Let r, r, and r, be the roots of x’ +3x² –5x-4=0, construct the equation whose roots are: 7 (r, +r, ), r, (r; + r;) and r; (r +r,).

Q: The slope of the tangent line to the parabola 2x + 4x + 5 at the point (3, 35) is: The equation of…

A:

Q: Apply derivative to determine the vertex of the parabola y = x² + 2x + 2.

A:

Q: 2. Find y in terms of x if = 6x² – 2x and the curve passes through the point (1, 5). -

A: We have to find the value of x if dydx=6x2-2x and the curve passes through the point (1,5).…

Q: aber of linearly 1 is

A:

Q: The tangent line equation of 2x6+y4=9xy at the point (1, 2) is ….

A: The tangent line equation of 2x6+y4=9xy

Q: Form the polynomial equation with integral coefficients whose only roots are given. 2,-1,1

A: Given roots are 2,-1,1 Now we have to find the equation of polynomial with

Q: Find equations of both lines through the point (2, –3) that are tangent to the parabola y = x2 + x.

A:

Q: A stationary submarine is 2 km due south of a ship which is steaming due east at a speed of 20 km/h.…

A: please see the next step for solution

Q: In Exercises 41-44, verify by differentiation.

A:

Q: The slope of the tangent line to the parabola y = 2x + 2x + 6 at the point (- 1, 6) is: The equation…

A: The slope of the tangent line to the parabola                      y = 2x2 + 2x + 6 at the point…

Q: Find equations for two lines through the origin that are tang net to the curve x²-4x+y²+3=0 .

A: We have given equation of curve x2-4x+y2+3=0. We also know that the slope of the line will be the…

Q: Calculate the directional derivative direction Q(5,4) 4 3√-3x²-5xy3 of at P (1,-2) in the

A:

Q: Prove the relationship =<- dt

A: we have to calculate  ddt&lt;px&gt;  .....(1) &lt;px&gt;=-ih∫ψ*∂ψ∂xdx .....(2) substituting equation…

Q: Find the equation of the tangent line  x2y-y3 + 6x= 8  at the (3, -2)

A:

Q: Find equations of both lines through the point (2, - 3) that are tangent to the parabola y = x2  + x…

A:

Q: The slope of the tangent line to the parabola y = 4x? + 7x + 2 at the point (– 4, 38) is: The…

A: Equation of parabola,  y = 4x2 + 7x + 2 Given point is (-4, 38)

Q: 2. Find the equations of both the tangent lines to the parabola y through the point (3, 16). :-

A:

Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point…

A:

Q: Find the tangent plane to the equation 4x2 + 3y2 – y at the point (-4,-1,68) Z =

A:

Q: Find all points on the graph of 3x 2 + 4 y 2 + 3xy = 24 where the tangent line is horizontal

A: Given:              3x2+4y2+3xy=24 We know the tangent line is horizontal when y'=0 So we want to…

Q: Find the explicit solution of the separable equation

A:

Q: A stretched string of length 20 cm is set oscillating by displacing it midpoint from the rest…

A:

Q: The slope of the tangent line to the parabola y = 2x“ + 2x + 6 at the point (1, 10) is: The equation…

A: Given,            The parabola is y=2x2+2x+6 and the point is 1,10.

Q: Find the equation of the line tangent to 3x²y + 4xy2 = 6x² + 5y at the point (1,).

A:

Q: Find the roots of 5sin^2x-8cos^5x=0, x_0=0.5, using Newton method

A: Concept Used: Newton Method xi+1=xi-f(xi)f'(xi+1) Consider 5sin2(x)-8cos5(x)=0So…

Q: Locate root of the equation x +x- 2 = 0 using fixed point method.

A:

Q: 17. Passes through the point (2, 1) and is perpendicular to y = -x+ 3.

A:

Q: Find equations of both lines through the point (2, −3) that are tangent to the parabola y = x2 + x.

A:

Q: Find an equation of the line through the point (1, 2) that is perpendicular to th = --x +3 Select…

A: The given question is solved below.

Q: Find the equation of th line perpendicular to the line 3y=2-4x and passing through the point (4,7)

A:

Q: Find equations of the two tangent lines to the graph of f(x) = x- that pass through the point (-1,…

A:

Q: Find the equation of the tangent line to 4x2 +y2= 8 at (1,2)

A:

Q: What kinds of changes occur in the Coefficients of a Nonbasic Variable when the original model is…

A: Answer is explained below

Q: What are the coordinates of the points in the graph of y2 – x² + 6x – 13= 0 in which the tangent…

A:

Q: Find the slope of the curve at the point (2,3) * x³ 2x + 1 3/2 1 O 1/2 O 1/4

A:

Q: Find the curve in the xy-plane that passes through the point (4,8) and whose slope at each point is…

A: The curve in the xy-plane that passes through the point (4 , 8 ). Slope at each point is 3√x . We…

Q: Find the homogenous linear equation with real, constant coefficients that is satisfied by:…

A: Given that  Required differential equation is satisfied by   y= 6 + 3xe^x - cos x

Q: Find the point on the line y = 4x + 3 that is closest to the origin. (x, y) =

A:

Q: find the derivatives complex funcation. {tanh¬'(iz +2)}-1,

A: fz=tanh-1iz+2-1=1tanh-1iz+2 It is known that tanh-1x=11-x2 so it follows:…

Q: Find an interval of length 1/4in [1, 2] containing a root of the equation x^7 + 3x − 10 = 0.

A:

Q: Explain theorem of Wronskians of Solutions?

A: To Find : Define the Theorem of Wronskians of solution

Q: What are the coordinates of the points in the graph of y² – x² + 6x – 13 = 0 in which the tangent…

A: As we know that; The slope of the horizontal tangent line is zero or m=dydxPx0,y0=0 Given;…

Q: Find the tangent line to the equation: f(x) 3x2 + 2x-1, when x= 2 %3D

A: Using equation of tangent formula.

Q: The slope of the tangent line to the parabola y 3x + 3x +7 at the point (- 5, 67) is: The equation…

A: Take the derivative and put the given point.

Q: Find the real root of the equation x^5-x^4-x^3-1=0, Which lies between 1.4 and 1.5. correct to four…

A: The given equation is: x5-x4-x3-1=0

Q: Find the equation of the tangent plane to the graph of f(x, y) = In (13x² 10y²) %3D at the point (1,…

A: Solution is written in below steps.

Q: Express the first four cumulants in terms of central moments.

A:

Q: Differentiate, and make sure to show all your work: 3z ²-2 Y= 5 cosh z

A: We have to differentiate the given expression, y=3x2-25cosh x Apply the quotient rule for…

Q: 3. Find equations of the tangent lines to 9x +16y-52 that are parallel to the line 9x-8y-1

A:

Q: Find all the roots of =-V3+j %3D |

A: In this question, the concept of De Moivre's Formula is applied. All n-th roots of a complex number…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.