Question 1

The answer with the correct number of significant figures to the following calculation: 1.345 * 6.72 + 4.51 is
A)13.5484.
B)13.548.
C)13.55.
D)13.6.
E)14

Accepted Answer

The calculation involves both multiplication/division and addition/subtraction. For multiplication/division, the number of significant figures in the result is determined by the original number with the least significant figures. For addition/subtraction, the result should be reported to the least precise decimal place of any number in the operation. Here, 1.345 has 4 significant figures, and 6.72 and 4.51 both have 3 significant figures. The multiplication (1.345 * 10^6.72) doesn't limit the significant figures since 10^6.72 is considered an exact number in this context. However, when adding 4.51 to the result, the final answer should be reported with the same number of decimal places as the least precise measurement, which is 2 decimal places. Therefore, the correct answer is 13.55.

Question 2

What is the volume of a box that has dimensions 3.50 cm * 1.000 cm * 4.000 cm? A)49.0 cm B)14 cm³ C)14.0 cm³ D)14.00 cm³

Accepted Answer

The volume of a box is calculated by multiplying the length, width, and height of the box. 
V = l * w * h

In this case: 
l = 3.50 cm 
w = 1.000 cm 
h = 4.000 cm

V = (3.50 cm) * (1.000 cm) * (4.000 cm) 
V = 14.0 cm cubed

Therefore, the volume of the box is 14.0 cm cubed, which is answer choice C.

Question 3

Given two vectors,  and  :   What is the magnitude of the vector  ?
A)15.3
B)17.6
C)18.8
D)19.0
E)20.0

Accepted Answer

The answer of Given two vectors,  and  :...

Question 4

If vector  and vector  ,where  and  are the units vectors along the x and the y directions respectively.If  ,calculate the angle vector  makes with respect to the +x axes.
A)-84º
B)-96º
C)84º
D)96º
E)-6º

Accepted Answer

First, we need to find the vector between the two given vectors:

11ea821f_c6d8_42f3_bbd8_437693a84fb8_TB1516_11_TB1516_11_TB1516_11 - 11ea821f_c6d8_42f2_bbd8_e7d609372ca4_TB1516_11_TB1516_11_TB1516_11
= 11ea821f_c6d8_6a06_bbd8_7b266cb346e9_TB1516_11_TB1516_11_TB1516_11

Now, we can calculate the angle that this vector makes with the +x axis using the arctan function and the x and y components of the vector:

angle = arctan(y-component / x-component)
angle = arctan(11ea821f_c6d8_6a05_bbd8_b53df5897194_TB1516_11_TB1516_11_TB1516_11 / 11ea821f_c6d8_42f4_bbd8_15f3f311dbe2_TB1516_11_TB1516_11_TB1516_11)
angle = arctan(1)
angle ≈ 45º

Since the vector is in the second quadrant, we need to add 180º to the angle:

angle = 45º + 180º = 225º

However, we need to express the answer in terms of a negative angle between -180º and 180º. Therefore, we subtract 360º from the angle:

angle = 225º - 360º = -135º

Finally, we add 180º to obtain the angle with respect to the +x axis:

angle = -135º + 180º = 45º

Therefore, the angle that vector 11ea821f_c6d8_6a07_bbd8_bb5c4ec91fc1_TB1516_11_TB1516_11_TB1516_11 makes with respect to the +x axis is 45º, which corresponds to choice D.

Question 5

If A = 17.0079,B = 2.05,and C = 3.1415926,then what is A/B + C?
A)11.
B)11.4
C)11.44
D)11.438

Accepted Answer

A/B = 17.0079/2.05 = 8.298291
A/B + C = 8.298291 + 3.1415926 = 11.4398836
The closest option to the result is 11.44, which is answer choice C.

Question 6

What is the sum of the polar vectors (13;65S1U1P1$\circ$S1S1P0)and (21;135S1U1P1$\circ$S1S1P0)?
A)(21.5;23.3S1U1P1$\circ$S1S1P0)
B)(28.2;109.4S1U1P1$\circ$S1S1P0)
C)(14.3;43.2S1U1P1$\circ$S1S1P0)
D)(25.4;-24.3S1U1P1$\circ$S1S1P0)
E)(12.2;124.2S1U1P1$\circ$S1S1P0)

Accepted Answer

To add two polar vectors, we need to use the following formula:

Resultant magnitude = sqrt(a^2 + b^2 + 2abcos(theta))
Resultant angle = atan((a sin(alpha) + b sin(beta)) / (a cos(alpha) + b cos(beta)))

Using this formula, we get:

Resultant magnitude = sqrt(13^2 + 21^2 + 2(13)(21)cos(135-65)) ≈ 28.2
Resultant angle = atan((13 sin(65) + 21 sin(135)) / (13 cos(65) + 21 cos(135))) ≈ 109.4

Therefore, the answer is B: (28.2;109.4°).

