8) Find the unit tangent and unit normal vectors T(t) and N(t) for r(t) = (t, t², t²).

Q: Given sinα=0.802 and sinβ=0.812 with both angles' terminal rays in Quadrant-I, find the following:…

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Q: Evaluate the integral by interpreting it in terms of areas. *18 |x - 9| dx

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Q: roblem 5. A cup of coffee has temperature of 200 degrees Fahrenheit and is placed in a room that has…

A: Topic:- Newton law of cooling

Q: Find the curvature and the radius of curvature at the point t = 0. x = e cos(t), y = et sin(t), z =…

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Q: A rectangular solid (with a square base) has a surface area of 37.5 square centimeters. Find the…

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Q: The equation of motion of a particle is s = t³ - 27t, where s is measured in meters and t is in…

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Q: 47-48 Find equations of the tangent line and normal line to the curve at the given point. 47. y =…

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Q: The non-homogenous solution of the following equation by using variation of parameter method y" +y =…

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Q: Find dy/dx: solution in handwritten 1. y = 5* (** + dx VE х4 3 -x²,

A: Using leibnitz rule for integral.

Q: Is the function a power function. If it is, write it in the form f(x) = kxP, and state the values of…

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Q: Use Chain Rule to find ds given w = Vr² – 2y + z² and r = cos (st), y = -2s Int and z = s –

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Q: Let C be the parametric curve defined by x(t) = t² – t – 2, %3D |y(t) = t3 . 1 t² +t. 2 - (-2) 3…

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Q: Solve the differential equation 2xy + y²) dx + (x² + 2xy-y²) dy = 0

A: A homogeneous differential equation is one in which the degree of the function f(x,y) is the same as…

Q: Solve the system using Cramer's Rule. - x + 2y = - 5 4x + 5y = 32 Find the determinant D…

A: D=-1245D=-1(5)-2(4)=-5-8D=-13Dx=-52-325Dx=-5(5)-2(-32)Dx=-25+64Dx=39Dy=-1-54-32Dy=(-1)(-32)-(-5)(4)D…

Q: A rectangle is bounded by the x- and y-axes and the graph of y = (6 - x)/2 (see figure). What length…

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Q: Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Maximize z = 3x…

A: Here, the feasible region by the curves x+y≤1034x+y≤160y≥23x,y≥0 is:

Q: Find an equation of the line tangent to the curve r = sin 30 at the point where 0 =

A:

Q: Consider the vectors. 6i- j, -8i + 4j (a) Find the dot product of the two vectors. -52 (b) Find the…

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Q: What does the graph of the parametric equations x(t)=3−t and y(t)=(t+1)2, where t is on the interval…

A: t x=3-t y=(t+1)2 (x, y) -3 6 4 (6, 4) -2 5 1 (5, 1) -1 4 0 (4, 0) 0 3 1 (3, 1) 1 2 4…

Q: solve the following equation 2sin3x+sin2x+1=0, on the interval 0<x<2pi

A: 2sin(3x)+sin(2x)+1=0Let f(x)=2sin(3x)+sin(2x)+1 , 0&lt;x&lt;2πThe graph of f(x) is shown below:

Q: Problem 4. Part (a) Part (b) 5ln(3-x) = 4 Do both parts. Write the sum using sigma notation:…

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Q: A radar, using the polar coordinate system, detects that an airplane is currently located at the…

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Q: 4n – 9 5n + 4 S - Given that sequence {an} = { (а) Show that the sequence is monotonically…

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Q: Solve the integral Sa 16 tani? 7+x²

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Q: n 9 = k=1 Note: Your answer should be in terms of n.

A: Solve the given

Q: In 2000, the population of a city was 76,000. The population had grown to 111,000 by 2011. If the…

A: We have to find the year.

Q: X-Z The iterated integral J = g(x, y, z) dy dx dz is equivalent SS 0z0 to which of the following…

A:

Q: A student is asked to determine the polar coordinates (r, 8) corresponding to the Cartesian…

A: Let's find.

Q: Solve the given initial-value problem. y'' + 4y' + 5y = 35e−4x,  y(0) = −2,  y'(0) = 1 y(x)=

A:

Q: 4 Water drips into a conical container, which is orientated point downwards, at a rate of 100…

A: This is a problem related to mensuration. Based on the formula for volume of cone and derivative…

Q: f(x)=x√ 36 = x² ntercepts (x, y) = (x, y) = (x, y) = elative minimum (x, y) = elative maximum (x, y)…

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Q: 9. A and B are unit vectors with an angle of 120° between them. Determine 3A +2B and it's direction.

A: We have to find the vector addition.   A→+B→=A→2+B→2+2A→B→cosθ

Q: dy 1 dx 3y3 By the method of separating the variables y = x3 y = Vx+ c Option 1 Option 2 y = vx + c…

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Q: Problem 2. Do both parts. 8 Part (a) Find the sum: 12 4 + +· 3 9 27 81 Part (b) Solve the equation…

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Q: 3. An airplane with an airspeed of 80 meters per second is due east, gaining altitude, and has a…

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Q: Solve the system using Cramer's Rule. - 6z + 2y + 6z = – 14 - 3z - 4y + 5z = – 6 - 5z + 3y –2z = 1…

A: To solve the following system of equations bu using Cramer's…

Q: Consider the polar equation defined by r = 5 cos(2 sin 6), where 0<0< 27. Determine the missing…

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Q: Give a formula for the nth positive even integer: Here is a theorem: 1+ 2+3 + ... + n п(n+1) n = Use…

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Q: If x-8 A B then the value of A is (x+1)(x-2) x+1 x-2 and the value of B is

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Q: Find the area under the graph of the function y=2-x-x² over the interval [-2,1].

A: Given query is to find the area under the curve.

Q: Given the series E Vn9 +1 Vn9 1. n=1 Explain why the limit comparison test is applicable to check…

A: Using limit comparision and p test.

Q: Given the general solution for a system X' = AX, X=C 2 + C2 e and 2 find the value of Ci & C2. 4 the…

A: Given;  X'=AX X(0)=(2            4).

Q: 2. Let f(x)=x-3x² a. Determine all x-values where f(x)=0 b. Fill in the table below with the…

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

Q: Given the relation x³z² + sin(3xz - 2y) - 3√9+7x3 = 5y -23 implicitly defines z as a differentiable…

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Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: Height is given by f(t)f(t)=-16t2+420t+6t =11.5

Q: 6. During the worst 4-hr period of a hurricane the wind velocity in miles per hour is given by v =…

A: The average value of the function is given by;0≤t≤4v(t)=1b-a ∫abv(t) dt     =14 ∫04(5t-t2+100) dt

Q: If A =27+7-, B =-T+27-4k, and A +B +C =27+7+ 2k, what is C? 7.

A:

Q: Match the function with one of the graphs below using horizontal asymptotes as an aid. Am 0.5 0.5

A: This question is based on graphing a function using horizontal asymptote.

Q: Suppose that sec(t) = 3/2 and that tis in quadrant IV. Find the exact value of tan(t). -3/2 -$5 O -…

A: 1 +tan2(t) = sec2(t) In Quadrant 4th , secant and cosine are positive. Note : As per our Guidelines…

Q: A person's weight increases with height through approximately the end of the teenage years. Dan's…

A: In this question ,we can find Dan's weight .