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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.

9. 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
help_outline

Image Transcriptionclose

9. 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

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check_circleAnswer
Step 1

To calculate Δy,

y = (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
help_outline

Image Transcriptionclose

y = (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

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Step 2

To calculate...

Differentiate 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
help_outline

Image Transcriptionclose

Differentiate 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

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Tagged in

Math

Calculus

Derivative

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