Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral that is used to find the average value. DO dx

Q: # ZZ Convert the following equation in Cartesian (rectangular) coordinates into the equivalent…

A: Use trigonometry function

Q: What is the 6th term of (x - 1)¹0?

A: Given problem:- what is the 6th term of (x-1)10

Q: y = In (cot 8x)

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Q: Solve the given differential equation. All solutions should be found. (3y² + 2xy) dx - (2xy + x²) dy…

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Q: Use the graph below to fill in each entry of the grid with positive, negative or zero. y = f(x) f''…

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Q: Question 8 f the Cartesian coordinates of a point P are (0, 1, 1), then the cylindrical coordinates…

A: Convert Cartesian coordinate to cylinderical coordinates

Q: a) b) 1 2 3 + 2.2 3.2² 4.2³ 1 1 1 1 + + 1.3 2.4 3.5 4.6 + + 4 5 5.24 6.25 1 + n(n+2) + + +. 1…

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Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

Q: Evaluate the integral. (Use C for the constant of integration.) x² - 64 dx - +8

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Q: If s(t) 813 122-48t6, where t2 0 represent the position of a particle traveling along a horizontal…

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Q: A straight river flows east at a speed of 11 mi/h. A boater starts at the south shore of the river…

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Q: 1. Find the sum of the following infinite sequence: 40, 20, 10, …

A: A detailed solution is given below.

Q: -3t gallons each hour, t hours after a 13. The way Professor Waner drives, he burns gas at the rate…

A: To find out the number of gallons of gas he burns after 13 hours.

Q: Apply Green's Theorem to evaluate the integral. $(3y + x)dx + (y + 5x)dy C: The circle (x - 3)² +…

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Q: The graph of y g() is shown below. The areas trapped between the curve and the x-axis are given…

A: Here is the solution

Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: Question 2 A. B. A system of linear equations is given below. 2x + y + 2z = 1 x + 4z = 2 y = 2z = 1…

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Q: e. at the course h the courf. e obtained fr eln (1-t) - dt 1-t A ed to you in any form is ed on [√x³…

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Q: Using integration by parts for getting the integral of ex cos 2x will give way to another…

A: To find  ∫excos 2x dx we use the integration by parts and it will give another integral in which we…

Q: A rectangular bird sanctuary with one side along a straight river is to be constructed so that it…

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Q: 1. f(x) = 3x + 2, [−2, 2], ƒ (c) = 5 2. f(x) = x² − x + 6,[1,4], ƒ (c) = 10 3. f(x) = 2/2, [-3,-1],…

A: According to the guidelines, we are answering first three subparts. Please repost the remaining.…

Q: Which point is on the line parametrized by the following? O (-1, 2, 3) O (3, 2, 0) O (0, 0, 0) O (1,…

A: This question can be solved using the equation of line in three dimensional space.

Q: Evalu‎ate ∫C (x + 2y) ds, w‎here C is the cu‎rve defi‎ned by y = √(4 − x2), for x ∈ [0, 1]

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Q: The region R is bounded by y = √x and y = x³ is revolved about the y-axis. Find the volume of the…

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Q: 2. Create a graph of a function which satisfies all of the given conditions. D = {x € R|x = -2} •…

A: The function satisfies the…

Q: Evaluate S√9-4x² dx a. 0.285 b. 0.123 c. 0.423 d. 0.365 e. NONE OF THE ABOVE

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Q: 1. d²y dy +6- dt² dt +8y=-4 cos(3t)

A: We need to solve D.E. As per Bartleby's guidelines we can solve one question from multiple question.…

Q: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

Q: The function √x² + 2x is equal to (x + 1)² + 1 Option 1 √(x + 1)² - 1 Option 2

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Q: In spherical coordinates, the equation below describes what? O a plane O a cone O a sphere O a…

A: topic- spherical coordinate system

Q: The surface parametrized by 7(u, v) = (u, v, u - 2v) is a plane O a hyperboloid a cone a cylinder

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Q: Find the solution of the given initial value problem. 9 cos t y' y = y(π) = 0, t-9, t> 0 y(t) = =

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Q: Express the vector v with initial point P and terminal point Q in component form. P(3, 3), Q(5, 5)

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Q: (x² + 4) dy 山 3. y(2) = 0

A: we know that ∫dxx2+a2=1atan-1xa+C,  where a>0 see below the answer and calculation

Q: Assume that x and y are both differentiable functions of t and are related by the equation y = cos…

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Q: 5) A Cramer's Rule question: Suppose tickets to a football game are priced according to whether the…

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Q: a. Find an equation of the tangent line at x = a b. Use a graphing utility to graph the curve and…

A: Equation of the line :         y-y1 = m (x-x1) ; where , 'm' is the slope of the line .

Q: V1 - (In x)² x ln x VI dx

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Q: X p(x, y, z)=xz²+sin (y) ex

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Q: Please

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Q: da d²y +6- dx dx² + 11 dx+6y = ex + cosx бу

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Q: d. dx √2√x+3+x e. S da x√4x + 1 f. dx x√4x²+1

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Q: Use the surface integral in Stokes' Theorem to calculate the circulation of the field F = x²i+…

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Q: State what the Divergence Theorem says, using your own words. You may assume that E is a solid in R³…

A: We can state the Divergence theorem .

Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

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Q: 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258 (c) 82 (d) 734…

A: Given problem:- 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258…

Q: Find the Fourier transform of Hint: Use the integral formula Se-¹² du = √π e-a²₁²

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Q: 1. What is the smallest number that can be exactly divided by 2, 3, 4, 5 and 8? 120 20 12 24 2. What…

A: A detailed solution is given below.

Q: An airplane takes 3 hours to travel a distance of 1560 miles with the wind. The return trip takes 4…

A: This question can be solved using the concept of speed,time and distance.

Q: Show that if u + vand ủ – v are orthogonal, then the vectors u and must have the same length

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