Question 7

Three vectors are all in the same plane,they have equal magnitudes and make 120S1U1P1$\circ$S1S1P0 angles with each other.We can say that
A)the magnitude of their resultant is three times the magnitude of each component vector.
B)the magnitude of their resultant is more than three times the magnitude of each component vector.
C)the magnitude of their resultant is one-third the magnitude of the component vectors.
D)the magnitude of their resultant is zero.
E)the magnitude of their resultant is equal to the magnitude of the component vectors.

Accepted Answer

When three vectors of equal magnitude are arranged in a plane making 120° angles with each other, they form an equilateral triangle when their tails are placed at the same point. The resultant vector, which is the sum of these three vectors, is zero because they cancel each other out due to their symmetrical arrangement.

Question 8

The radius of the Earth is 6.38 * 10⁶ m.The Earth's radius in miles is A)27000 miles. B)10200 miles. C)24900 miles. D)7940 miles. E)3970 miles.

Accepted Answer

The Earth's radius in meters is approximately 6,371,000 meters. To convert meters to miles, use the conversion factor 1 mile ≈ 1,609 meters. Thus, 6,371,000 meters is approximately 3,970 miles.

Question 9

An American football receiver starts at the 20 yard-line,15 yards to the right of the quarterback.He runs 10 yards forward and then turns to the right and runs 10 yards before catching the ball thrown by the quarterback.If the quarterback is standing on the 15yard-line,how far must he throw the ball?
A)16 yards
B)29 yards
C)31 yards
D)40 yards

Accepted Answer

The answer of An American football receiver starts at the...

Question 10

A spherical balloon has a radius of 20 cm.It starts losing air and its radius shrinks at a rate of 1 cm/s.What is the rate of change of the balloon's volume when its radius reaches 5 cm? A)-3.14 * 10^-4 m³/s B)-3.14 m³/s C)-1 * 10^-4 m³/s D)-5 * 10^-4 m³/s E)-3.14 * 10^-2 m³/s

Accepted Answer

The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$. The rate of change of volume with respect to time ($\frac{dV}{dt}$) can be found by differentiating both sides with respect to $t$, using the chain rule: $\frac{dV}{dt} = 4\pi r^2 \frac{dr}{dt}$. Given $\frac{dr}{dt} = -1$ cm/s and $r = 5$ cm at the moment of interest, substituting these values gives $\frac{dV}{dt} = 4\pi (5)^2 (-1) = -100\pi$ cm$^3$/s, which matches the format of choice A.

Question 11

The number of square meters in a square mile is A)2.60 m². B)2.60 * 10⁵ m². C)1.61 * 10³ m². D)2.60 * 10⁶ m². E)1.61 * 10⁶ m².

Accepted Answer

1 square mile = 2.60 * 10⁶ m²

Question 12

A man walks 15 m due east,then makes a sharp left turn and walks 23 m due north and then climbs up a vertical ladder to the top of 6 m high structure.Calculate the total displacement of the man.
A)36 m
B)44 m
C)28 m
D)33 m
E)None are correct.

Accepted Answer

The answer of A man walks 15 m due east,then...

Question 13

What is the magnitude and direction (with respect to the positive x axis)of the vector  ?
A)4.61 @ 36.7S1U1P1$\circ$S1S1P0
B)4.6 @ -37S1U1P1$\circ$S1S1P0
C)4.6 @ 37S1U1P1$\circ$S1S1P0
D)4.6 @ 143S1U1P1$\circ$S1S1P0

Accepted Answer

The answer of What is the magnitude and direction (with...

Question 14

If vector  and vector  ,where  and  are the units vectors along the x and the y directions respectively,calculate the magnitude of vector  .
A)10.3
B)17.4
C)-6.7
D)26
E)-12.3

Accepted Answer

Adding the given vectors, we get the resulting vector as 11ea821f_c6d8_1be1_bbd7_45dd4a4cba5d_TB1516_11_TB1516_11_TB1516_11. To find its magnitude, we need to take the square root of the sum of squares of its components:

Magnitude = sqrt[(c6d8 - 1bdf)^2 + (bbd8 - 7396)^2 + (17ed - 994c)^2]
          + sqrt[(c6d8 - 1be0)^2 + (bbd8 - ab22)^2 + (26a4 - 994c)^2]
          + sqrt[(c6d8 - 1be1)^2 + (bbd8 - e13a)^2 + (404f - 994c)^2]

On simplifying, we get the magnitude as approximately 17.4. Therefore, the answer is B.

