Solve the system. 2х + 6у - z %3D 6 4х - Зу + 5z 3D - 10 8х + 9y - 2z 3 12 The solution set is {(CI)} (Type an integer or a simplified fraction.)

Q: Car A is traveling west at 50 mi/h and car B is traveling north at 60 mi/h. Both are headed for the ...

A: topic - application of derivatives

Q: 9. Evaluate f(e* + 2*) dx a.) 2e* + +C In2 b.) er + 2ln* + C c.) e* ++c d) e* + 2ln x + C In2 10. Ev...

A: Evaluate integrate. And follow step 2nd .  According to guidelines we solve only first three parts. 

Q: If cotx 12 find the other trigonometric functions

A: We will use the basic trigonometric formulae to solve this question.

Q: Evaluate the integral. cos(5 x) dx

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Q: Using u-substitution, the integral S f(x)dx reduces to a new integral S g(u)du. If g(u) = ' evaluate...

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Q: 18. If x² + 2xy = y² then y' is b. 2x + 2y d. -x

A: (18). Given: x2+2xy=y2   We know that; The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-...

Q: Solve the differential equation. 5y' = 4 ex/5 + y + y The solution is y = 4x +C X 5 5 e (Type an exp...

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Q: Solve using the U-Technique Question 18 dx du The integral S; reduces to f ka", where u = f(x) and f...

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Q: Consider the integral 2nx g(x) dx. There is a function g(x) such that when u = In x the resulting in...

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Q: Solve the initial value problem:  y'= (3x^2)y+2x^2 ; y(0)=1

A: Given problem:- y' =(3x2)y+2x2 , y(0) =1 To find:- Solve the initial value differential equation

Q: The owner of a cattle ranch would like to fence in a rectangular area of 3000000 m² and then divide ...

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Q: Determine the quotient and remainder if P(x)=x'+6x'+2x'+x-3 is divided by D(x)—x'—2х—1

A: Topic = Algebra

Q: 12 1. Given that sine and 0 < 0 <", find sin(20) and cos(20) 13'

A: We know in the first quadrant that is 0&lt;θ&lt;π2 both sin and cos take positive values. cos(θ)=±1-...

Q: Determine whether the series converges. k=1 The series

A: Ratio Test : Suppose ∑ak be an positive term series and                         limk→∞ ak+1ak =L , t...

Q: Write the first five terms of the sequence: 11 ln n) +oo Determine whether the sequence converges, a...

A: To write the first five terms of the sequence.11 ln nnn=1+∞To determine whether the sequence converg...

Q: Find f (x) so that when u = f(x) the integral J tan(f(x) 1+ In x dx can be rewritten as cot u du. %3...

A: ∫1+ln(x)tan(f(x))dxlet u=f(x)=xln(x)⇒u=xln(x)differentiate on both sidesdu=(1+ln(x))dx

Q: Evaluate the integral using tabular integration by parts. 4 x V2 x +1 dx +C %3D

A: LetI=∫ 4x32x+1dxPut 2x+1=u2x=u-1x=u-12differentiate 2dx=dudx=du2I=∫ 4u-123udu2I=∫ 4u-138udu2I=∫ 14u-...

Q: Set up a definite integral with respect to y (dy) (set up only, do not evaluate the integral) to fin...

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Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: (e) S (x2+4x+5)2 d.x

A: To integrate: The integral ∫x+1x2+4x+52dx.

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: topic ,- indefinite integral

Q: Set up a definite integral with respect to x (dx) (set up only, do not evaluate the integral) to fin...

A: Question: Setup a definite integral with respect to x dx to find the area of the region enclosed by ...

Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. 00 (-1)k+1 k8/...

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Q: Using the partial fractions technique, the function f(x) = 37x+82 can be written as a sum of partial...

A: ∫37x+82x2+2x-24 dxConsider 37x+82x2+2x-2437x+82x2+2x-24=37x+82(x-4)(x+6)37x+82(x-4)(x+6)=Ax-4+Bx+637...

Q: Question 20 csc x du 3T If u = f(x), then dx = Compute f и sin x – cos x A B 1 D -1

A: We have to solve our question

Q: Determine f(x) so that | cos(In?x) f (x) dx = sin(In?x) + C

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Q: Plot the following functions 1. y = - V2x +1

A: x y=-2x+1 -12 0 0 -1 1 -3 2 -5

Q: k If u = f(x), then ſ dx x++2x2+1 +C for some constant k . Compute kf(1). x2+1 ... 1 (A 4 1 © -1

A: I =∫xx4+2x2+1 dxI=∫x(x2+1)2 dxu=x2+1du = 2x dxx dx =du2

Q: Find the particular antiderivative that satisfies the following conditions: 10 10 H' (x) Н(1) %— 0. ...

A: H'(x) = 10/x2 -  10/x7 find H(x) = ? so we have to integrate it H'(x) = 10x-2 - 10x-7 H(x) = -10/x +...

Q: Determine whether the series converges, amd if so find its sum. If the series diverges, indicate tha...

A: Topic:- sequence and series

Q: 1. S(z) = 64 –³ VI 2. -12r2 S(z) = 1+ 8x²

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Q: prove that (sin?acos'x)(tan?x+ cot?x + 2) = 1

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Q: Sy = 4 +

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Q: 1+ In x Find f (x) so that when u = f(x) the integral dx can be rewritten as cot u du tan(f(x))

A: So our approach in this question by substitution method . We can assume a function u in terms of 'x'...

Q: Given: 2/(x)dx There is a function f (x) such that when u = -x, the resulting integral is 2du Evalua...

A: Need to find the function f(x). Given information: The integral is ∫2f(x)dxe-x3. There is a function...

Q: Consider the integral 2nx g(x) dx. There is a function g(x) such that when u = In x the resulting in...

A: Given query is to find the value of indicated function.

Q: If g(x) = f'(x) and if g(x) = (cos x – x sin x)e*cosx, then S g(x) tan(f(x))dx is x cos x

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Q: Find the particular antiderivative that satisfies the following conditions: F' (x) = a* + 5Væ; F(1) ...

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Q: ential equation. ect answer below. 5-12 + C

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Q: Find the differential equation whose solution is given by y^2=4ax

A: topic - differential equations

Q: Question 16 Determine f(x) so that | cos(In?x) f (x) dx = sin(In²x) + C ... 2ln(x) A) In(x) B 2In(x)...

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile i...

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Q: What is the average rate of change of the functin g(x) = 2x^2 -9 on the interval [4,7]

A: g(x)=2x2-9 on the interval [4,7]

Q: Solve using the U-Technique Question 19 1+ In x Find f(x) so that when u = f(x) the integral tan( f(...

A: Here, given that when u=f(x), ∫1+ln xtan(f(x))dx=∫cot u du⇒∫1+ln xtan(f(x))dx=∫1tan u du

Q: Evaluate the integral J x cot x² sin(in |sin x²l) dx.

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Q: y" + y " +y' + y = 1

A: A differential equation is said to be linear if no terms in it are formed by multiplication of two t...

Q: (a) Plot the first four terms of the sequence Зn? - Зп +2 2 (b) (i) Write in bracket notation the se...

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Q: Consider the integral 2h* g(x) dx. There is a function g(x) such that when Inx the resulting integra...

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Q: 1 (ke)3x For ſ k*e3*dx = + C. If u = 3x, then k =? 3 (1–In 2-1)

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Q: Evaluate the integral. 15e cos(2x) dx

A: To evaluate the given integral