axy' + bxy' +cy = 0 characteristic equation is, ar + (6- a)r +e= 0 case I: two different real roots → y=C,x* +C,x* case II : two equal real roots →y-C,x +Cx* Inx case III : two conjugate complex roots → yC, cos(Blnx)+C, sin(Bln x)) 4xy+17y 0 is given. 1- the solution of the given cauch-euler diff.equation is I+y-C,x' +C,x? II →y-C,r" +C,r² Inx II → yC, cos(In x)+C, sin(In x) IV → y"(C, cos(21n x)+C, sin(21n x) V →y*C, cos(2x) +C, sin(2x)) OA) IV OB) I OC) V OD) II OE) II

Q: -48 6

A:

Q: 4. 10p-p-2

A: The given expression is : 10p2-p-2 To factorize the given expression.

Q: z'dz 214

A: We have to find ∫x2 dxx3+4.

Q: くl0 l0x+チ

A: Given inequality is, 110x+7≤10.

Q: 1 dx

A:

Q: a3-16a

A: a³−16a ⇒a(a²−16) ⇒a(a² −4²) ⇒a(a+4)(a−4)

Q: 8(a+9) =

A: Given,           8(a + 9)

Q: 60 27 2. + $6

A:

Q: 3. H-8)- (4-8) -10

A:

Q: 9 – 4x > –3

A: The given inequality is 9-4x>-3

Q: A car costs x wholesale. The price the dealer pays is given by the function s(x) = = x-1 – 200 where…

A:

Q: 10 - 6 / 5 - 3

A: Given,

Q: х3 — 2х dx х — 1 -3 10. 2

A: Given: I=∫23x3-2xx-1dx For evaluating given integral, we substitute x-1=t…

Q: Find the values of sec-1 1.5

A: sec-11.5

Q: 27-3 Det A=-1 5 - 4 690

A: DetA=  2   7  -3-1  5  -4   6  9     0=+25-49   0-(+7)-1-4   6   0+(-3)-1  5   6  9…

Q: Graphs of Rational Functions Determine the rational equation for each graph shown, beginning with y…

A: Given Starting function is y=1x     Translation theory- 1. If graph is shifted towards right by p…

Q: Determine the value of

A: we have to determine the value of z to correspondingprobability value is 0.0400

Q: Which graph represents the following ellipse (z+1)ª + 16 (v-3)° 36 = 1?

A:

Q: 36-9z

A: Given that:36-9z

Q: [-1 ] 5 8 1,

A:

Q: 28 Σ

A:

Q: Simplify. [21 -28] 70 -35

A:

Q: x3 f) x2+2x+1

A:

Q: -95 dt †2

A:

Q: 2 x -dx 6. Jo 1-x

A:

Q: Z-6=7

A: Complex variable equation.

Q: -3 -2 -1 1 2 0000000 3.

A:

Q: 3 dx-6x

A:

Q: 1 13 + x xp-

A: We will solve the integration.

Q: (8,-1)+(2,1)

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.