Find the area of one petal of the rose curve r = 3 cos 30.

Q: Find u · v, u · u, ||v||, (u · v)v, and u · (3v). = (3, 12), v = (-4, 3) (a) u• v (b) u•u (c) ||v||2…

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Q: (a) Graph the equations in the system. (b) Solve the system by using the substitution method. (x+3)°…

A: Using substitution method.

Q: Find the arc length of the parametric curve. x = e', y = et, z = v2t; 0<t < 8 L ||r'(t) × r"(t)||…

A: Given parametric curve x=et  , y=e-t  , z=2 t   ;  0≤t≤8

Q: Consider the following. u = (-9, -6, 4), v = (6, -7, 0) %3D (a) Find the projection of u onto v. (b)…

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Q: Jx + 2x f(x)=- 7х — 4х? 8.

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Q: Evaluate the integral. 9 17 1+ x2 dx V1- x2 +C

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Q: 里() t² + 5 1 lim t一+05t2 +6'2t (?, ?)

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Q: 6. The two figures are similar and regular solids. Find their mass if the sum of their mass is 120g.…

A: Given information: 1. Given pyramids are regular pyramids. 2. Both pyramids are similar. (Hence…

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Q: Describe the graph of the equation. r = -9i+ tj + (r² – 1) k O It is a parabola in the x = -9 plane,…

A: Let's find.

Q: S) Vx + 7 dx

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Q: If e = then %3D 4. sin(0) = %3D cos(0) = Give exact values. No decimals allowed!

A: Follow the procedure given below.

Q: 2. Determine if the given sequence converges or diverges. If it converges, what is its limit? (a) {…

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Q: 3. Is the function f(x) = csc2 + sec x- cosr even, odd, or neither? Show algebraically. %3D 4. Write…

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Q: Consider the following. 3D(6,-1,0) v = (-2, 3, 0) u = %3D Find u x v. Determine if uxvis orthogonal…

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Q: Suppose a person travels at a rate of 4 ft/hr toward the foot of a street lamp pole 51 ft high. The…

A: Solution: Let  H denotes the head of the person and P denote the top of the pole.  At any instant…

Q: I just need help solving this integral

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Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

A: The given function is;  f(x)=-6x/(6x2+8).

Q: 11T If 0 = then 6 sin(0) = cos(0) Give exact values. No decimals allowed!

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Q: Use the ratio test to discuss the Con vergence or divergence of the seríes which s the Sum from n1to…

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Q: Consider the following. u = 3i - j - k, v = -i + 5j + 7k (a) Find the projection of u onto v. (b)…

A: A detailed solution is given below

Q: If the function / is continuous for all real numbers and if f(x)= ² when x*-2, x+2 then f(-2) = O…

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Q: Find the equation of the tangent line to the curve (a lemniscate) 2( +y) = 25(x - y) at the point (-…

A: 2(x2+y2)2=25(x2-y2)2(x4+y4+2x2y2)=25x2-25y22x4-25x2=-25y2-2y4-4x2y22x4-25x2=-25y2+2y4+4x2y2different…

Q: F the curve. -)i + sin(nt)j

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Q: Profit. Suppose the profit of a product is modelled by the function f(x) = 2x3 – 30x² + 126x + 3 The…

A: First we find critical points then check absolute maximum values.  Answer is maximum value is 165 at…

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A: To solve the following problem

Q: Given the series: k=0 does this series converge or diverge? O diverges converges If the series…

A: The given series is ∑k=0∞-16k. To check convergence of the series we use ratio test. Suppose we have…

Q: llowing series determine if the series converges or diverges cence or divergence. (e) Alternating…

A: We have to check the given series is converges or diverges according to the given information

Q: (e) Alternating Series Test: Σ (-1)"-2 3n + 3n

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Q: nin m Find the distance between the point and the line given by the set of parametric equations.…

A: This question is based on 3-d line.

Q: Consider the following. g(x) = (5x – x³) h(x) = (3x + 4) f(x) = (5x – x³)(3x + 4) Find g'(x) and…

A: gx=5x-x3hx=3x+4fx=5x-x33x+4

Q: y y=x + 1 x = 4 y= 0

A: Area , A = ∫∫R dy dx

Q: 2 2 Write the equation in polar form: x + y = 225 %3D

A: Given,               x2+y2=225

Q: Find r'(t), r'"(t), and r'(t) · r"(E). r(t) = (t2 + 7t)i – 2t?j (a) r'(t) (b) r"(t) (c) r'(t) ·…

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Q: F (x, y, z) = x²yz² – 3xy°z + 2y°z²

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Q: Find a and b such that v au + bw, where where u (1, 2) and w - v- (0, 6)

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Q: Find the mass of the sphere x2 + y2 + z2 = a2 where the density at any point is two times the…

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Q: Question For the function f(x) given below, evaluate lim f(x) and lim f(x). f(x) = 5 sin (4x³) If…

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Q: EVALUATION. Do as indicated. Write TRUE if the statement is true otherwise write FALSE. 1. The given…

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Q: Solve the following and show the complete solution. Find D,f at P: f(x,y) = sin(8x – 5y); P(5,8)); u…

A: Given,            fx,y=sin8x-5y ; P5,8 ; u=35i-45jTo find : The directional derivative, Duf at P.

Q: Find the derivative of the function described. (Rx5) 4х-2 5. у 3 3x+4

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Q: Many statistics courses cover a topic called multiple regression. This provides a means to predict…

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Q: The world population at the beginning of 1990 was 5.3 bilion. Assume that the population continues…

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Q: Find sets of parametric equations and symmetric equations of the line that passes through the given…

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Q: For the sequence defined by: a1 = 2 2 + 1 An %3D An+1 Find: a2 %3D a3 = %3D %3D esc ->

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Q: f(x) = (sin x – 1) cos x on 2'2.

A: I am attaching image so that you understand each and every step.

Q: Find an equation of the plane through (0, -9, – 1) that is perpendicular to the line x - 2 = 3t, y +…

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Q: Evaluate the following limit using L'Hospital's rule. lim (cos(6x))) Provide your answer below: lim…

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Q: Find the following. (0, 1), v = (5, -5) (a) lu|| (b) v|| (c) ||u + v|| (d) (e) ||v|| u+v

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Q: 1. If x = cos t and y = sin? t, then dy/dx is 2. Find Zxyx if z = xe?y + ye2x. 3. If s 10 t? + 80/t,…

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