If a cubic equation has a lead coefficient of 2 and a y interce know about the end behavior as x 00? O /(r) 2 O f(#) > oO O f(2) - 00 Of()→- 5

Q: 2. Eliminate the arbitrary constant on the given equation: y = C₁e-²x + De4x

A: Given  y=C1e-2x+De4x

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1600 – 0.005x2 - 0.01y?,…

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Q: If dy = dz, what is the equation of y in terms of x if the curve passes through (1, 1)? General…

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Q: In which form should we look for the particular solution of: Y” + y = x3cos(x)

A: Let y=yc+yp be the general solution, where yc is complementary function and yp is particular…

Q: (² + 1)³yy'(t) = 1(y² + 4)

A: Given:- (t2 +1)3y y'(t) =t(y2 +4)  To find:- General solution of given differential equation

Q: GIVEN: (xn , yn) = (1, 3), (2, 4), (4, 7), (5, 9) Determine the best-fit quadratic curve that…

A: GIVEN: (xn, yn)=(1, 3), (2, 4), (4, 7), (5, 9) we have to determine best-fit quadratic curve that…

Q: Q1/a- Write an equation of the Line that passes through point: P1 (-2,0), P:(2,-2)? b- find any locl…

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Q: A SERIES ELECTRICAL CIRCUIT WHICH YOU ARE TESTING FEATURES A CAPECTIOR (C) CHARGING VIA A IMS…

A: Resistance =1M ohm=10⁶ ohm Dc supply =12V Voltage across capacitor = 2V  Time = 4sec

Q: [2] Determine homogeneous the roots of the auxiliary equation y=x²-ecosx for a linear equation with…

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Q: : A plate whose shape is given by x 2+y 2 ≤ 1 is heated so that the temprature T(x, y) at the point…

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Q: Use variation of parameters to find a particular solution of y"- 2y' +y = 14xie" Yp(x)

A: y''-2y'+y=14x32ex find the roots for the homogeneous system  r2-2r+1=0 r-12=0 r-1=0 r=1 for one real…

Q: Q5. A. Solve the Euler-Cauchy equation xy - 4xy + 6y = 0

A: The given questions are four individual questions. As per bartleby expert policy, only one…

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

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Q: 1. Eliminate the arbitrary constants on the given equation: y = C1 + C2e¯ -2x 2 Eliminato

A: Given

Q: 5. Given that a cubic equation x" + ax" + bx +c = 0 has zerOS a, B and y. Show that aßy = -c.

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Q: Use variation of parameters to find a particular solution of y"- 2y' + y = 14xie Yp(x) =

A: Auxiliary equation for the given equation:

Q: What is the auxiliary equation for y"+by'+c=0, b & c is constant. What are the condition for this DE…

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Q: 3) Solve y"-4y't13y y0)=-l sy'co)= 2

A: The given differential equation is                                                     y''-4y'+13y=0…

Q: 1nd the general and definite solutions of the diIference equations

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Q: Prove that the following equation has no natural solutions x? + x +1 = y².

A: we have to prove that given equation has no natural solution

Q: 5. Given that a cubic equation x° + ax² + bx +c= 0 has zeros a, ß and y. Show that aßy = -c.

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Q: Show that the general cubic equation y3 + by2 + cy + d = 0can be transformed into an equation of the…

A: To find the equation of the form

Q: 4. Give the graphical significance of the constant k for the equations of the form y=(x-h)³ +k

A: Given curve is y=(x-h)3+k

Q: Find the general solution to  y''+ y' = 1 + 2sin(2t)

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Q: Suppose that x-y" + axy' + by = 0 has the general solution of the following form: y = C,x³ + C2x³ In…

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Q: Suppose that z = 3 – i is a root of the equation - ax" + bx + cx + d = 0, a,b, c, d E R

A: given one root of the equation ax7+bx4+cx+d=0. a,b,c,d∈R is z= 3-i we know that complex roots occurs…

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: Show that a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of the…

A: To show that  a riccati equation with constant coefficients y'+ ay² + by + c = 0 has a solution of…

Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1). %3D

A: For part a). Given that                      y' = 2(2x-y) =4x-2y                      y' + 2y = 4x…

Q: The equation f(x)= x² -e* has a solution [-1, 1]. With po= -1 p1=1, calculate p2 using the the…

A: The secant method uses the formula: xn+2=xn-f(xn)⋅xn+1-xnf(xn+1)-f(xn) to perform the iteration. The…

Q: determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. Do not…

A: This is 3rd order differential equation. Solution consists of two parts 1. Complementary…

Q: y" + 2y' = 2te

A:

Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: Use variation of parameters to find yp of x²y" - 2xy' + 2 y = -12 x(1/2) given that yi = x and y2 x2…

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Q: In this problem we outline a different derivation of Euler's formula. .Show (formally) that y = eit…

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Q: In this problem we outline a different derivation of Euler's formula. Show (formally) that y = eit…

A: Given that, y = e^(it) Differentiating with respect to t we get, y' = dy/dt = ie^(it)…

Q: A cubic equation f(x) = 0 has one real root a and two a, ß+iy and B-iy respectively on the Argand…

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Q: 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.

A: We have to discuss the graphical significance of given equation.

Q: List the roots of the auxiliary equation for a homogeneous linear equation with real  constant…

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Q: 3. Suppose = f(). (a) Given y(xo)= Yo, when does this equation have a unique solution? (b) Make a…

A: suppose dydx=fymx (a) given yx0=y0, when does this equation have a unique solution? we have  y'=fymx…

Q: Apply the appropriate method to solve the Cauchy-Euler equation 2x²y "+ 5xy'+ y = x² – x

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Q: Use undetermined coefficients to find the particular solution to y'' + y' – 3y = 4t + 5 Yp(t) = %3D

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Q: Find the general solution of each nonhomogeneous equation. 1. y" + 4y= 8

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

Q: A tree frog jumps along a parabolic path given by y =-0.15x +1.2x, where x is the frog's horizontal…

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Q: 1 Solve 1 3D7 for z. y. 1-

A: 1x-1y-1z=7

Q: (g) Any separable equation M(x)+N(y)y' = 0 is also exact. %3D

A: Since you have asked multiple question, we will solve first one for you. If you want other question…

Q: Eliminate the arbitrary constant a from the equation (z - a) + y = a O = + 2ry' O = + 2ry Ov =+ 2ryy

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Q: Use the intermediate value theorem to show that the equation x^3+x^2−2x+1=0 has a solution i the…

A: (note - I assume i as iota) f(x) = x3+x2-2x+1 At x= -1,      f(-1) = (-1)3+(-1)2 -2(-1) +1…

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.