Find 7'(t), given r(t) = = 7' (t) = = (= 7t² -2t 3 -2t3 +5' 2t2 +6' -2t - 1

Q: The position function for a falling object is given by s(t)=−16t^2+v0t+s0, where s(t) is the height…

A: Given: The position function of the problem is with vo= 45 and so=0 And the function is  s(t) =…

Q: Let f(x) = 8 + 2x2. (a) Estimate the area under the graph of f, the x-axis, and the lines x = −1 and…

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Q: f(t)= 140/3 t^2 + 3000 does concavity for f(t) change . t is in days

A: Given : f(t) = 140/3 t2 + 3000

Q: Solve 2sinx- V3 = 0 on interval [0,2 t)

A: We have to solve  2sinx - √3 = 0 on interval [0 , 2π)  Since ,  2sinx - √3 = 0  2sinx = √3

Q: c. x = t3 and y = 2t2 /2, 0<ts v3 3 d. x = t2/2 and y = (2t + 1)7/3, 0<t< 4 %3D

A: 1)x = t3  &amp; y = 2t22,  0≤t ≤ 32)x = t22  &amp; y = (2t + 1)323,  0≤t ≤ 4

Q: 6) Suppose that the price of an Iphone (in dollars) is given by 6t p(t): 4 + 3e²/t . = 300 + t+2 t2…

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Q: g(t)=t^{3}+4 t

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Q: USC Tolx)=1 and Ticx) = X to find %3D Te (X)and T3(X)

A: Given that, T0x=1 and T1x=x. It is known that, x2=12T0+T2 and x3=143T1+T3. Obtain the value of T2x.…

Q: 1) y=-3x-2

A: y=-3x-2 when x=0, y=-3(0)-2⇒y=-2 when y=0, 0=-3x-2⇒x=-23

Q: An object moving along a horizontal coordinate line has directed distance s(t) = t - 6t2 + 9t + 11…

A: s(t)=t3-6t2+9t+11 Differentiating with respect to t s'(t)=ddt(t3-6t2+9t+11)=3t2-6*2t+9+0=3t2-12t+9…

Q: Q2-Prove that

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Q: If the price of 35 tons of steel is RO 250,000. Find the cost of 900 kg (Kilogram) of steel.

A: Given that the price of 35 tons of steel is RO 250,000.

Q: s(t)=3t^2−9t,    t≥0   -Over what interval is the particle moving in the negative direction?  -Over…

A: Given position of the particle: Displacement Function: st=3t2-9t, t≥0 Here, s in feet and t is in…

Q: 16 = dx / x7 3/5+4x⁹

A: This question has been solved without using trigonometric substitution

Q: The acceleration of an object (in m/s²) is given by the function a(t) = 6 sin(t). The initial…

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