= The velocity of a particle moving along a line as a function of time is given by v(t) = Find the distance that the particle has traveled after t = 6 seconds if it started at t your answer to 3 decimal places. Hint: t² + 10t + 21 = (t + 3)(t + 7) Add Work Submit Question 82 t² + 10t + 21 0 seconds. Round

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A: We can solve this as follows:

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A: We have to fill up the table

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A: as per company guidelines we solve only first question when multiple question being posted

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A: Here we have to find the derivative of the function.

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A: We have to find out continuity property

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A: To find the intervals , first find the values of x at which function is zero because it will change…

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Q: 5. Solve the initial value problem cos(x) y with y(0) = 3.

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A: Topic = Differential equation

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Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

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A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

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A: Topic- Domain of a function

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A: Here we have to find the solution of given differential equation.

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A: As given that limx→af(g(x))=flimx→ag(x)And also we know that limx→af(x)n=limx→af(x)n, where n is a…

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Q: 10. If x represents the solution set from the number line above, which of the following describes…

A: As per policy only first question is answered. The given is dark from x = -2  to x = 5.

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A: Given that fx=∫axx2dx we have to find the value of f'd, for a=6 and d=16 use the formulas:…

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Q: Só 1 x²+7x+10 A. B. C. D. 3ln 2-ln 2 3 3ln 2+ln 2 3 3ln 2-ln 2 5 3ln 3-ln 2 3 dx

A: The given integral, ∫011x2+7x+10dx use the integral formula, ∫dxx+a=lnx+a+C

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A: Solution :6.fx=2xx+3limit definition of derivative…

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A: The given function is gx=-4x+1-3 we have to find its parent function and transformations.

Q: whats the imaginary part 2 − 4i

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A: The roots of a quadratic equation ax2+bx+c=0 are given by x=-b±b2-4ac2a

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A: Percent of increase of a value= (new value - old value)*100/old value

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Q: Determine if the function is continuous at the given poi 1 x: x + 2² x ²50 } at x = 0. > 1. f(x) =…

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A: The given equation is; x4-4xy=c.

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Q: Solution- 0 +(x1 2 4 X +(x) 2 S 12 62 We use How tom's divided difference here 0 2 3 25 5 , 2 4 62 1…

A: To find newton divided difference table ,  For 3rd column , we will use formula   (f(xi +1) - f(xi)…