Graph the equations 1. y= x²+4x+3/2x²+3x+1 2. y²= x+3/2x²+3x+2 3. r= sin 0+ 2cos²0 4. r²= sin2 0 - 3cos0

Q: 8 +10x-32+x? cos 2x 4 Find : (a) y = %3D x2

A: Given y we have to find dy/dx as shown below

Q: 1. (xy' – y) cos ( 2у COS -3x4

A: Since you have asked multiple questions, we will answer the first question. If you need answer for…

Q: (s,+)=(-3,1) X=5?+2+? y= 6st a) 4s x sinly) + 6+x?coscy) at (-3,1) b.) 8tx Sincy) + 6sx? Coscy> at…

A: GIVEN  (s,t)=(-3,1) X=s2+2t2  Y=6st substituting the value of s,t for X and Y we have  X=(-3)2…

Q: 4T then 3 If 0 = sin(0) = %3D Give exact value.

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Q: Graph: y = 2 sin 27x, 0 s xs 2.

A: To graph: y=2sin2πx,     0≤x≤2 Solution: We know, for a sine curve of the form: y=asinbxAmplitude…

Q: 1. 2. (D² -3D+2)y=sine-*

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Q: Solve: Tanxdy+ y°Sin²xdx=0, y(0)=1 а. у"(3-Сos2x)-2 b. у(-2х + Сos2х) -1 d. y(-1+ Cos2x) — х с. у?…

A: This question is related to differential equations, We will solve it using given information.

Q: 3. Draw the graphs of: y = 2 sin (2x) y = 3 cos (.5x) a.) b.) c.) y = tan(2x)

A: (a) Sketch the graph as shown below.

Q: Determine an equation of the graph shown below. 4 21 y = 3 sin 2 x- - 1 Oy- -2 cos 2x y = 3 sin 2 x+…

A: Graph: In a cartesian coordinate system, a graph represents the points of the form x, y, where y is…

Q: Find a particular solution to y" + 36y = 24 sin(6t). %3D

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Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…

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Q: solve it

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Q: Find an equation for the graph. 8) C) y=2 sin x D) y = 3 sin x A) y = 2 sin 37x B) y = 3 sin 27x

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Q: Use Superposition approach to find the genral solution of the following equation: y" – 2y' + 3y = -6…

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Q: 8. 2/3 cos¹/3 sin dt 0

A: The given integral is;  Cos4/3(t/2) Sin(t/2), limit from 0 to 2pi/3.

Q: 1 is (s+3)* + 4 cos3t a) 3 cos2 b) c) 2 sin 2r d) 3 sin 2r

A: I will use the rules of inverse Laplace transform.

Q: The equation corresponding to the graph shown below could be:“ (플, 1) (2ñ, }) TT 1 A y = 2 cos x+1 1…

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Q: 2x y" + 4y' + 5y = cosx

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Q: 3 r = sin 0 + 6 cos 0 О За? + (у — 3)? —— 1 %3D 6æ² – (y – 3)² = 1 D y+6x = ! 1 3. Dy+6x = 3 у+ 3х —…

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Q: (b) у" - 4у %3D (2? — 3) sin(5a

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Q: 16. Eliminate 0 from the following equations : and y = b.Sec0 i) x= a.Csc0 ii) x= Sin0+ Cose and y =…

A: we use Trigonometry identities to eliminate parameters from equations

Q: Match the equation to the graph. y 2 sin 30 - 1 %3D Sn / 3n 7n 21 4.

A: y=2sin3θ-1Use the form  a sin ( b x − c ) + d  to find the variables used to find the amplitude,…

Q: What is the equation of the graph below? 0.5 5 T/6 10 0.5 = CoS ( 2x 3 ) y = sin ( 2x + y = sin ( 2x…

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Q: What is r 1- O Option 1 2 2 sin 0-3 cos 0 3 y = ² x + 1 2 x² + y² = 2y²-3x Option 3 in Cartesian…

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Q: 3. The equation that best represents the graph shown below is 4 -2 A. y = 4 sin(2x)+2 В. y =-4…

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Q: Find an equation for the graph. -1 Oy = -5 sin O y= -5 cos (2x) y = -5 cos Oy = -5 sin (2x)

A: Draw the waveform as shown in below and then compared with the given graph then find the value of A…

Q: 4 Find (b) y = 9. sin 2x.

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Q: Find an equation for the graph. O A. y= 3 sin 2x O B. y= 3 sin 5x OC. y=2 sin - O D. y=2 sin 3x

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Q: 5. (D² + 16)y = 24 cos 4x – 32 sin 4x

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Q: 3. In the equation y = sin1 x, if x = 0, then y = 0.

A: We have to use the inverse sin function and the interval -π2,π2. We have to recall the trigonometric…

Q: 3. 2 +X-1 dy 2=Sin (cos 8x) %3D

A: 1) Given that y=4x35-6x2+x2-1 y=4x35-5x2-1 we have to find the derivative of 'y' with respect to 'x'…

Q: 8. y"+y = 3 cos 2.xr,

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Q: A particular solution of the equation y(4) + 2y" + y = 9 cos(t) + 2et – 5t is of the form

A: See the detailed solution below.

Q: day Find y, of 2+ + 6y = 51 cos 3x. ... a.) y, = - cos 3x + 4 sin 3x b.) y, = cos 3x-4 sin 3x c.) y,…

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Q: The equation (tan²x+3y²)sec²xdx + (3tan²x + y²)dy=0 can be solved by

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Q: Find the solution. y'= 1 + 3ytanx 3y cor x=ctanx + 3sinx – sin³x 3y tan?x=c+3sinx – cos?x © 3y…

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Q: Question 2 Differentiate y= (3 cos x – 2 sin (2r))² A y' = [-6 cos x + 4 sin (2x)][8 cos (2x) + 6…

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Q: COS 10T - i sin 10TT 3 3 GT+ 3 of 學 4T COS 27 + 40 3 C1) - 1 2

A: Use trigonometric ratios

Q: Which of the following equations can be used to describe the graph shown above? oy = 3 sin(2x) + 1…

A: First option is correct

Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

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Q: What is the equation of the graph below? 2 10 15 -1 -2 -3 O y = 3 sin(x) O y = 3 cos(2x) Oy = 3…

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Q: Graph the epitrochoid with equations x  =11 =cos t - 4 cos(11t/2), y = 11 sin t - 4 sin(11t /2)

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Q: What is r = -12 2 cos 0-7 sin e 2y - 7x = -12 in Cartesian form? x² + y² = -12 2x-7y

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Q: . Obtain in two ways the general solution of (r+ sine – cose ) dr+r(sine + cose ) de = 0

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Q: The equation (sin 2.x- 2y cosx) dx = 2dy is linear O yes O No Bernoulli s equation can be…

A: All the questions has been solved with explanation in step 2 and step 3.

Q: Match the graphs with the correct equation below 1. y=3+ sinz 2. 3. 4. y = -3+ cosz y = sin 2 y =…

A: The given functions are1. y=3+sin x2. y=-3+cos x3. y=sin 2x-π24. y=cos 2x-π2

Q: Question 6 Find the solution. (D4 + 18D2 + 81)y = 0 y = (c, + c,x) cos3x + (c,+cx) sin3x. B y = (c,…

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Q: Find 2: (a) y = cos(1 1x + 5x)

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Q: (x € [0,x] T: sinx + cos(2y) = 1, y e -. 4: 4.

A: Given, sin x+cos2y=1

Q: (2D – 5)y = sin 2x – 7 cos 2x -

A: