Evaluate the integral. 1 [ ²₁ (U+6) (u + 6)(u − 7) du

Q: Given the vector →u=⟨6,-2⟩, find the magnitude and angle in which the vector points (measured…

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Q: 5 30-60-90 Triangle 30 12 x 12 2x Ratio of Side Lengths x:x√3:2x=1:√3:2 60% x=254144=169 x = 1169…

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Q: State the coordinates of the intercepts, stationary points, and the inflection point of p(x) = 2x³ −…

A: According to question,Given Function,px = 2x3-3x2-36x+5

Q: Find the length of the curve. 2 x= (2t+1)3/2 3 Osts 12 The length of the curve is. (Simplify your…

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Q: equations, eliminate the parameter and identify the shape of the curve. Sketch the curve and…

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Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. 14 n M8 Σ…

A: If the ratio of the limit value less than 1 then the series is absolutely convergence and greater…

Q: Use the model for projectile motion, assuming there is no air resistance and g = 9.8 meters per…

A: height h=1.1meters Initial speed=105 meters/second  Angle  = 30° above horizontal

Q: Use a triple integral to find the volume of the solid bounded by the graphs of the equations. z = 6…

A: We have to find the volume of the solid bounded.

Q: Given the function fƒ(x) = −2x³ – 12x² – 18x + 1, determine the intervals where the function is…

A: Application of derivative

Q: If h(x) = 8x³ + 8x²-3x - 2, what is the x coordinate of the inflection point for the graph of h(x)?…

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Q: Sasha has a boat that has a speed of 12 km/h in still water. At what angle upstream should she head…

A: We have to find angle.  We can use relative velocity concept for this.

Q: (a) Find the differential dy of y = tan 5x. (b) Evaluate dy for x = 1π/4, dx = -0.1. dx (a) dy = =…

A: y = tan5x

Q: Consider the function f(x) = 2x^3 - 3x. a) Find f'(x) using the definition of the derivative.

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Q: ģ t b= 6 5 C = 4 d = 3 1 -4 -2 -1 -+-+ -3 -4 & To acheive this graph, a = 5 The plot above is…

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Q: (12) The point (2, 3) is on the unit circle in second quadrant. Find the x-coordinate of this point.

A: We have to find the x-coordinate of the given point. For this we will use Pythagorean theorem.

Q: Find the volume of solid generated by revolving the region bounded by the curves y = √x +2.y=x-2x =…

A: The region bounded by curves y=x+2 ,y=x-2,x=-2 and x=2 Graph

Q: An airplane hasjan airspeed of 400 km/h and is heading due west. If it encounters a wind blowing…

A: Draw the speed of the plane and wind as vector then find the angle uaing trigonometry formula.

Q: 1 x²√√x² +9 S dx

A: Using the integration u-subsituation method

Q: Use the ratio test to determine convergence or divergence. If the ratio test is inconclusive, use…

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Q: Find a mathematical model representing the statement. (Determine the constant of proportionality.…

A: To solve the following

Q: 21. dy dx = X xy + y Hint: Let u = x2.

A: Question 21:We have to solve the differential equation:dydx=xx2y+y3

Q: Secx Q2/ Find the derivatives of S√√1+t² dt sinx

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Q: Consider the vector field F= ·1.² F-dr along the curve C: F(t) = 4 con(t)i + 4 sin(t)), 0≤1≤…

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Q: Find the surface area of the part of the plane z = 4+ 5x + 2y that lies inside the cylinder x² + y²…

A: The surface  area of the of the part of the plane z=4+5x+2y  that lies inside the cylinderx2+y2=16

Q: y sin(x) = x sin(y²)

A: y sin(x2) = x sin(y2)

Q: If f(x) = ln(cos²x) then f'(x) is Ignore "Give your reasons" below. There is no need to give a…

A: f(x)=ln(cos2x) We have to calculate f'(x)=? We know f'(x)=d/dx(f(x))

Q: A. The function f(x)=√x² + 1 has a critical point at x =

A: according to bartleby guide line we do only first part of multiple questions. (A)  given,…

Q: Find the solution with steps of the Cauchy problem for the differential equation: 2(xy'+y)=xy^2,…

A: NOTE: Refresh your page if you can't see any equations. . ...............(1) substitute  take…

Q: [ f(x, y, z) ds. f(x, y, z) = x² + y² + z² S: x² + y² = 9, 0≤x≤ 3, 0≤z≤x Evaluate

A: We need to solve integral.

Q: Determine the slope of the tangent line, then find the equation of the tangent line at t = 6 x = 5…

A: Given: x=5 sint ; y=2 costWe have to find the slope of the tangent line, then we have to find the…

Q: The linear approximation to f(x) = √49 + 2x at x = () is y = A + Bx where A is is and where B

A: fx=49+2x ; x=0

Q: 3) Consider the series 33-n 5-n+1 n=1 i) Show that the given series is geometric series. ii)…

A: Given series is ,                ∑n=1∞33-n5-n+1 we have to show the given series is geometric series…

Q: Find​ E(x), ​E(x^2​), the​ mean, the standard deviation and​ variance, over the given​ interval, of…

A: The probability density function and the interval is given below               fx=113…

Q: A. The function f(x) point at x = B. The function y = interval x √²+1 has a critical concave up on…

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Q: The matrices A, B, and C are defined as follows: 4 A = -(-²) 0-( -8) c-(i) B Carry out the indicated…

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Q: (2 pts) Find the Taylor polynomial of degree 3 of the function f(x)=arctan(52) at a = 0. T3(x) =

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Q: x²(x- 十

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Q: Find the mass of a lamina bounded by y = 4√√x, x = 9, and y = 0 with the density function o(x, y) =…

A: Given that lamina bounded by y = 4x, x=9, y=0  with density function σx,y= x+2. We have to find the…

Q: (16) Perform the following calculation and simplify. 1 3 1 I 43 3

A: 1-1343

Q: Check the existence and uniqueness of a solution of the following Initial Value Problem: AP (T-A) dx…

A: We need check the existence and uniqueness of a solution of the following Initial Value Problem:…

Q: Suppose that f(x, y) = xy. The directional derivative of f(x, y) in the directional and at the…

A: f(x,y)=xy  then find the directional derivative .

Q: Let f(x) = x³ + 12x² - 27x + 16. (a) Use the definition of a derivative or the derivative rules to…

A: Since you have posted multiple subparts question in this question which are not interlinked so i…

Q: 21. Please express sin(t³) dx as a limit of right regular Riemann sums. a. Ax= b. Xk =

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Q: b Answered: 63 4-3- y = g(x)- TR X…

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Q: 1) Solve the following differential equations a) (6y²-x²+3) dy -3x²+2xy-2 dx b) y = 3y+e³xy 3x-3

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Q: Let h be a continuous function, with its first derivative given by h '(x) = 4x³ - 10x² + ex.…

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Q: x(0) = 1+3 sin(0) y (0) = 2 - 4 cos (0)

A: Convert Cartesian equation

Q: Find the area under one arch of the cycloid. x=2a(t-sint), y = 2a(1-cost) The area is (Type an exact…

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Q: Question If p(-9) = -5, p(-1) = 3, h(-9) = include "h(-1) =" in your answer.) Provide your answer…

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Q: (co cos 4x + sec 5x) dx

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