Find the velocity, acceleration, and speed of a particle with position function r(t) = (5 cos t, −3t, 5 sin t) v(t) = { a(t) = ( |v(t) = "

Q: Given r(t) = 9t² i + 18tj and t = 1, find the tangential and normal components of acceleration. ат…

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Q: JENCES AND SERIES: onvergent or divergent and, if convergen 23 an 20 ,n=1,2,3,...

A: The answer is given below:

Q: The function f is graphed below. State the values that fulfill the following requirements. If there…

A: Please see the below picture.

Q: Consider the points A(3, 5, 1), B(7, -1, 0) and – C(-1, 3, 4). Find 2AB + BC. O(-1, 2, 3) O(0, -10,…

A: The given points are A3,-5,1, B7,-1,0 and C-1,-3,4

Q: 8. Determine the dot product of u = [5,-3,1] and v=| 1v=[2,-2,3].

A: Please see the below answer.

Q: e) 9x³ + 6x² + 18x + 12

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Q: X 2 Find x² +1 -dx

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Q: 3 If ƒ (x) = 2 + x, evaluate Σƒ (k+1). k=1

A: We can answer the question as below.

Q: 4. [2 marks]. Solve the following system of equations using the Gauss-Jordan elimination method: -2x…

A: If you don't understand any step please comment.

Q: Solve the following initial value problem for the unknown function y(x) a) y' = 2xy², y(1) == b) 2…

A: Topic:- application of integration

Q: Consider the rational function f(x) = x²-x-6 x²+3x (i) Factorise the numerator and denominator. (ii)…

A: As per guidelines, we must answer only three of the subparts of a question given. So, I answer the…

Q: Find the equation of the tangent line to f(x) = 4x² -5x+2 at (-1,11).

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Q: dv/du = (u — v)² — 2(u - v) - 2.

A: Here, the given DE is: dvdu=(u-v)2-2(u-v)-2...(1) Substitute u-v=p differentiating it with respect…

Q: 5. Determine whether the following are rational numbers: (a) 2² +27¹; (b) log₂ 3; (c) 2+√2. (d) If…

A: We have to find if the given numbers are rational or not.

Q: Find the curvature (t) of the curve r(t) = (−4 sin t) i + (−4 sin t)j + (1 cost) k

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Q: e) 3 (12x²-108) 2 x + x - 12

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Q: Solve the following system of equations using the Gauss elimination method 4x - 3y + 2z = -16 -3x -…

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Q: A- Find the solution y(x) of the differential equation +=(x), the initial dx conditions y(0) = 1, y'…

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Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A: Given f(x)=1xa=1

Q: U V U a) f(x) = sin x The trigonometric function pictured here is b) f(x) = csc x O c) f(x) = sec x…

A: we need to find which trigonometry function has the following graph

Q: Which of the following represents a possible equation for a sinusoidal function with an amplitude of…

A: answer is in next step. please give a like!!

Q: Find all intervals on which f(x) is increasing. f(x) = x³ + 7x² + 15x + 45

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Q: Sketch the region enclosed by y = 7x and y = 9x². Find the area of the region.

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Q: Suppose f(x, y, z) = (a) As an iterated integral, 1 x² + y² + z² and W is the bottom half of a…

A: Triple integral

Q: (4) (g) S 40t2 4t²+25 - dt S du = u-atan-¹"+C u² u²+a² (be sure to list the parameters: a,b,u,…

A: Given ∫40t24t2+25dt   And use ∫u2u2+a2=u-atan-1ua+C

Q: 1. Factor the following completely. a) 16x² - 100 b) 15x²-3x - 12

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Q: A piece of cardboard measuring 13 inches by 12 inches is formed into an open-top box by cutting…

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Q: Let the position function of a particle be r = <t, t2,0〉. Find the tangential component of the…

A: Let the position function of a particle be r=t, t2, 0.To find the tangential component of the…

Q: 18. y = 3x + 2 20

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Q: = Approximate the area under the curve y = x² from x with 6 subdivisions. 3 to 6 using a Right…

A: We have to approximate the area under the curve using Right Endpoint Approximation.

Q: 1. The function f is continuous on the interval [3, 13] with selected values of x and f(x) given in…

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Q: 1. Find the volume of the solid that results when the shaded region is revolved about the indicated…

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Q: Test Σ n 1 2" n! for convergence

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Q: 1. According to Kanye East (not to be confused with Kanye West), (ux v) × w = u × (v × w). Is this…

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Q: Solve for the General or Particular Solution of the following Linear Differential Equation. dr de 4…

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Q: Find the arc length of the curve on the interval. r(t) = t²i + 12tj, 0≤t≤ 6 The figure shows the…

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Q: Verify that the following function is a probability mass function, and determine the requested…

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Q: Σa_₁ (-_^_-) n² 'n n+1 Select one: O True O False is convergent.

A: To determine whether the following statement is True or False.∑n=1∞ nn+1n2 is convergent.

Q: For the following equation, find Answer: dy da || y = -4x5 8x³ + x² +9x

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Q: Use the graph of the function f(x) shown below in order to determine all values of a in the interval…

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Q: Determine the exact solutions to cos: O ○ 0=160=² ○ 0-5,0- 7x 0= 6 6 O O 0 7x 6 5x 6 R 0= =,0= 6 11x…

A: We can answer the question in the following steps.

Q: 4. The population, P, of a school of fish t years after being released in a new habitat is given by…

A: The solution is given below

Q: A piece of cardboard measuring 10 inches by 8 inches is formed into an open-top box by cutting…

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Q: Use following se k Z K-I the integral test Series to decide converge

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Q: The depth (in feet) of water at a dock changes with the rise and fall of tides. The depth is modeled…

A: Given: The depth function: D(t) = 2sinπ4t+5π4+5 Depth is changing at 6 a.m. t = 6

Q: Given that f(x) = x²h(x) h(-1) = 4 h' (1) 7 = Calculate f'( − 1).

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Q: Find the length of one turn of the helix given by r(t) == cos(t)i + sin(t)j + 1 1 99 25 -tk.

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Q: dy Find in each of the following: (be sure to use proper notation and simplify) dx (a) (b) y = sin¹…

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Q: 2. Suppose a population of insects grows exponentially, there were 130 insects after the third day…

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Q: (a) Find the velocity function. v (t) = (b) Find the acceleration function. a (t) = PY PW POY

A: A particle moves according to the position function st=e4tsin5t To find the velocity and…