The position of an object attached to a spring is given by s (t) = cos(4t) — —sin(4t), - where t is time in seconds. When 0 < t < 3, how many times is the velocity of the object equal to 0? O Zero O One O Two O Three O Four

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Q: 1. The minimum possible perimeter for a rectangle with an area of 529 m² is

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

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A: r1(t)=6t i+ 4t2 j+ 4t3 kdr1dt=6 i +8t j +12t2 kr2(t)=t4kdr2dt=4t3 k

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A: We can find the required 2nd derivatives as below

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A: Follow the procedure given below.

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A: Solving

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A: Given matrix is  A=-2011-10-1-21 A matrix is non singular if determinant of the matrix is  non zero…

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A: f(t)=116,0001+5500 e-tA)when epidemic begin;t=0f(0)=116,0001+5500=21.087The number of people…

Q: ind the area of the blue region. It is the area under the curve. y y = 3x+1 y=7-x 6 8 4 2 4 00

A: Follow next step

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Q: > Question 22 if y = log3 x find y' xina 01 2/xina

A: To differentiate..

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A: Using mean value theorem.

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Q: 10 F [TOF If f(x) dx = 16 and 5 Isro f(x) dx 10 f(x) dx = 5, find the following. S

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Q: Decide if the limit exists. If it exists, find it. x²-25 a. lim b. lim X-5 x+5 x²-36 x-5 x-5

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Q: Use the formula к(t) 390 t¹4 k(t) (4 + 210 t¹3) = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = t²i+t¹5j X…

A: Use derivative for finding the curvature .

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A: Solve the following

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Q: 9) Evaluate the following indefinite integrals a. [(5x¹ + x² + x) dx b. 9x²(x³ +5)*dx c. S7 C. dx…

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Q: ∫12v (7+6v2)9 dv Evaluate indefinite anti-differentiation

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Q: Let f(x) = x³ - 3x². Find the absolute minimum value of f(x) on the interval [1, 4].

A: The given function,  f(x)=x3-3x2 on the interval 1,4

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Q: lim (x² + e-z)(z-¹ csc z) +0+*

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Q: The finate finear pattern 20;17;14...-103.Calculate number of terms in the sequence ?

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A: To solve the given equation.

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A: Solution of given question is written in below steps.

Q: 6. Evaluate the following integrals. 1/4 (2) [¹ sec³ πt dt

A: 6. ∫014sec3πt dt Note:    Multiple questions are given, we are answer with only one question.

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Q: Find the arc length L of the graph of r(t). r(t) = t3 i+t p j+126t2 k, 3≤t≤6

A: r(t)=t3 i +t j+126t2 kdxdt=3t2dydt=1dzdt=252 t3≤t≤6

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A: Two multiple choices questions are given. These questions are from algebra and calculus. We have…