22. Given that4 cos 0 + 3 sin 0 = R sin(0 + a), the value of R and tan a are respectively 3 A 25 and- 4 B 5 and- 3 C 25 and D 5 and

Q: 4 TT 37. tanα < a < T; cos B = 2' 50 < B < -- %3D 3 2 2

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Q: If y= In(4 tan (4x) ), then y' tan(4x) = Select one: 04/(1+x² ) O None O 4/(1 + 16 x² ) 01/(1+ x² )…

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Q: Question 3 S sin 7y sin 2y dy is equal to O m cos 5y- 18 Cos 9y + C 10 O sin 5y - sin 9y + C O TO…

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Q: Let o,= 2 (cos 45° + i sin 45°), @,= (cos 30° + i sin 30°), calculate a. @j @2= b. o, / 0,= с. О d.…

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Q: (b) Compute sin 20. Hint: sin 20 = sin(e + 0)

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Q: 15. Given that sin(1.4) = 0.99, determine the value of sin(2T +1.4). 2n 0.99 O 0.99 27 + 0.99 O…

A: Given : sin(1.4) = 0.99  sin(2π+1.4) = ?

Q: Q1: Determine -8 sec 7x (-4 cos? 7x + 6 tan 7x) dx. 32 sin 7x – 7 48 sec 7x + C 7 A -- В -224 sin 7x…

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Q: Which of the following is a possible solution to y" + 16y = 0 O y = tan(4x) y = cos(2æ) O y = sin x+…

A: SOLUTION IS GIVEN BELOW

Q: Let z = 8(cos 50° + i sin 50°) and w=2(cos 30° + i sin 30°). Express in the form r(cos+ i sin 0):…

A: Here we can use the following formula to find the results eiθ=cos θ+i sinθande-iθ=cos θ-i sinθ

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: Stan 2xdx O-In(cos 2x) + C O-In (cos 2x) + C O-In (sin 2x) + C O tan² 2x 2 + C

A: INTEGRATION

Q: 15 and x terminates in guadrant III. 17 Find sin2x, cos 2x, and tan 2x if sin x= - sin 2x cos 2x %3D…

A: The solution is given in the next step.

Q: In the process of calculating that: cos³ (112) de a substitution is made in the variable u, then it…

A: Given query is to find the integral after substitution.

Q: 9 sin sin 2O° =Y 1o) cos cos 70 = a4 24 1)Sin Sin 7o = X 24 12) cos cos 20 = _ x %3D 24 24 20

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Q: Given that sĩn = %3D 2 |cos 플 호 and COS %3D sin = cos 4 = show without Ee using a calculator that…

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Q: What is the general solution of (sin 0 – = 0 ? 2rcos? 0) dr + rcose (2rsind + 1) do O sin 0 rcos e =…

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Q: Fill in each blank so that the resulting statement is true.

A: STATEMENT-1 Given equation is, sinx=22⇒sinx=12 The General Solution of the equation in the interval…

Q: If ſ cos* xdx = Ax+B sin 2x+C sin 4x +D, then {4,B,C} equals S3 1 1] 18 32 4 [3 1 1 (b) 8 4 32 ƒ1 1…

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Q: Compute / sin? æ dæ. sin 2x + C 4 sin a +C 3 cos 2x + C 4 2 sin 2x + C 4 cos 2x + C 4 2

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Q: er +6 近 。 Oe) sin(2a) Od) cos(2x) T SOƆ 7 5 Ob cos(x²) + 2x (,r)so) (e O ap UIS .2 hip If y =…

A: Topic :- Derivative Correct option = C

Q: 3. Which of the following is the particular solution to the ODE. y" + 4y = cos(2x) 1 x sin(2x) 4 A.…

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Q: 32. If 2 sin 0 cos 0 cos 0 =0, where 0 <0 < 2n, then the exact values of 0 are 57 0, 3 O0, 5. 7, ,…

A: Given : 2sinθcosθ - cosθ = 0 Where, 0 ≤ θ ≤ 2π To find : Exact value of θ?

Q: Answer: The approximate value of sin 29° is O sin 29° s 1( 29x 2 180 6)+ O sin 29° V3 ( 29x O sin…

A: Please see the explanation below

Q: Evaluate / 7 cos 4ædx. 7 O a. 7 sin 4æ – sin 4x + C O b. None of the choices. Oc. 7 -sin 4x 4 7 sin…

A: Consider the given integral, I=∫7cos34xdx take the constant outside the integral, I=7∫cos34xdx now…

Q: .3 29. dr 18 31. 1/2 sin (x/2 + 1) d

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Q: 18.) Suppose x = R cos(0) sin($), y = R sin(0) sin($) and z = x² + y? + z? = R²Y R cos(). Verify the…

A: Given

Q: If A=2(1-cos 0)â, – pyâ, (1– cos ¢)â, – ppâ, +zcos² þ⸠, what is 4 8. V•A ?

