Find a vertical line x = k that divides the area enclosed by x = square root of y , x = 2 , and y = 0 into two equal parts using a dy slice.

Q: Solve (2y³ – x³) dx + 3xy² dy=0; y(1) = 1 a. x² (5y³ + x³) = 4 y? (5y3 — r3) =0 x² (5y³ x ³) = 4 O…

A: Given that, the differential equation is 2y3-x3dx+3xy2dy=0.…

Q: lve y' = 14xy – 2x, y(0) = 11 x) =

A: Topic:- application of integration

Q: If 2x² + 3x + xy = 3 and y(3) = — 8, find y' (3) by implicit differentiatio

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Q: For a function y = f(x), show that the curvature is given by к(x) = Hint: Parameterize the function…

A: Show that the curvature is given by kx=f''x1+f'x232

Q: Evaluate the piecewise function at the given valuesof the independent variable. f(x) = { 5x+3 if x<…

A: Given piecewise function is  f(x) = { 5x+3 if x&lt; 0            { 4x+7 if x ≥ 0 We have to find…

Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9 [(u - 2) du Submit…

A: Topic:- application of integration

Q: 5. dy/dx = sin(x + y). ANS. x+c = tan (x + y). sec (x + y).

A: Please see the below picture for detailed solution.

Q: 8 S 1 Inxdr a. 0 b. 1 C. -1 ||

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Q: -4 -3 -2 -1 у 1 -1 -2 1 2 3 X

A: We can find the answer in the following steps.

Q: 1.Use interval notation to determine f(x)

A: Concept: The graph of a function: The graph of a function is the set of all points (x,y) in the…

Q: Cliff left point A at 8:00 A.M. walking east at 3 kph. Renz left point A at 9:00 A.M. walking north…

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Q: Need

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Q: Find the differential dy of the given function. (Use "dx" for dx.) √ dy y = 2√x +

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Q: This can't be correct because the equation of the tangent line was incorrectly transcribed.  The…

A: Note: Since, the student has asked to solve the given problem with correct transcribed way so that…

Q: 5. Which of the following expresses √175 in simplest form ? a) 5√2 b) 5√7 c) 7√5 d) 9√5

A: Given that, the number is 175.

Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

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Q: Find the area of the surface. The part of the plane 3x+2y+z=6 that lies inside the cylinder x² + y²…

A: Since, the equation of the cylinder is x2+y2=4 and  3x+2y+z=6⇒z=6-3x-2yParameterize the surface of…

Q: 7. Simplify the radical expression √7 a) 26 b) √35 c) 14 d) 196

A: The given radical expression is 7×28 use the algebraic properties, am×bm=abm

Q: Consider the function f(x) = 6x¹0+ 3x5 - 2x³ - 3. An antiderivative of f(x) is F(x) A is and n is…

A: The given function fx=6x10+3x5-2x3-3 use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C

Q: I. Find dy/dx of the following: COS X √4-3x² 7. y In- 8. y In, 6. y = In(In x) 9. y + ln xy = 1

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Q: Solve the differential equation [cos (2y) — 3x²y²] dx + [cos (2y) - 2x sin (2y) - 2x³y] dy - a. sin…

A: Given: cos2y-3x2y2dx+cos2y-2xsin2y-2x3ydy=0

Q: Find the exact length of the curve. r(t) = (51, 3cos (1), 3sin (1)), -4≤1≤4 OA. 16√3 OB. 0 OC. 8/26…

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Q: Suppose that p(t) is the growth rate of a population of bacteria at time t minutes. What does 15…

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Q: Use interval notation to determine where f(x)>0. 2. Use interval notation to determine where f(x)>6.…

A: The objective is to use interval notation to determine where f(x)&gt;0. 2 and use interval notation…

Q: 6) Evaluate 0.8 1 0 dx 4x² +4

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Q: [2re™² dr a. 2xe*² + C b. x20x³ 3 @. ex² + C d. x²e² + C + C

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Q: 70. S tan-1 x dx 1+x²

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Q: Convert the following equation to Cartesian coordinates. Describe the resulting curve. r= - 4 cos…

A: We  have given polar equation  r=-4cosθ-6sinθ Using cartesian equations x=rcosθ y=rsinθ x2+y2=r2 Put…

Q: Evaluate the following integral using trigonometric substitution. 2 x dx 2 (49+x²)² S What…

A: Given ∫x2dx49+x22

Q: 14. 2y dx + x(x² In y − 1) dy = 0. -

A: To find the solution of the given differential equation.

Q: S 3 T 2 For the above rational function f(x)= 3 Q 17 2x² +2.5 . identify the interval on which f is…

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Q: 1. A ball is thrown upward from the top of a 12 meter high building at a speed of 25 meter per…

A: Given quadratic equation is H(t) = -17t2 + 25t + 12

Q: Evaluate the following integral using integration by parts. Sxe ³x d dx Use the integration by parts…

A: We have given to find integral  ∫xe3x dx Let,  I=∫x e3x dx Using integration by parts ∫u dv=uv-∫v du…

Q: A woman standing on a hill sees a flagpole that she knows is 70 ft tall. The angle of depression to…

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Q: A manufacturer can produce 4320 cell phones when a dollars is spent on labor and y dollars is spent…

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Q: etermine whether the following relation represents y as a function of -4 -3 -2 -1 y 1 -1 -2 2 3 1 2…

A: Topic:- function      Definition :- The domain is the set of all the input values of a function and…

Q: Solve the differential equation dy da - y²+7xy+16x² x² a. x + y = O b. x Y = ; when x = 1, y = 1 5…

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Q: Question 13 (1 point) ✓ Saved Which of the following CANNOT be an acceptable direction vector for…

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Q: Jeu with the top of the building.) Two sides of a right triangle ABC (C is angle. Give an exact…

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Q: 4x² - 4x + 6 1x²³ + x² - 6x 3 use partial fraction

A: The objective of the question is evaluate the indefinite integral help of partial fraction.

Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: We have to solve the integral

Q: Consider the region R bounded by the functions f(x) = 3x and g(x) a. (4,2) b. (4,1) c. (22², ²) C.…

A: Region R is bounded by the functions f(x)=3x, g(x)=x2+2 Their intersection points…

Q: Question 7 (1 point) ✓ Saved The point (1, 2, 4) is on the line 2+³ = 1+4 = 25 True False

A: We have given equation of the line x+35=y+44=z+53 Put x=1,y=2,z=4 1+35=45 Similarly, 2+44=64=32…

Q: Consider the function f(x) = r? – 5 +4 x + 1 a. Find the first derivative. f'(x) = b. List any…

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Q: [1/3 Points] f(x) = DETAILS PREVIOUS ANSWERS Find an expression for the function whose graph is the…

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Q: Let R be the region bounded by the following curves. Find the volume of the solid generated by…

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Q: functions f (x) = 2 and g(x) = 1 (i) Consider the (a) Write down the domains of the functions f (x)…

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Q: 3 Compute the rotated area bounded by x = y, x = 8 and x-axis about y-axis

A: Please note that as mentioned only the last question is solved.

Q: Let R be the region bounded by the following curves. Find the volume of the solid generated by…

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Q: -4 -3 -2 -1 -5-4 5 4 3- 2+ 1 -Y -2+ -3+ -4+ -5+ 2 3 4 5 X

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