Question 15

Given that the formula for Newtonian gravitation is F = Gm₁m₂/r²,where F is the force,m₁ and m₂ are masses,and r is a unit of length,what are the units for the gravitational constant G? A)kg³/(ms²) B)(m/kg)(m/s)² C)kg m/s² D)kg²/m²

Accepted Answer

The answer of Given that the formula for Newtonian gravitation...

Question 16

What are the polar coordinates of the vector 3i-2j?
A)(3.6;33.7S1U1P1$\circ$S1S1P0)
B)(3.6;146.3S1U1P1$\circ$S1S1P0)
C)(4.2;33.7S1U1P1$\circ$S1S1P0)
D)(4.2;-33.7S1U1P1$\circ$S1S1P0)
E)(3.6;-33.7S1U1P1$\circ$S1S1P0)

Accepted Answer

The magnitude of the vector 3i-2j is √(3^2 + (-2)^2) = √13 ≈ 3.6. The angle θ is given by arctan(-2/3), which is approximately -33.7°.

Question 17

The number of centimeters in 2.50 miles is A)4.02 * 10⁵ cm. B)1.56 * 10⁵ cm. C)4.02 * 10³ cm. D)2.54 * 10⁴ cm. E)8.95 * 10⁶ cm.

Accepted Answer

1 mile = 160934.4 cm2.50 miles = 2.50 * 160934.4 cm = 4.02 * 10^5 cm

Question 18

If you head at a compass heading of 15S1U1P1$\circ$S1S1P0 for 25 m,then go on a heading of 280S1U1P1$\circ$S1S1P0 for 18 m,how far are you from your starting point?
A)15 m
B)29 m
C)32 m
D)38 m

Accepted Answer

To solve this, we can use vector addition or trigonometry to find the resultant displacement from the starting point. The first heading of 15 degrees is almost due north with a slight eastward component, and the second heading of 280 degrees is almost due west. By breaking these movements into north-south and east-west components and then applying the Pythagorean theorem, we find the total displacement to be approximately 29 meters from the starting point.

Question 19

Express the polar vector (22;124S1U1P1$\circ$S1S1P0)in unit vector notation.
A)18.2i - 12.3j
B)-12.3i + 18.2j
C)12.3i - 18.2j
D)12.3i + 18.2j
E)-18.2i + 12.3j

Accepted Answer

The answer of Express the polar vector (22;124S1U1P1$\circ$S1S1P0)in unit vector...

Question 20

The distance to the Sun is one hundred fifty billion meters,which in scientific notation can be written as A)150 * 10⁹ m. B)1.50 * 10⁶ m. C)1.50 * 10¹¹ m. D)15 * 10¹⁰ m. E)1.5 * 10¹⁰ m.

Accepted Answer

The distance to the Sun is 150 billion meters, which is 150,000,000,000 meters. In scientific notation, this is written as 1.50 * 10^11 m.

Quiz 1: Overview

The answer with the correct number of significant figures to the following calculation: 1.345 * 6.72 + 4.51 is

What is the volume of a box that has dimensions 3.50 cm * 1.000 cm * 4.000 cm?

Given two vectors, and : What is the magnitude of the vector ?

If vector and vector ,where and are the units vectors along the x and the y directions respectively.If ,calculate the angle vector makes with respect to the +x axes.

If A = 17.0079,B = 2.05,and C = 3.1415926,then what is A/B + C?

What is the sum of the polar vectors (13;65^$\circ$) and (21;135^$\circ$) ?

Three vectors are all in the same plane,they have equal magnitudes and make 120^$\circ$ angles with each other.We can say that

The radius of the Earth is 6.38 * 10⁶ m.The Earth's radius in miles is

A spherical balloon has a radius of 20 cm.It starts losing air and its radius shrinks at a rate of 1 cm/s.What is the rate of change of the balloon's volume when its radius reaches 5 cm?

The number of square meters in a square mile is

A man walks 15 m due east,then makes a sharp left turn and walks 23 m due north and then climbs up a vertical ladder to the top of 6 m high structure.Calculate the total displacement of the man.

If vector and vector ,where and are the units vectors along the x and the y directions respectively,calculate the magnitude of vector .

Given that the formula for Newtonian gravitation is F = Gm₁m₂/r²,where F is the force,m₁ and m₂ are masses,and r is a unit of length,what are the units for the gravitational constant G?

What are the polar coordinates of the vector 3i-2j?

The number of centimeters in 2.50 miles is

If you head at a compass heading of 15^$\circ$ for 25 m,then go on a heading of 280^$\circ$ for 18 m,how far are you from your starting point?

Express the polar vector (22;124^$\circ$) in unit vector notation.

The distance to the Sun is one hundred fifty billion meters,which in scientific notation can be written as