f(t) = t3 − 15t2 + 72te) Find the total distance traveled during the first 7 s.

Q: G) Fnd dy by Ruplicit differen tiation X +4x +15 44 -J = 36

A:

Q: Q4) ut A = :) al let fox)- 2x_4x+5 and g(x)= x?42x + 11, Fiind + 2X + 11, Find @ A ; DA ; © PCA);…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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A: Given,                 f(t)=3e-2tcoshln2t

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A:

Q: 4 x2 + 4

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A: Let's find.

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A: fx,y=x2y2-8x+yxyfx,y=xy-8y+1x   fx=y-x-2=0 Also, fx=y-1x2 fy=x+8y-2=0   So,  fxx=2x3 fxy=1fyy=-16y-3

Q: J1 x²+f(x) dx < o? Justify your answer by either showing it is true or providing a counterexample.

A: .   L

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A: After changing the order of integration, solve it.

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A: Solution: The objective is to find the value of dy

Q: %3D 3. If GH = 7x + 18 and JK = 81, find x. H G 丰 K 廿 世

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Q: Į va | Vi(t? + 6t +7) dt. 4. Find

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Q: d. y =x (n* + e*)6

A: Given that, y = x (πx + ex)6 And we have to calculate the differentiation of the given function,

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A:

Q: 1.f AXYZ - ARST, find RS. 40 3x +2 Sx -3 T. 60

A: Triangle Question

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Q: d²y Given that x +y³ = 2, prove that dx2 4.

A: Given: x3+y3=2   As we know that; The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2

Q: dy Q5/ Find by using chain rule dx y vt2-5+t, x tv4t + 8 +7

A:

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A: For a simple bivariate regression, the linear correlation coefficient and R-square will be the same…

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A:

Q: The traffic flow rate (cars per hour) across an intersection is r(t)=400+600t−150t^2, where tt is in…

A: given traffic flow rater(t)=400+600t-150t2at t=0 hour time is 6 amat t=1 hour time is 7 amhence we…

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A: Given function is:  f(x)=402xe−0.74x2+353 The interval is:  1≤x≤5

Q: Show steps please.

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A: Given that: ∫2dt(t-3)t2-6t+5

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A:

Q: 5. (D2 – 5D + 6)y = 18x2 + 12e2* (Assume yp = Ax² + Bx + C + Ee2x)

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Q: f(t) dt = 5x¬1 2+ t5

A:

Q: Is the equation t²y' (1) t + 4 - separable? y?

A: t2y't=t+4y2

Q: y''+6y=6+x By using i) Method of undetermined coefficients ii) Method of variation of parameters…

A: i) Given that y''+6y=6+x Take m=ddx m2+6=0m2=-6m=i6 Hence the homogenous solution is…

Q: Q2 by using Simpsons Rule method to find ,n=6 5 1 dx х 2

A: use sub interval for finding the integral.

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Q: Q(x, y) = 42x1/5,A15 Where Q is the output in millions of units of product.

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Q: 4. f(t) = V3 – 2t , find f""(t) %3D

A:

Q: Find the total differential. 6x + y w = 4z - 8y

A: The given function is: w=6x+y4z-8yw=f(x, y, z)

Q: Find the total differential. 9х + у w = 4z - 5y dw = Submit Answer

A:

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A: We will find the maximum acceleration of the projectile as following.