Question

question 6, 7 and 8 pls

State how many significant figures are proper in the results of the following calculations. (a) (36.84)(300)(46.210)(1.86) (b) (84.88)^2 (c) (2.9 times 10^-19) (3712) The magnitude of vector A is 25 m, and it points in the positive y direction. Vector B is added to A and the sum A + B points in the negative y direction with a magnitude of 17 m. What are the magnitude and direction of vector B ? magnitude m direction A radio station antenna is 35 km away, 16 degree north of west with respect to an origin on a map. An office building is 34 km away, 36 degree east of north with respect to the origin. How far is the office building with respect to the radio station antenna, and in what direction is the office building as measured from the antenna? (a) the office building's distance from the antenna (b) the office building's direction from the antenna, measured counterclockwise from due east degree

Answer 1

Question 6:

The significant figures of a numbers are digits in a figure that express the precision of a measurement. This include all digits expect leading and trailing zeros.

Some Examples,

Example 1:

452.30 has four significant digits

Example 2:

745,000 has three significant digits

Example 3:

0.00005600

In this digit:

• Zeros after decimal before no-zero numbers are not significant. 0.00005600
• All nonzero numbers are significant. 0.00005600
• In a decimal, zeros after nonzero numbers are significant. 0.00005600

(a) (36.84) (300) (46.210) (1.86) = 949926.0312

All the digits of a number 949926.0312 are significant. Therefore the numbehas 10 significant figures.

(b) (84.88)² = 7204.6144

All the digits of a number 7204.6144are significant. Therefore the number has 8 significant figures.

(c) (2.9 * 10^-19) (3712) = 10764.8 * 10^-19 = 1.07648* 10^-15

All the digits of a number 1.07648* 10^-15 are significant. Therefore the number has 6 significant figures.

Question 7:

Vector A has a magnitude of 25m in a positive y-direction.

The vector $\underset{A}{\rightarrow} + \underset{B}{\rightarrow}$ has a magnitude of 17 in a negative y-direction.

Let us consider $\underset{R}{\rightarrow}$ is a resultant vector of $\underset{A}{\rightarrow} + \underset{B}{\rightarrow}$ . Therefore, we can write,

$\underset{A}{\rightarrow} + \underset{B}{\rightarrow} = \underset{R}{\rightarrow}$

Let's put the values,

$25 + \underset{B}{\rightarrow} = -17$

           $\underset{B}{\rightarrow} = -17 - 25$

           $\underset{B}{\rightarrow} = -42$

Therefore, the magnitude of $\underset{B}{\rightarrow}$ is 42 m in a negative y-direction.

Question 8: