The plane with equation = (6,-2,3)+a(1,3,0) + b(2,2,-1) intersects the y- and z- axes at the points A and B respectively. Determine the equation of the line that contains these two points.

Q: Which of the following describes the graph of g(x) = -In(4 — x)? 8 7 5 4 2 2 -30-9-8-4 -6 -10 6 8 9…

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Q: Find the vertical shift of the sinusoidal function. fx -3πT -2T Simplify any fractions. T 6 5 ★ تلا…

A: Concept: The sine function's general form: y=Asin(Bx+C)+D The vertical shift: This is the vertical…

Q: 20. Which of the following is a direction vector for the plane with Cartesian equation 3x-2y-52+3-07…

A: Given problems:- 20. Which of the following is a direction vector for the plane with Cartesian…

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Q: By using Euler method, Solve these questions 3.3 2 2 XD² + 2XD + XD=Y=6

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Q: The projected population of a certain ethnic group(in millions) can be approximated by p(t) =…

A: Solve the following

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Q: 5 (x+4)³ For the function f(x) = exist, enter Ø as your answer. X -4.1 -4.01 -4.001 -4.0001 -4.00001…

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Q: The position function of a particle is given, in metres, as s(t)=t 4-10t 3+36t 2+10t+12 where t ≥0…

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Q: 24. Which of the following lines is not parallel to the other three? a. 7=(3,-5,-3) + s(2,-3,1), s e…

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Q: Determine whether the function defined is one-to-one. f(x)=√/32-x² -X www Is the function…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: 1. Let = =(3, 2, 1) and 5 = (-4,3₁-1) e) Evaluate (3a+46) (3a - 4b). f) Find the angle between a and…

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Q: Solve the initial value problem. 1. y'=4xe2x²cosx - ytan x, where y(0)=1

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Q: (a) Given functions f(x) = 3x+2 and g(x) = x³ - 1, find fog and the inverse of fog. 4. (b) Use the…

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: Find the directional derivative of f(x, y) = √√xy at P(3, 5) in the direction of Q(3.920, 0.795). 1.…

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Q: The doubling period of a bacterial population is 10 minutes. At time t = 80 minutes, the bacterial…

A: Given: The doubling period of a bacterial population is 10 minutes. At time t =80 minutes, the…

Q: Expand the expression sqrt34cos(7x-C), where C=arctan(5/2). Final answer should have the format…

A: Solve the following

Q: 5. A 210-N mass is suspended from a horizontal beam by two cables that make angles of 29° and 53°…

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Q: Sketch a graph of f(x) 5 4 3 2 1 -5 -4 -3 -2 -1 - 1 { 0 if x ≤ - 2 x + 1 if -2 2 2 3 4 5 Open Dot…

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Q: Please find the gradient of f(x, y) = ln(x² + xy²) at (2, 1)

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Q: (i) Find the shortest distance from the origin to the line 3x + y = 6 and give the coordinate of the…

A: We have to solve given Questions.

Q: = 3-5x + 2x². Calculate the following values: Let f(x) f(a) = f(a+h) = f(a+h)-f(a) h = for h 0

A: This question can be solved using the concept of function.

Q: Consider the following function. Function f(x) = 8x4 - 6x³ - 165x² - 37x + 60 (a) Verify the given…

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Q: Consider the following polynomial function. f(x)=x (x-1)(x + 1)² Answer the questions regarding the…

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Q: Below is the graph of y= log₂ x. Translate it to become the graph of y= log₂ (x+2)+4. X -6 -4 -2 2 ?

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Q: Q6. Find the volume of parallelopiped formed by the vectors , and .

A: Given :a=<2,-4, 5>b=<-1, 0,-3>c=<3,-5,-3>

Q: 8 Y + 2√² + 2y = 10x + 25

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Q: Q1. Find the distance between the points A (-1, 3, 7) and B (2, -1, 6).

A: The given points A(-1,3,7) and B(2,-1,6).

Q: 3)Evaluate the following integral by using Trigonometric Substitutions Method. dx √√9x² +9

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Q: (x² - 12x + 9) dx (x²-3x + 2)²

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Q: Find the open intervals where the function f(x) = − 2x³ + 6x² +172x-3 is concave upward or concave…

A: The given function f(x)=-2x3+6x2+172x-3

Q: The growth rate of a town's population after t years is P'(t) = 420 t². If the town's current…

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Q: 1. The effectiveness of studying for an exam depends on how many hours a student studies. For a…

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Q: Determine whether each equation is true or false. 1. f sin x dx = cos x + C 2. fcos x dx = sin x + C…

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Q: For the function f whose graph is given, state the following. (If the limit is infinite, enter 'co'…

A: Given graph:-

Q: 6. Find the general solution of the PDE. The solution u is a function of x and y. U = x-yz +y³

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Q: Find the equation of the curve that passes through the point (1, 3) and has a slope of at any point…

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Q: 2x + y + z = 1. 7. Find the tangent vector r' (t) and unit tangent vector T(t) at the point with t =…

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Q: Q1// Converting r= 12 cos 0 r = 12 cos 0 from polar to the equation of a circle?

A: Given problem:- Converting r = 12cos(θ) from polar to the equation of a circle?

Q: Solve 5^(x-3)=2^(6x-8)

A: Topic = Algebra

Q: # √² + y = 2 Y = 10 + 3X

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Q: Q6) Find the Area bounded by the curves y = √x and x = 2y-y² ,with sketch.

A: The objective of the question is determine the area bounded by the given curves.

Q: Q7) Calculate AC. BC and (A + B)C. Also, verify that (A + B)C=AC + BC 6 71 [0 1 1] B= 1 0 2 If A =…

A: Follow the procedure given below.

Q: Alex wants to design a beach cabana tent with a rectangular box shape. The tent will have two square…

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Q: 3. (3y² + xcos xy) + (3x² + ycos xy) = 0 dx a) y + sen xy + x³ = 0 y² + sen xy + x³ = 0 y² + sen y +…

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Q: Find a function F(x) satisfying the given conditions. 1. F'(x) = 2x ; F(1) = 2 2. F'(x) = 3x² + 2;…

A: To find a function Fx satisfying the given conditions.1 F'x=2x; F1=22 F'x=3x2+2; F-3=-323…

Q: 3 co ós co -6 -3 144 -4 Let y = ,V1= 5 -1 Compute the distance d from y to the subspace of R4…

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Q: For the matrix B shown below, determine the value of the element b32. If the element is not defined,…

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Q: A differentiable function g(x) has only one local maxima at x = 1. It is also known that g" (1) 0…

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Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…