27. r = – 3(1 + sin 0)

Q: 3. Obtain in two ways the general solution of (r + sine - cose ) dr + r (sine + cose ) de = 0

A: Use substitution method

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

A:

Q: |6. Determine two values of x between 0° and 360° that have sin x 2

A:

Q: 5. S 11 sin ( 4x – 6y) cos ( 6x – 4y) dy - -

A:

Q: 5 dr dy Suppose x and y are functions of a third variable t. If sin²(x) + cos²(y)=- and dr - 2, what…

A:

Q: Show that L-1{ = (sin hat sin at) s4+4a4, 2а2

A: To find Inverse Laplace transform of ss4+4a4: write ss4+4a4 as  ss2+2a22-2as2 Then the denominator…

Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: | sin(4z) cos(7z) dz.

A: To find:∫sin4zcos7zdz

Q: f/² sin (1) 4x ; (**) sin (²) COS (²) dx (Consider initially the first 2 terms)

A: ∫vn dv =vn+1n+1+C

Q: sin (2t + 1) - dt cos? (2t + 1) 31.

A: Use trigonometric substitution method for solving the integral.

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: 7/2 S 3 cos (x) sin°(æ) dx =

A:

Q: 1- d/dz [cosz] = -sin z

A:

Q: Show that L{cos at} = S s² + a² Hence find L{sin 8t sin 6t}.

A:

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x %3D

A: NOTE:according to company rules I need to solve first question when multiple questions are posted

Q: dt cos (2 sin 21) /1– 4r

A:

Q: 5. Find y', if y 2cosx sin2x – sinx cos2x %3D

A:

Q: (3.2 cos 2x+2 -dx. 1.8 1+ In x Use NINT on the calculator to evaluate:

A: We have to evaluate ∫1.83.2 cos 2x + 21 + ln x dx.

Q: 1. y = In (3 – 4 cos x) + (4x – 5)5 2. y = x² tan x 3. y = x5 sin2x cos 4x %3D

A: We will answer the first three questions as per our guideline. Please resubmit the other question…

Q: 3. sin 3z cos 5z dr

A: Here we have to evaluate I=∫sin3xcos5xdx

Q: cos(2x) dx 1 In |1 – sin(2x)|+c 2 - 1 – sin(2x)

A: Note: It is assumed that the question is asking to test of the validity of the given equation.   It…

Q: f'(t) = sin 8t - cos -/-

A: You are correct

Q: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

Q: dr de sin - r- cos + eª cos = 0

A:

Q: S cos(3r)(sin(3x) +5)10 dz Select one: (sin(3z)+5)" 11 +C O (sin(3r) + 5)"+C (sin(37)+5)" 33 +C…

A: Consider the integral: I=∫cos3xsin3x+510dx……1

Q: (2 cos 2x+ 3 sin 2.x) 7. evaluated at x = 1 rad

A: Given query is to find the value of the expression at x = 1.

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: (1 + cos 7t) 2 sin 7t dt

A: Here we use u-subsitution to evaluate the integral. d(cosx)dx= -sinx

Q: 1 os( 1 (sin(7z))* =| x)+ cos( x)

A:

Q: 3 8) 1--sin (2t) = sin' (t) + cos (t) sin(t) + cos(t)

A: Given,            1-12sin2t=sin3t+cos3tsint+cost

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: 1. Given x = r2 cos(20) and y = -r² sin(20)

A:

Q: .15 S sin²4y cos>4ydy

A:

Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

Q: 2y 1 + cos 3x - 4.x + 3y sin 3.r = 0 %3D dr

A: 2y-1x+cos3xdydx+yx2-4x3+3ysin3x=0 Rewrite the above ODE in the form of Mdx+Ndy=0.…

Q: dx 1 + sin(ax) %3D

A:

Q: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

A:

Q: 13T (b) sin-(sin(- -)) = %3D 11

A:

Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

A:

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

A:

Q: 1. dz (1² + 5)² 2. COs z dz 3. sin 3r cos 5z de

A: Given: I1=∫x3x2+52dx, I2=∫excosxdx, I3=∫sin3xcos5xdx

Q: "+25y 4r sin(51) – 2e" cos(5t)

A:

Q: 3 Q19- if z =- 4x³y sin sin (x³y) əz find əx

A: We want to find partial derivative of the given function.

Q: * /2 2 sinh (sin 0) cos 0 d0

A:

Q: 9. (2 sin x – 3 cos x) dx • T/2 - T/2 -

A: We use Trigonometry table for final answer  and cos(-x) = cos(x)  sin(-x) = -sin(x)

Q: Suppose x and y are functions of a third variable t If sin2(x) + cos²(y) =- and dr dy what is the…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.