Question

[CALCULUS] [HELP PLEASE]

7. The edge of a cube was found to have a length of 50 cm with a possible error in measurement of 0.1 cm. Based on the measurement, you determine that the volume is 125,000 cm^3. Use tangent line approximation to estimate the percentage error in volume.

0.6%
0.9%
1.2%
1.5%
1.8%

A point on a damped spring has motion given by s(t)=2e^(-1.5t) s in(2(pi)t), where s is measured in centimeters and t is measured in seconds. Choose which of these is the graph for the velocity function for 0 < or equal to t < or equal to 4

Answer 1

(7)

error percentage is 0.6%

(8)

Graph-C

Explanation:

(7)

we are given cube

Let's assume edge of cube =x

so, volume of cube will be

`V(x)=x^3`

we are given

V=125000

so, we can find 'x'

`125000=x^3`

`x=50`

So,

`a=50`

now, we can use linear approximation formula

`L(x)=V(a)+(x-a)V'(a)`

`L(x)=V(a)+(\Delta x)V'(a)`

we have

`\Delta x=0.1`

we can plug a=50

`L(x)=V(50)+(0.1)V'(50)`

`V(x)=x^3`

we can find derivative

`V'(x)=3x^2`

now, we can plug x=50

`V'(50)=3(50)^2`

`V'(50)=7500`

now, we can plug these values

and we get

`L(x)=V(50)+(0.1)* 7500`

`L(x)=V(50)+750`

`L(x)-V(50)=750`

so, error is

`error=750`

now, we can find percentage error

Percentage is

`=(750)/(125000)* 100`

=0.6%

so, error percentage is 0.6%

(8)

we are given

`s(t)=2e^(-1.5t)sin(2\pi t)`

We will find derivative

To get velocity , we will find derivative

`s'(t)=(d)/(dt)\left(2e^(-1.5t)\sin \left(2\pi t\right)\right)`

we can use product rule

and we get

`s'(t)=-3e^(-1.5t)sin(2\pi t)+4\pi e^(-1.5t) sin(2\pi t)`

so, we get velocity equation as

`v(t)=-3e^(-1.5t)sin(2\pi t)+4\pi e^(-1.5t) sin(2\pi t)`

now, we can draw graph

we can see that firstly , we get maxima and then minima

so, our graph would be

graph-C........Answer