2.3.27 Find equations of all tangent lines to the graph of y = 4x + 40x? • 125x + 118 which pass through the point (- 1, - 7) (not on the curve). Write the equations in order of increasing slope. y = y= y = (Simplify your answers. Type your answers in slope-intercept form.)

Q: : Let x and y be non-parallel vectors. Prove that (x + y) and (x - y) are vectors perpendicular to…

A: For two vectors A→ and B→, the angle between them is θ. The dot product of these vectors…

Q: Prove that the magnitude of the vector

A: To prove: magnitude of a vector M→(x,y)=M

Q: Problem #4: The temperature at a point (x, y) on a rectangular metal plate is given by 100 T(x, y)…

A:

Q: What is the scalar product A*B if A=Xi+Yj and B=Xi-Yj?

A: Given data: Two vectors A→ = Xi^+Yj^B→ = Xi^-Yj^ Required: The scalar product

Q: Write the given vectors in terms of its components and the corresponding unit vector and then verify…

A:

Q: In Problem,the vector v has initial point P and terminal point Q.Write v in the form that is,find…

A: Given that Position of P is = ( 0,0) Position of Q is = (3,4)

Q: Evaluate the given integral. Jx²Inxdx

A:

Q: show that the function y(x)=Ax^n (A and n are constants) will give a straight line on a log-log…

A: The provided function is expressed as y=Axn

Q: / The vectors A and B are given by A=-2î –3j and B = i -2j. nd 1.AxB and verify thatAxB =-BxÃ. 2.…

A: Given values:- A→=-2i^-3j^ ----(1) B→=i^-2j^ ----(2) (1) Let (R→) be the resultant value of A→×B→…

Q: In the graph given below, at the point A, the second derivative (dy/dx?) is B O a. posititve O b.…

A:

Q: The operation used to obtain a scalar from two vectors is

A: Dot product of two vector quantity gives a scalar quantity . Let  'a' and ' b' are  two vector  then…

Q: Find the gradient of following scalar function: |5x+7y°+3z' r = V

A: SOlution: the gradiant is given by for the scalar funciton F(x,y,z) dF = i dF/dx +jdF/dy + kdF/dz

Q: Given the two points P(1,2,3) and Q(2,-2,1) find the vectors

A: Tail of both 'vector lies on origin

Q: Find the equation of the osculating plane for the curve (rt) = costi + sintj + 2tk) at t=0. %3D Find…

A: A. Given curve is: Osculating Plane is given by the formula: now, This is the equation of the…

Q: Show that if a matrix is orthogonal and its determinant is +1, then each element of the matrix is…

A: Let A is an orthogonal matrix with determinant equal to+1. Orthogonal matrix, AAT=1…

Q: If f is a scalar function and v = [v1, v2, v3] is a vector field. Show that div(fv)=f divv+v·∇f

A:

Q: Write the following x2+y2=16 in polar form.

A: The given expression can be written as below,

Q: Find the divergence and rotation of the following vector A=i(x^2+y^2)+j(y^2+zx)+k(z^2+xy)

A:

Q: The distance vector from pointA (2, –3,1) and B(1,5, –3)

A: given point A =( 2 , -3 , 1)  therefore A→= 2ax-3ay+1az. point B = (1,5,-3) B→= 1ax+5ay-3az.where…

Q: Find the indicated trapezoid approximations to the following integral. 10 | 7x dx using n = 2, 4,…

A: Write the given values of this problem. ∫2107x2n=2,4,8

Q: As an illustration of why it matters which variables you hold fixed when taking partial derivatives,…

A: The variable  win terms of x andz is\ x=yzy=xz Then w=xy=xxz=x2z

Q: In the graph given below, at the point B, the second derivative (d'y/dx?) is B O a. infinite O b.…

A: The second derivative tell us whether the curve is Concave Up or Concave Down. If the second…

Q: Let C be the plane curve given parametrically by the equations : x(t) = t² - t and y(t) = t² + 2t -…

A:

Q: Let θ be the angle that the vector A vec. makes with the +xaxis,measured counterclockwise from that…

A: There are two physical quantities in nature- scalar and vector. Scalar quantities are those which…

Q: O Find the coefficient of (mu)

A:

Q: Derive the matrix for rotation around the x-axis 30

A: Basics of Rotation matrix: Rotation matrix is  used to perform a rotation in Euclidean space. The…

Q: nates of point N. 2) Write the vector KM in terms o

A:

Q: In the graph given below, at the point B, the nature of gradient (dy/dr) is A 4

A: Ans : b) zero

Q: What is the vector product of the following vectors? Show your solution  ?=3?+5?−2?   ???…

A:

Q: 1. Compute the divergence and curl of the given vector function: xy2 ,4x² – 3z) 2z F(x, y, z) = (7x…

A: Bartleby's guidelines allowing answer only the first question

Q: In the graph given below, at the point B, the second derivative (d²y/dx²) is В

A: Point of inflection: point of inflection is a point on a curve at which the curvature (slope)…

Q: prove that F(x, y, z) = (3x² + .

A: Solution:

Q: Consider the curve described by the parametric equations x =t+ cos t, y = 2 – sin t. Compute the…

A: Slope or tangent to a curve in  X-Y plane is given as dY/dX.

Q: If the direction E in space 1 is given as shown below and the magnitude E, = 5 volt. Find E, in…

A:

Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

A: Given:-   Initial point: (1, −2, 0)               Terminal point: (1, −2, −3) Find:- unit vector in…

Q: given a circle of radius a, find by integration using polar coordinates (d) its circumference…

A:

Q: Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of…

A: The cross product property of vectors is given by:u×v=uvsinθ......(1)where,u and v are the magnitude…

Q: In the graph given below, at the point C, the second derivative (d'y/dx) is. C O a. zero O b.…

A:

Q: Show that the order of addition of three vectors does notaffect their sum. Show this property by…

A: If vector P and Q are at angle θ each other,   Consider vector A=3m towards east, vector B=4m…