  9. A particle is moves with the position function given by s(t) = t3 - 9t2 +15measured in seconds ands in feet.а.Find the velocity and acceleration of the particle at time t.b. When is the particle at rest?Find the velocity and acceleration at t = 2 secd. When is the particle speeding up?When is the particle slowing down?с.е.1510. Let y (1+x), x= 0, Ax=.01. Find:Дуb. dyc. Ay-dya.11. A metal rod 15 cm long and 5 cm in diameter is to be covered (except fothick. Use differentials to estimate the volume of insulation.2. A paper cup has the shape of a cone with height 10 cm and radius 3 cmcup at the rate of 2cm'/sec, how fast is the level rising when the wate3. The radius of size 5 soccer balls is estimated to be 4.5 inches with a mstimate the maximum error in the calculated voludifferentials

Question

I need help with number 10. help_outlineImage Transcriptionclose9. A particle is moves with the position function given by s(t) = t3 - 9t2 +15 measured in seconds ands in feet. а. Find the velocity and acceleration of the particle at time t. b. When is the particle at rest? Find the velocity and acceleration at t = 2 sec d. When is the particle speeding up? When is the particle slowing down? с. е. 15 10. Let y (1+x), x= 0, Ax=.01. Find: Ду b. dy c. Ay-dy a. 11. A metal rod 15 cm long and 5 cm in diameter is to be covered (except fo thick. Use differentials to estimate the volume of insulation. 2. A paper cup has the shape of a cone with height 10 cm and radius 3 cm cup at the rate of 2cm'/sec, how fast is the level rising when the wate 3. The radius of size 5 soccer balls is estimated to be 4.5 inches with a m stimate the maximum error in the calculated volu differentials fullscreen
Step 1

To calculate Δy, help_outlineImage Transcriptionclosey = (1+x)5 Ay=(1+x+Ax)(1+x) 15 Substitute x-0 and Ax-0.01 Ay=(1+0+0.01)-(1+ 0) Ay=(1.01)-() 15 15 Ay=1.1609-1 Ay 0.1609 fullscreen
Step 2

To calculate... help_outlineImage TranscriptioncloseDifferentiate both sides with respect to x, d d - (v)= (1+x)'s dxc dxc dy = 15 (1 + x)" dy 15(1+x Substitute x 0,dx-0.01 dy 15(1+0) 0.01 - dy 0.15 fullscreen

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