Significant digit: Non zero digit are always significant.
Given number is 0.0065.
Here
Significant figure is 2
And decimals are 4.
Hence 0.0065 has 2 significant figure and 4 decimals.

Question

asked 2021-02-06

How do you calculate the following retaining the correct number of significant figures \(\displaystyle{12.432}\times{3}=\) and \(\displaystyle{208}\times{62.1}=\)

asked 2021-03-21

In the figure below, the rolling axle, 1.43 m long, is pushed along horizontal rails at a constant speed v = 3.36 m/s.

A resistor R = 0.325 ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field B = 0.0850 T vertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?

A resistor R = 0.325 ohm is connected to the rails at points a and b, directly opposite each other. (The wheels make good electrical contact with the rails, and so the axle, rails, and R form a closed-loop circuit. The only significant resistance in the circuit is R.) There is a uniform magnetic field B = 0.0850 T vertically downward. Calculate the induced current I in the resistor and what horizontal force F is required to keep the axle rolling at constant speed?

asked 2020-10-20

Consider the quantity\(a^{2}\ -\ b^{2}\) where a and b are real numbers.

(a) Under what conditions should one expect an unusually large relative error in the computed value of \(a^{2}\ -\ b^{2}\) when this expression is evaluated in finite precision arithmetic?

(b)cWs 4-digit (decimal) rounding arithmetic to evaluate both \(a^{2}\ -\ b^{2}\ and\ (a\ +\ b)(a\ -\ b)\ with\ a\ = 995.1\ and\ b = 995.0.\) Calculate th relative error in each result.

(c) The expression \((a\ +\ b)(a\ -\ b)\ is\ algebraically\ equivalent\ to\ a^{2}\ -\ b^{2},\) but it is a more accurate way to calculate this quantity if both a and b have exact floating point representations. Why?

(a) Under what conditions should one expect an unusually large relative error in the computed value of \(a^{2}\ -\ b^{2}\) when this expression is evaluated in finite precision arithmetic?

(b)cWs 4-digit (decimal) rounding arithmetic to evaluate both \(a^{2}\ -\ b^{2}\ and\ (a\ +\ b)(a\ -\ b)\ with\ a\ = 995.1\ and\ b = 995.0.\) Calculate th relative error in each result.

(c) The expression \((a\ +\ b)(a\ -\ b)\ is\ algebraically\ equivalent\ to\ a^{2}\ -\ b^{2},\) but it is a more accurate way to calculate this quantity if both a and b have exact floating point representations. Why?

asked 2020-11-05

Test the claim that the proportion of people who own cats is significantly different than \(50\%\) at the 0.01 significance level.

Based on a sample of 300 people, \(41\%\) owned cats

Hint: To get the number of successes, multiply

\((\%\ who\ owned\ cats)(n)\rightarrow(41\%)(300)\)

The test statistic is: ? (to 2 decimals)

The p-value is: ? (to 4 decimals)

Based on a sample of 300 people, \(41\%\) owned cats

Hint: To get the number of successes, multiply

\((\%\ who\ owned\ cats)(n)\rightarrow(41\%)(300)\)

The test statistic is: ? (to 2 decimals)

The p-value is: ? (to 4 decimals)

asked 2021-04-13

As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

asked 2020-12-29

Marks will be awarded for accuracy in the rounding of final answers where you are asked to round. To ensure that you receive these marks, take care in keeping more decimals in your intermediate steps than what the question is asking you to round your final answer to.

A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places.

(a) What is the probability that exactly one 3 is rolled?

(b) What is the probability that at least one 3 is rolled?

(c) What is the probability that exactly four of the rolls show an even number?

A fair 7 -sided die with the numbers 1 trough 7 is rolled five times. Express each of your answers as a decimal rounded to 3 decimal places.

(a) What is the probability that exactly one 3 is rolled?

(b) What is the probability that at least one 3 is rolled?

(c) What is the probability that exactly four of the rolls show an even number?

asked 2021-05-09

The dominant form of drag experienced by vehicles (bikes, cars,planes, etc.) at operating speeds is called form drag. Itincreases quadratically with velocity (essentially because theamount of air you run into increase with v and so does the amount of force you must exert on each small volume of air). Thus

\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)

where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.

Part A:

Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.

Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.

Part B:

A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).

Assume the following:

The top speed is limited by air drag.

The magnitude of the force of air drag at these speeds is proportional to the square of the speed.

By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?

Express the percent increase in top speed numerically to two significant figures.

\(\displaystyle{F}_{{{d}{r}{u}{g}}}={C}_{{d}}{A}{v}^{{2}}\)

where A is the cross-sectional area of the vehicle and \(\displaystyle{C}_{{d}}\) is called the coefficient of drag.

Part A:

Consider a vehicle moving with constant velocity \(\displaystyle\vec{{{v}}}\). Find the power dissipated by form drag.

Express your answer in terms of \(\displaystyle{C}_{{d}},{A},\) and speed v.

Part B:

A certain car has an engine that provides a maximum power \(\displaystyle{P}_{{0}}\). Suppose that the maximum speed of thee car, \(\displaystyle{v}_{{0}}\), is limited by a drag force proportional to the square of the speed (as in the previous part). The car engine is now modified, so that the new power \(\displaystyle{P}_{{1}}\) is 10 percent greater than the original power (\(\displaystyle{P}_{{1}}={110}\%{P}_{{0}}\)).

Assume the following:

The top speed is limited by air drag.

The magnitude of the force of air drag at these speeds is proportional to the square of the speed.

By what percentage, \(\displaystyle{\frac{{{v}_{{1}}-{v}_{{0}}}}{{{v}_{{0}}}}}\), is the top speed of the car increased?

Express the percent increase in top speed numerically to two significant figures.

asked 2021-01-02

The number multiplied on both sides of the equation \(\displaystyle{0.9}{x}-{4.3}={0.47}\) in order to clear of decimals.

asked 2020-12-02

If $2000 is invested at an interest rate of 4.5% per year, compounded continuously, find the value of the investment after the given number of years. (Round your answers to the nearest cent.)
a) 2 years
b) 4 years
c) 12 years

asked 2021-03-30

A long, straight, copper wire with a circular cross-sectional area of \(\displaystyle{2.1}{m}{m}^{{2}}\) carries a current of 16 A. The resistivity of the material is \(\displaystyle{2.0}\times{10}^{{-{8}}}\) Om.

a) What is the uniform electric field in the material?

b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?

c) What is the displacement current density in the material in part (b)?

d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?

a) What is the uniform electric field in the material?

b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?

c) What is the displacement current density in the material in part (b)?

d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?