Find the volume of a pyramid with height 21 and rectangular base with dimensions 5 and 7 using integration.

Q: Consider the following given function and given interval. f(x) = 10 sin(x) - 5 sin(2x), [0, π] (a)…

A: Given data÷ fx=10sinx-5sin2x Interval : 0,π   From part a) the value of favg=20π   fc is given by…

Q: The graph of the polynomial f(x) is given below. If f(x) has degree 4, find the factored equation…

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Q: 28.y= I 4+4

A: We have to find derivative

Q: 9. Consider the equation 2 5cos x + 4cosx = 1. a. Put the equation in standard quadratic…

A: The given trigonometric equation is 5cos2x+4cosx=1

Q: £f*. S: z = 18, x² + y² ≤ 1 Evaluate (x - 2y + z) ds.

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Q: Graph the function given below by moving the vertical asymptote, then the value of the -intercept.…

A: Let's draw the graph.

Q: Find the slope of the graph of the function at the given point. Use the derivative feature of a…

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Q: Use Theorem 7.1.1 to find L{f(t)}. (Write your answer as a function of s.) f(t) = e* sinh t L{f(t)}…

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Q: maximum

A: if you specifically asking to how to find maximum and minimum value. Please refer to the image below…

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: I have stated the used formula in the solution

Q: Use Stokes's Theorem to evaluate F. dr. Use a computer algebra system to verify your results. In…

A: Here,  g(x,y)=49-x2G(x,y,z)=z-g(x,y)

Q: If the work required to stretch a spring 2 ft beyond its natural length is 12 ft-lb, how much work…

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Q: (2) √ 2²² dx S 9-x² (2) > fx(x + 1)¹ dx

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture and a…

Q: Evaluate : L {15} = Blank 1

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Q: a. Find the nth-order Taylor polynomials of the given function centered at 0 for n = 0, 1, and 2. b.…

A: a. Given that, the function is fx=e-10x. Note that, the Taylor series expansion for the function fx…

Q: 3 A merry-go-round has a radius of 4 m and is spinning at a rate of 0.5π radians/s. Bill is standing…

A: Formula used: Circumference of circle = 2π×radius of circle  velocity =  angular velocity × radius

Q: Consider the function f(x) = x² - 98x² + 4, −6 ≤ x ≤ 15. This function has an absolute minimum value…

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Q: ) . Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: = If cot(x) Give exact answers. sin (²) cos (77) tan(72) = 18 5 = Submit Question (in Quadrant 2),…

A: I am attaching image so that you understand each and every step.

Q: Let f(x) Then f'(x) = 3 sin x 6 sin x + 2 cos x m = The equation of the tangent line to y = = f(x)…

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Q: ST sinx + 2 cos x dx

A: we have to evaluate the integral ∫0π sinx  + 2cosx dx

Q: Consider the function below. f(x) = √64-x² What is the Domain? What is the Range? Enter your answer…

A: Domain of  64-x2 :We must have 64-x2≥0So,  Solution:  -8≤ x≤ 8  Interval Notation: -8, 8

Q: The equation r(t) = (t + 7) i + (√3t) j+ (3t²) k is the position of a particle in space at time t.…

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Q: (2xcot(x) csc²(x)) dx

A: Given problem:- ∫2xcotxcsc2xdx

Q: (c) (d) x² + 4x +3 √√x y = 2(11x + 4)³ y =

A: As per student request , I solve only (c) and (d) part. (c) The function is given as , y=x2+4x+3x…

Q: Find the sum. 6 Σ k k = 2

A: Here we have to find the sum.

Q: Evaluate the following integral: S₁ S² == dydx −1 1 y

A: Given integration: ∫-14∫1ex2y dydx

Q: Let R be the region in the plane bounded below by the parabola y = x² above by the line y = 2x. Then…

A: Use application of integral for finding the area of curve between two curves.

Q: find area of abc triangle with given parts A=29.6 degrees b=10.7 in c=6.6in

A: Use sine law

Q: Let R be the region in the fourth quadrant bounded below by the parabola y=x²-3 and above by the…

A: Use double integral

Q: Find the domain of the function in interval notation  g(x)= x/ x^2-49

A: We need to find out the domain of the function given.

Q: If the radius is 9 cm, and the central angle is 80 degrees. Find the following a) Arc length,s b)…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: NOTE: Refresh your page if you can't see any equations. .

Q: 3) . Is the differential equation linear? y' = y + ey YesNo       PLEASE SHOW STEP BY STEP .

A: answer is in next step. please give a like !!

Q: 2. ∞ Σ Find the sum of the convergent series: n=1 1 4n2 –1

A: Find the sum of the convergent series 1/(4n2-1) from n= 1 to infinity.

Q: 4. The height h in centimeters of Shuntaro's pogo stick from the ground as he jumps on it since s…

A: We have to find the height at given times.

Q: Evaluate the following integral using trigonometric substitution. dx 2 x - 289 " || X> 17 dx 2 x² -…

A: The objective is to evaluate the integral using trigonometric substitution.

Q: Find the curl of the vector field F. F(x, y, z) = 4x² + 7y²j + 5x²k

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Q: Identify the rational function whose graph is given below. Note the x-intercept of the graph is a y…

A: topic:- function

Q: Given data points: (-2, 1), (-1, 2), (0,1), (1,2), (2,1) Calculate the error vector and the error…

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Q: ds Find the particular solution of dt H|2 1 = cos-t

A: The given equation is;  ds/dt = cos (t/2).

Q: (1) ſ [ (x³ + 2 + 7 ) dx (3) cos³x dx (2) √ x³ (2) x3 e3x+1 dx (4) sin x sin 2x dx

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Q: 5 1 So (125 + 25x + 6) dx 6o S X (1 + x²)3 dx / 1 + x² dx 1

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Q: a) Let f(x)=-3x² + 4x. Use definition of the derivative Equation 3.4 to compute f'(x). (No other…

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Q: Express the function in the form f o g. f(x) = g(x) = F(x) = sin(x)

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Q: what

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Q: an I ask how the maximum and mininmum points were obtained?

A: We need to find max and min points.

Q: So sin¹ (6x) cos (3x) dx

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Q: 15. 1/√/2 X 1+ 4x4 dx

A: We need to evaluate :

Q: a and d needs a solution

A: This question is related to Laplace transform and differential equations, we will solve it using…