Consider the differential equation y" – 11y" + 28y = 0 Write the auxiliary equation of the given differential equation. Find the general solution of the given differential equation.

Q: Activities in Logarithm dy Find the dx 1. y = In(x? – 7x) -

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Q: 8. Find the magnitude and direction angle of the vector u = (-5,-2).

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Q: Find the arc length L of the graph of r(t). r(t) = 10 cos(t)i+ 10 sin(t)j+ tk, 0<t< 2n

A: To find the arc length of the given graph.

Q: Directions: Solve the derivatives of the following functions using the rules in differentiation…

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: Solve the following initial-value problem using Laplace transforms. y′′−y′−2y= 5 sin(x); y(0) = 1,…

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Q: d d. [r1(t) · r2(t)] andr:(t) × r2(t)] first by differentiating dt dt the product directly and then…

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Q: Evaluate the integral (3x – 1)(V+ 1)da. -

A: In this question we have to find the Integration.

Q: Evaluate F. dr. F(x, y) = xi + yj C: r(t) = (7t + 6)i + tj, 0st<1

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Q: f(x + Ax) - f(x) D. APPROXIMATE DERIVATIVES f (x) Ax 7.) y = x2 +7x – 10

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Q: B. Directions: Determine whether the following functions are continuous on the given interval. x-5…

A: 1).f(x)=x-5x2-x-6f(x)=x-5(x-3)(x+2)⇒Function is discontinuous at x=3 and -2And 3∈(-1,3)Therefore…

Q: QUESTION 6 A museum charges $10 for an adult ticket and $5 for a child ticket. On a given day, 46…

A: Let the number of adult tickets be x and the number of child tickets be 46-x. Then by using the…

Q: Find the absolute maximum and absolute minimum of 9(t) = t/4– t on the interval [0.8, 2.8]. Enter…

A: topic - application of derivatives

Q: f(2) = - 4z' - 2 a) Determine the intervals on which f is concave up and concave down. f is concave…

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Q: 2. 01> 7 ( (E) 1<1<2 and 5 <r<6 OA 旧0 OB 近。

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Q: x +1 Evaluate the integral dx. Vx2 + 2x + 3

A: Note: for given integral none of the option is correct match.I have solved as per integration by…

Q: f(x + Ax)-f(x) D. APPROXIMATE DERIVATIVES f(x) = Ax 8.) 2A

A: Given function f(x)=2x

Q: A car rental agency rents 190 cars per day at a rate of 31 dollars per day. For each 1 dollar…

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Q: Find the limit. NOTE: Enter the answer using round brackets. t² + 8 1' lim t→+∞\ 9t² + 10't (?, ?)

A: We can solve this as follows:

Q: /13 3 Find the first four terms of the binomial series for the function (1+ 2x)°. The first term is

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A: Given C1r=cosθ+1C2r=2cosθ

Q: For Item # 1- 2: The IOM company describes the cost C in pesos of producing x units by the function,…

A: Given cost function.

Q: -8 6. 8 -8 (a) Where is f(x) 0? (d) Where is f(x) > 0? (e) Where is f(x) negative? () Where is f(x)…

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Q: NG) Find T(t) and N(t) at the given point. T r(t) = 8 cos(t)i + 8 sin(t)j+ tk; t = T()= NE) -| ||

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Q: Solve

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Q: VI. Write the equation of the line that has the indicated slope and contains the indicated point.…

A: We know that equation of line passing through the point (x1 ,y1) and having slope m is,…

Q: Given the following optimization problem: max(500-q)q-50q q*=50 O True O False

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Q: For Item # 9 - 10: A company manufactures fuel tanks for automobiles. The total weekly cost of…

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Solve for the volume of the solid generated by rotating the plane bounded by the equations below…

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Q: f(x) = 2° – 4.5z2 – 12x – 2 a) Find the first and second derivatives. f'(z) = f"(z) = b) Identify…

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Q: Work Problem Write step-by-step solutions and justify your answers. Find the general solution of the…

A: The given differential equation is: y'''-3y''+2y'=0 So, we can also write as; D3-3D2+2Dy=0 The…

Q: 20. Write the equation of the line that has the indicated slope and y-intercept. Express final…

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Q: 4 cos(x) = 4 cos(x)i - 4 sin(x)j -4 sin(x) u3D( )i+( ) j

A: solution is given below

Q: Find the area bounded by the curve y = 4x - x2 and the lines x = 0 and y = 4.

A: topic - area bounded by curves

Q: 100e0.1z thousands of Over the next 5 years, a company projects its continuous flow of revenue to be…

A: To find the expected profit of the company

Q: х3-х-1 4. S (х-1)(x?-х)

A: To evaluate the given integral.∫x3-x-1x-1x2-x dx

Q: Problem 1. Which gives the Laplace transforms of the given time-domain function? Let a = %3D 2 O…

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Q: 200 N 250 N 120° 145° V

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Q: A manufacture has been selling 1100 television sets a week at $420 each. A market survey indicates…

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Q: t2 + 5 1 lim →+∞\ 9t2 + 10' 2t (?, ?)

A: Given

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A: we have to find the integral.

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A: Solve it.

Q: Find the third order derivative of y = In(cos(2x))5. %3D A. y' = -40sec² (2x)tan(2x) %3D В. у' 3…

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Q: The vat shown in the accompanying figure contains water to a depth of xo = 1.9 m. Find the work…

A: To find the work require to pump all the water to the top of the vat. Given, 9810N/m^3 as the weight…

Q: 3. x² + 5x + C .2

A: Derivative of xn is ddxxn=nxn-1.

Q: da Evaluate the integral dx. sin x cos x (a) In sec a| - In |sin r| + C (c) In |csca- cot c+ In sin…

A: Given problem:-

Q: 4. Sdx

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Q: Evaluate the integral. 37/4 3 sec e tan e de -7/4

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Q: Q3/ Find the area of zone bounded by curves: y= x , y= 3x+8

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Q: Evaluate the definite integral. e6t i + e¬j +t k )dt O e6 - i - e- 6. + (e* – 1) i – (e-1 – 1) j + k…

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Q: Find the maximal area of a right triangle with hypotenuse of length 2.

A: Given:     Hypotheses length = 1