Given the curve r(t) = (cos 3t, sin 3t, 2t) Find the following unit vectors and simplify your final answers.

Q: (2) A force of 4 N will stretch a rubber band 0.04m. Assuming that Hooke's Law applies, how far will…

A: Note: Hooke's law: F= kS Where F is force  k- elastic constant S-strain   Work formula: W= F.S…

Q: Find an equation for a plane P that: meets the x axis at the point where x = a, meets the y axis at…

A: Here plane passing through the points (a,0,0) , (0,b,0) and (0,0,c) We know that equation of plane…

Q: Find the fluid force on the vertical side of the tank, where the dimensions are given in feet.…

A: Fluid force=∫abρh(y)d(y)dywhere ρ is the density of liquid            h(y)  horizontal length of the…

Q: 7. Find the arc length of the curve r(t) = (cos³ (t), 0, sin³ (t)) from t = 0 to t = FIN 2

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Q: Find the domain and range of the function graphed below. Domain: 3 -5 -4 -3 2-1 Range: 2 1 123 -2 -3…

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Q: r2 Find y" if y=3(1-5x²) 4- 2 - 5r – 8

A: second derivative of function is given below

Q: tan x cos √√y dy = 2 y 4 + sin² x dx

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Q: Find the equation of the line tangent to the graph of f(x) = √√√x-4 at x = 8. Provide your answer…

A: Given Function:- fx=x-4

Q: 4. The movement of a certain glacier can be modelled by d(t) = 0.01t² + 0.5t, where dis the…

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Q: a. limx→o f(x) MATH 190: CALCULUS Exam 1 Problem 1: The graph of f(x) is given. Find each limit or…

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Q: The domain of the function is the interval (Number Number f(x)= √₁-

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Q: Suppose C is a constant and that O 1 0 1 2 exists. Then this limit must evaluate to 2 lim x→0 2…

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Q: 2 Show that the total length of the astroid x¾ + y³ = a³, which can be parameterized as x = acos³0,…

A: Solution is here

Q: 1. Differentiate y = √e(72²-2) (a) by using the chain rule directly with functions f(x) = VI and…

A: Given, y=e7x2-23

Q: Find the average value have of the function h on the given interval. h(x) = 4 cos(x) sin(x), [0, π]…

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Q: Complete the table. (Round your answers to five decimal places. Assume x is in terms of radian.) 3…

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Q: Graph the following system of linear inequalities.     3x − 2y   ≤   4 −4x + y   >   −6

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Q: 4. X dy dx 2 + 2y = x²

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Q: 3. An aluminum rod 8m long has linear density √2+1 kg/m. Find the total mass and average density.

A: Total mass of a rod of length l of having linear density ρ(x) is ∫0lρ(x)dx.Average density…

Q: The population of deer in a forest can be modeled by 630 +2960 P(x) = 3x + 8 where x is the number…

A: According to our guideline we are supposed to answer only the first 3 sub-parts of the question. If…

Q: f(x) = -6x + 17

A: The given function is: f(x)=-6x+17

Q: Let ƒ(x) = tan(x)and g(x) = sec(x). Find [ƒ(x) + g(x)]. da d dx −[ƒ(x) + g(x)] = d dx d dx [ƒ(x) +…

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Q: We want to compute the following limit a) As t approaches 0, this gives an indeterminate form of the…

A: Topic- Simplification we are given,limt→02t3-9+5twe need to simplify by using rationalization so…

Q: 2. Find the general solution. a) a' = -(2/t)x+t. b) y'+y=e². c) x² + 2tx=e-t² 1. First-Order…

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Q: Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F(x) and G(x) are the functions whose graphs are…

A: Here, P(x)=F(x)G(x)⇒P'(x)=G(x)F'(x)+F(x)G'(x)   (used the product rule of the…

Q: Problem 5. Suppose that F and G are antiderivatives of f and g, respectively. Show that, in general,…

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Q: 8. Find the position function r(t) given that ā (t) = (-1,-1, -1) and (0) = (-5, -5,5) and 7(0) = 0.

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Q: 17. lim x² + 3x

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Q: Find f'(x) by using the definition of the derivative. [Hint: Use (x + h)5 = x5 + 5x¹h + 10x³h² +…

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Q: 10. B. (Å×ů) | Run A X = lyz2 -382 zxyz 으으 oxy t 으 olo p = xyz = 아름 - 3x22 2x42 으 해 고 ㅎㄹ | C.) 2 92…

A: To determine the mistake done by the student and to correct the solution provided by the student.

Q: Is the function, whose graph is drawn in Fig. 7. continuous at the following values of x? Figure 7…

A: To solve the problem of differentiability by seeing the graphs of the function.

Q: b) g(x) = 11x³ - 4 g ¹(x) = 19

A: Since you have asked multiple question, we will solve one question for you as per our guide line. If…

Q: Find the general solution (x² +1) 4x + 3xy = 67

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Q: If I know the characteristics of the graph of a sinusoidal function, how can I write an equation for…

A: If I know the characteristics of the graph of a sinusoidal function, then to explain how can I write…

Q: Given that S [₁² f(x) dx = 3, ²9(2) dz = 2 g(x) dx 39(x) - [² f(x) — 2 dx.

A: Given ∫02fxdx=3        ....1∫02gxdx=2      ......2

Q: Evaluate f f (x) dx if f(x) 06 O 12 8 O 14 = Į [2x X 1 if x ≤ 3 if x > 3

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Q: Find the volume of the solid generated by rotating the region bounded by y = x² and y = 6x-2x² about…

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Q: Section 1: Solve each AABC. Give angle measures to the nearest tenth of a degree and side lengths to…

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Q: 1. Fill in the derivative rules learned in class on: d dx [c] = d dx -[e] = = d dx d dx [x²] = =…

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Q: 37. Cost of Transatlantic Travel A Boeing 747 crosses the Atlantic Ocean (3000 miles) with an…

A: see below the answer and calculation As per bertleby guideline I have to solve only 3 subparts. So…

Q: c) h(x) = h ¹(x) = 19 x + 4 d) j(x)=√x + 11 j¹(x) =

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Q: Given f(x) = x²-3x+2 x+6 which of the following statements are true? Select the correct answer…

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Q: Find and sketch the domain of the function. f(x, y)=√y+√9-x² - y² y

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Q: Consider the function ab a b |a| g(x) = TT a sin²(x)+1 kx+1 2x+1 a) What is the condition on a in…

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Q: b) By factoring from the numerator and denominator appropriately, rewrite g(x) = ab Answer: 90 4 a b…

A: Given query is to find the g(x) and the indicated limit.

Q: Use the formula below to find the instantaneous rate of change of the function at the given x-value.…

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Q: Use the formula below to find the slope of the tangent line to the curve at the given x-value. √x at…

A: Slope of the Tangent line (m)=1/4

Q: If find f'(x) f(x) = = 5x² tan x sec x

A: Given :fx=5x2tanxsecx

Q: Show that every symmetric (то) 3х3 в а) 2х2 square is a multiplication table of a group Latin

A: A Latin square is an n×n array filled with n different symbols, each occurring exactly once in each…

Q: The angle measures of AJKL are in radians. J sin (7) L = 11 AA What is the value of sin ()? Enter an…

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