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Q: e csc 20 In (ecos 2 ) Ince cos CoS 20 28) Sin2 20 OP

A: Given integral is ∫ecsc2θlnecos2θsin22θdθ since lnex=x, so lnecos2θ=cos2θ The integral becomes…

Q: Consider (e cos 4 + ie sin 4) (11+12:) cos 4+ ie sin 4) (11+12i) 3DZ What is the general value of z?…

A: Euler's formula is given as that e^(ix) = cos(x) + i sin(x).

Q: 1.4 The integral 2 sin (15ax) sin (10a.x) dx equals: (a) (cos (5ax) – cos (25ax)) da (b) (sin (5ax)…

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Q: 2. If 90° < 0 < 180° and cos 0 =-, find sin. %3D 11/3 11/3 3 ) - 3V11 11 O 3/11 11

A: We know that the trigonometric identities :  cos x = 1 - 2 sin2 (x/2)

Q: 9/8 2* CoSメーenp and X=/t+] its dus

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: 11 Ifx = Arc cos then x is equal to 1) 120° 2) 150° 3) 210° 4) 300°

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Q: 0. If 180° < 0 < 270° and cos e = -, find sin 20. %3D 13 O- 16V105 169 O 16/105 169 O sV105 169 O -…

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Q: V. Determine c, and c, so that y(x) = c, sin 2x + c, cos 2x + 1 will satisfy the conditions y(r/8) =…

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Q: Find all solutions to the equation: [sin(x)+ 1]2cos(x)-3]=0. Зп + 2nk, x = + 2nk, x = 11m + 2nk,…

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Q: 7.32. Prove that for 05sr, -( . ) cos 2 cos (a) a(e -a) = sin 3r sin ba (6) (r-) - 7.33. Use Problem…

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Q: 10. If h(x) = x²2cos 2x, then h'(1) = A. 4cos 2 B. 2· 2cos 2x (1 + In 2) C. 21+cos 2 D. 21+cos 2 (1…

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Q: Q/ IF y = Sim ܠܐ 10²² (4) y = 3/² sin(x) cos(x) Prove that

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Q: Given that cos(2t) = 2 cos (t) – 1, it follows that L{cos"(t)} =;( +:). O True O False

A: We need to find Laplace Transform of f(t) = cos2(t) But , cos2t = 2cos2(t) - 1  ⇒ 2cos2(t) = 1 +…

Q: 17. If 2 tana tan?ß tan?y + tan a tan-ß + tan B tany + tan?a tan?y 1 (a. B.y e R. a. B.y (2x+1)…

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Q: and <B<m 6. Given sin B = %3D 3' 2 Give the exact values for cos B and tan 3 V5 tan 3 3. 2/5 cos B =…

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Q: Solve for O on Co, 2T) 6 sinio + 9 cos 0 -9-0 2 Sin O + 3cos o -3=0 Sin O +los? = Sm?O =1- cos?O…

A: Form the given trigonometric equation in the quadratic equation than solve by factorisation.

Q: 7. sin A = [ Select] %3D 8. cos A = [ Select ) 9. tan A = I Select)

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Q: sec 0 + In + 27+3 = -3 2 In y? + 327 – 4 = 1+ cos 20 2/1+ (tan 0)² + 2ln /y + 22 = -3

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Q: 1. If x-y? = 25, then y" = %3D a.) b.) c.) - d.) - 2. If y = cos(3x+1), find y' a.) 3 sin(3x+1) b.)…

A: Given:   (1) x2 - y2 = 25    (2) y = cos(3x+1)

Q: One of the correct steps to evaluate A sin²20d0 [² B cos 40d0 C) None Ⓒ//ww D do + sin²20d0 Ⓒ = [ √…

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Q: What is the general solution of sin 0-2rcos²0) dr + rcos0 (2rsind + 1) de = 0 ? %3D O sin 0 rcos²0…

A: Given differential equation is: sinθ−2rcos2θdr+rcosθ2rsinθ+1dθ=0

Q: 4 Find 20(4 sin(x)) cos(x)dx if Ax)dx = 16 %3D O a.-160/3 O b. No correct answer O C. -80 Od. 160/3…

A: Consider: ∫04fx dx=16. Evaluate: ∫0π220f4sin xcos xdx. Let 4sin x=t. Differentiate. 4cos x dx=dtcos…

Q: Solve the following problem = 0; (x, y) E (0, 1) × (0,1), + u(0, y) = u(x, 0) = u(1,y) = 0, и(т, 1)…

A: In this question, we have to solve the Laplace equation by separation of the variable.

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related. 

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.