find dy/dx and dy/dx2, if : x = a(cosθ + θsinθ) and  y = a(sinθ - θcosθ)

Q: A trough is filled with a liquid of density 8232 N/m3. The ends of the trough are equilateral…

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Q: f(x) = x³, y = 1, x = 1

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Q: A thick cable, 60 ft long and weighing 180 lb, hangs from a winch on a crane. Set-up the integral…

A: To find the work done.

Q: dx Using Rationalizing Substitution S- -=Sf(y)dy, find ff(y)dy- X√√x-1

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Q: 7. Differentiate y = log10 (x² + 1)² b. 4xlog10e x²+1 a. 4x(x² + 1) c. log e(x) (x² + 1) d. 2x(x² +…

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Q: Using Rationalizing Substitution · √ √x + 10 x+2√x +In(√√x-1)² +C °√x (√x + 4) + In (√x - 1)² +C…

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Q: 3. Find the derivative of y with respect to the appropriate variable. x y= 6sinh :

A: Solution: y=6sinhx3

Q: Evaluate the integral: S dx (x+6)(x-4) ← +C

A: Given problem:-

Q: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

A: find the equation of tangent and normal to the curve √ x-√ y=1 at (9,4)

Q: TYPEWRITTEN

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Q: Evaluate the integral given below. Check your answer by differentiating. NOTE: Enter the exact…

A: We have to find value of given Integral.

Q: The volume for solid of revolution between curves is the volume of the object between a curve f(x)…

A: We have to find the volume.

Q: Find the sum of the geometric series below: 5 5 5 + + 5+ + 3 9 2187 49200 A 6561 5465

A: Topic:- sequence and series

Q: 1 4. Differentiate (x² + 2)/²/2

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Q: Set-up the integral using vertical element for the volume of the solid obtained by rotating the…

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Q: Suppose that 3 of work is needed to stretch a spring from its natural length of 30 cm to a length of…

A: we know the work needed to stretch the spring W=12kx2 where x is the elongation. x=xf-xi=45-30=15…

Q: Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of…

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Q: 5. Use the arc length formula to determine the circumference of the circle defined by the equation…

A: To find the circumference of circle

Q: √x²-1 The value of the definite integral / dx is in the form F(b) - F(a), where a and b are the…

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Q: -1 33x 0 43x dx

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Q: √x+1 Using Rationalizing Substitution ·S= -dx = y2 + 4y+ 4in(y-1) + C, express the final answer in…

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Q: the sum of two numbers is 40. express their products as a function of one of the numbers.

A: Let's express product of two numbers as a function of one number.

Q: A helicopter takes off at an initial (ground) velocity of 175 km/h toward the west, climbing at an…

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Q: 1The graph of the volume for solid revolution between the curves y = x+1 and y = O around the x -…

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Q: Evaluate the given integrals. Please Show the complete solution. Then identify the u, du, and other…

A: hhh

Q: The demand for a certain type of cosmetic is given by p= 160-x, where p is the price in dollars when…

A: (a) Given that, the price demand function is p=160-x. Obtain the revenue function.…

Q: You are saying the scale factor the donut needs to be dilated is 25/1 And The glaze needs will be…

A: Given ,  A donut shop makes donuts that serve 1 person each. For a party the baker is asked to make…

Q: 4. Determine the CORRECT partial fractions for Ax+B C A. + (x²+9)² (x-3)² A B B. + (x²+9)²(x-3)²…

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Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A: The given function,       3x2+y3=2y2-x3y

Q: Evaluate the given limit of the following: lim (et + t)¹/t t-0+

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Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

A: find out the derivative of the function.

Q: At noon, ship A is 170 km west of ship B. Ship A is sailing east at 40 km/h and ship B is sailing…

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Q: e circular disk method is to be used to compute for the volume of the solid gene revolving the…

A: Top:- application of integration

Q: Determine the derivative of the following implicit function on a separate sheet of paper, assuming…

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Q: 14 Lys 9 -25+ dy = Vy

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Q: A cone-shaped water reservoir is 10 feet in diameter across the top and 12 feet deep. If the…

A: We have to find the work

Q: differentiate y = ln(lntanx)

A: y=ln(lntanx) We know that, ddx(lnx)=1x

Q: Use the graph to find the following limits. a. lim f(x) b. lim f(x) x--3 x-1 (...) a. Find lim f(x)…

A: Limit of a function at a point will exist only if right hand limit is equal to left hand limit of…

Q: Use the second curve fitting criterion to minimize the sum of absolute deviations for the model y =…

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Q: Find a. (2x), a. .(2x) y and b. (2л, -2,-2) 11 Əw at the point (x,y,z) = (2, -2₁ - 2π) if w = x² +…

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Q: A milk truck carries milk with density 64.6 lb/ft3 in a horizontal cylindrical tank with diameter 6…

A: Please see the below picture for detailed solution.

Q: 5. Given the Standard Equation the DE, Identify the roots * d²y d³ y dx³ dx² + dx - 2- m: 1+ √2,0…

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Q: Let C(x) be the cost to produce x batches of widgets, and let R(x) be the revenue in thousands of…

A: Solve the following

Q: Evaluate the integral of the following: cos³ x+8 sin x cos²x+6 sin² x 2 cos²x -dx; cos x = 0

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Q: Given cos(8): = B 5 and the terminal side of 8 lies on the fourth quadrant. What is the value of sin…

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Q: Find all critical points of f(x) = 1 + 10x - x² and use the First Derivative Test to determine…

A: We are given f(x) = 1+10x-x2 We have to find critical points of f(x) and using first derivative test…

Q: a + bx² 3ax + bx³ - dx

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Q: Find x rounded to one decimal place. X = 30° 3 X

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Q: Evaluate the integral : S - (9x²+7x) (x−1)(x+1)² dx ← +C

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Q: dy dx 4x + y 2x+y

A: