1. The position of an object moving in space is given by R(t) = (cos 2t)i + (sin 2t)j + tk a. Find the velocity and acceleration of the object at arbitrary time t. b. Determine the curvature of the trajectory at time t.

Q: Show that 38 = -1 (mod 17). Using this, deduce that 3 is a primitive root of 17.

A: We need to show that 38≡-1mod 17. Since 34=81≡-4mod 17 ⇒38=342≡-42mod 17

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A: This is the application of derivatives. Find critical point.

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Q: If cos x = sin 2x = cos 2x tan 2x 4 5 csc x < 0, then

A: Given: cosx=45 and csc(x)&lt;0 To find: Values of sin2x, cos2x and tan(2x).

Q: 15. a. Prove the following identity using induction on k. n + n+ 2 n (") + (˜† ¹ ) + (˜ + ²) + ··· +…

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Q: Multiply. (√-12) (√-3) (√-12) (√-3) = (Simplify your answer. Type an exact answer, using radicals as…

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A: Given the Lap data Time Force (kg) Number of active motor units 0 s 48 4 15 s 43 3 30 s 38…

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Q: (b) coth (In(6)) Need Help? Submit Answer X Read It

A: Ln6 =1.7917.

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Q: 1. Perform the indicated operations given a = 15-2i, b= −3+2i, and c= -1-3i. Write the results in…

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Q: Consider the example of the Binomial. distribution X1 0 0.004 P (X=x) 2 0.041 0.165 0.329 4 0.329 5…

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Q: A qualitative look at a fish population Example. A population of fish is being monitored in a lake.…

A: At equilibrium points P'=0 . To find sign of P' we will take a value of t in that region and…

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Q: Given the following matrices A and B, find an elementary matrix E such that B = EA: You can resize a…

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Q: 3. Use cylindrical coordinates to compute the integral Z !!! √x² + ² dv D where D is the solid…

A: Evaluation of triple integrals, using change to cylinder coordinates

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Q: 21. An mxn upper triangular matrix is one whose entries below the main diagonal are 0's (as in…

A: Solution : - Proposition : A triangular matrix (upper or lower) is invertible if and only if all the…

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A: Since you have asked a question with multiple sub parts, we will solve the first three sub parts for…

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A: Firstly the statement is false. So for that we will consider two positive integers which are not…

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Q: ) What are two consequences when we have a wing (three-dimensional) instead of an airfoil…

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Q: A yard is made with 2 regular partitions. It will be made from 720m of fencing materials. Calculate…

A: The area of the yard is given by  length ×width=y×x+x=y×2x Therefore, the area of the partition is…

Q: Describe the possible echelon forms of the standard matrix for a linear transformation T where T: R4…

A: Answer)  Possible echelon forms are :A, F, G, I

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Q: 4. Consider v₁ 3 V2 = V3 = (a) Show that V₁, V2, V3 are linearly independent. (b) Find the dimension…

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Q: ou decide to make monthly payments into a retirement fund earning 4.75% compounded monthly.  Note:…

A: Given  monthly deposit =$130 rate =4.75% compounded monthly amount =$353000 Formula  A=P1+rnnt-1rn

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A: We have to plot the solution curve using the initial conditions. Comparing with the differential…

Q: HW: Using the standard inner product, determine which of the following pairs orthogonal vectors in…

A: As two vectors X and Y are orthogonal if  &lt;X, Y&gt; = 0.