Consider the following vector function. r(t) = (6√√2t, et, e-6t) (a) Find the unit tangent and unit normal vectors T(t) and N(t).

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A: Given that , Vector : v=3i^+7j^ Find the equation of line through point P7,3 perpendicular to v.

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A: Given differential equation:- (3x-y+1)dx-(9x-3y-3)dy=0

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A: Topic - Continuity and discontinuity We are given that f(x)=9x

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A: Let's find equation of plane.

Q: Find the x- and y-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.)…

A: The equation is given by 4x2+9y2=36                              .......1 To determine: the x- and…

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Q: Find the horizontal and vertical asymptotes of the curve. 9ex ex - 8 y =

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Q: f(x)=-4 3- 2- -3- Watch the values of f(x) as the x value changes. 5 What y-value is f(x) getting…

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Q: QUESTION 2. f(x)=3x2+26 What is the slope of this function when x = -9.7? (Round to the…

A: f(x)=3x2+26slope is f'(x)dxndx=nxn-1d dx(constant)=0

Q: 28. k(x, y) = = -7x 2x + 3y

A: Given;  K(x,y)=-7x/(2x+3y).

Q: b) A farmer wants to put a fence around a rectangular paddock which is part of his block (see…

A: A farmer wants to a fence around a rectangular paddock which is part of his block. Only three sides…

Q: 3. Show that the LP problem Minimize: subject to g(x1, x2) = 2x1 - 5x2 x₁ + x₂ > 2 - x12x₂ ≤0 x22x11…

A: Given:- Minimize: gx1,x2=2x1-5x2Subject to :x1+x2≥2x2-2x1≤1x1,x2≥0

Q: [1 −4 2 8 −1 −4 -1 2 -8 -6 -3| -4 7 -57 [1 -4 7 2 8 -1 0 0 -20 -5 -4 7

A: Given:- 1-47-528-1-42-8-6-3~1-47-528-1-400-207

Q: Find the area of the region that lies inside both curves. r = 4 + cos(?),    r = 4 − cos(?)

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Q: For f(x) = 2x² + 5, find the number c in (-3,-1) guaranteed by the Mean Value Theorem. (Use symbolic…

A: Mean value theorm If f( x ) is continuous in [ a , b ] f( x ) is differentiable in ( a , b )then a…

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A: Given equation:- st=55-16t-22 Here s is height of ball in feet and t is time in seconds

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Q: A quantity P is an exponential function of time t, such that P = 50 when t = 4 and P = 80 when t =…

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Q: compare the instantaneous rates of change of f(x)= sinx and f(x)=4sinx of the same values of x. what…

A: Given: f(x) = sinx f(x) = 4sinx Definition of instantaneous rate of change: Instantaneous rate of…

Q: 10. h(x) = -x-2| Domain: Transformation: Range:

A: Given that h(x)=-x-2Note:-As per bertleby I have to solve only first question. For answer to others…

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Q: Find the limit. (If an answer does not exist, enter D √x+7-6 X - 29 lim X→ 29

A: solution:-limx→29x+7-6x-29=limx→29x+7-6x-29×x+7+6x+7+6

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A: Given query is to find average value of the function.

Q: The rectangular coordinates (x, y, z) of a point are given. Find the cylindrical coordinates (r, 0,…

A: Given rectangular coordinates ( x , y , z ) → ( 1 , 3 , 3 ) we want to find out corresponding…

Q: 1. Find a recursive definition for the sequence 7, 11, 15, 19, 23,... Assume the first term in the…

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Q: The function f(x) changes value when x changes from xo to xo + dx. f(x) = 2x³ - 2x, x = 1, dx = 0.1…

A: We need to find approximation.

Q: For the position function s(t)= - 16t+111t, complete the following table with the appropriate…

A: Given: s(t)=-16t2+111t Time interval [1,2] [1,1.5] [1,1.1] [1,1.01] [1,1.001] Average…

Q: An espresso stand finds that its weekly profit is a function of the price, x, it charges per cup. If…

A: As per guidelines we can solve maximum 3 subparts. Please repost others subparts and mention the…

Q: Compute the area of the parallelogram with vertices A(2 1), B(5,0), -2) and D(4, -1).

A: We are asked to find the area of the parallelogram

Q: Find the zeros of the polynomial​ function, and state the multiplicity of each.…

A: We need to find zeroes.

Q: 14 cout 5. + 3+ 2 2 -2+ -3- ress play to show imation Watch the values of f(x) as the x value…

A: To determine what y‐value is fx getting closer to as x approaches 1 from the right side.

Q: Set up a double integral to find the volume of the solid region bounded by the graphs of the…

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Q: Find the angle between the vectors u = 5i - 6j and v= −i+j+4k. The angle between the vectors is 0…

A: The given vectors are;  u=5i-6j, v=-i+j+4k

Q: In 2013, a certain company's annual revenue was 74 billion dollars and growing at the rate of 3.4x +…

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Q: -3 S T -1 5 3- 2- 1. 0 -1- -2- -3- 2 3 5 Limits A function f(x) is continuous at an x value of aif…

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Q: r the following equation, determine the values of the missing entries. Reduce all fractions to…

A: We will find the required.

Q: The first-order differential equation y = y(1-y) ¶ has a stable equilibrium at y=0. has an unstable…

A: For the autonomus differential equation dydt=f(y)we say that equilibrium solution y0 isStable if all…

Q: Calculate the integral, assuming that f(x) dx = 2 and g(x) dx = 15. (Give your answer as a whole or…

A: Given ∫05f( x )dx = 2 ∫05g( x )dx = 15

Q: From a fixed point, a surveyor locates a pole at 222.2 ft due east and a building corner at 325.7 ft…

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Q: √6x³y-5xy³ +7x²y-9xy² Homogeneous Degree

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…