: (16) A ladder 13 ft long rests against a vertical wall. If the bottom of the ladder slides away from…

A: Solving the problem

Q: 1. Describe in words the region of R³ represented by the equation or inequalitie (a) -1<r<5

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Q: 5. Given a = 47 - 7k in R³, determine a) a in component form b) la (exact value)

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Q: Find a general function for an arithmetic sequence with a6=2 and a12= -16

A: To find a general function for an arithmetic sequence with  and .

Q: Find the area of the region bounded to the right by x = y + 2 and to the left by x = y². + 543-2…

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Q: 1) Find: lim x→ 4 x² - 16

A: We are required to find:

Q: (9) Find the derivative: f(x) = cos(lnx) + log₁0 x

A: 9.The function is

Q: Determine the intervals where the following functions are continuous. 3. f(x) = √25-x² 4. g(x)= x²-9

A: Continuity of a function:A function is continuous at a point if the function is defined at that…

Q: dy dx a) y = 4x² cosx Find Simplify. 2 tan x b) y=- X

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Q: A school's Phys Ed department is selling activewear to raise money for new equipment. They are…

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Q: evaluate the following limit

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Q: 9. Determine the value(s) of k such that (2k, 3, k + 1) x (k-1, k, 1) = (1, -2,2).

A: (2k, 3,k+1)*(k-1, k, 1)=(1,-2,2)Find the value of k.

Q: Find the vertical asymptotes (if any) of the graph of the function. (Use n as an arbitrary Integer…

A: A vertical  asymptote is a line x=a where the graph tends towards positive or negative infinity as…

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Q: Find the area under the graph of y = x + 2 on the interval [-1, 2]. ਲਗੀਆਂ 54-2-1 1 2 3 4 5 3 4 n

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Q: f(x) = In(2x + 4), 9x - k, x -1

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Q: x1 x³ - 1 D)] sin x - cos x 13. tan x - 1 Svig SIUSI PH e21 HI -1 15. lim lim x→/4 We

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Q: 8. (a+b) The angle between vectors a=3 units and units anda is 90°. Calculate 5 to one decimal…

A: The angle between vectors  and  is 90 degrees.

Q: Calculate the double integral. J (2y + xy-2) dA, R = {(x, y) | 0 ≤ x ≤ 2,1 ≤ y ≤ 2}

A: We have been asked to calculate the double integral.Region

Q: Use the graph below to find the indicated limits. If a limit doesn't exist, state DNE. If v doesn't…

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