An airplane on autopilot took 5 hours to travel 3,475 kilometers, what is the unit rate?

The distance from the Earth to the moon is about 239,000 miles. Rewrite the distance in scientific notation.

egoroff_w [7]

Answer:

2.39 x 10^5 miles

Step-by-step explanation:

Although it is not usually written, there is always a .0 at the end of a number unless there is a specific decimal that was given.

So, the number here is 239,000.0 and if you count the number of spaces that the decimal needs to move in order to be in the correct spot for scientific notation (which is always after the first number), there is 5 spaces.

Therefore the answer is 2.39 x 10^5 miles.

4 0

2 years ago

A person starts walking from home and walks: 4 miles east 3 miles southeast 3 miles south 4 miles southwest 3 miles east find to

Fantom [35]

A geometry program can show you the total displacement is about 10.14 miles.

_____
You can use a vector calculator to find the solution, too. Using bearing angles, the sum is
4∠90° + 3∠135° + 3∠180° + 4∠225° + 3∠90° ≈ 10.1390∠141.6354°

_____
If you want to do it by hand, you can recognize the sum will be
7 miles east + 3 miles south + 3 miles southeast + 4 miles southwest

Distances that are not in the direction of one of the coordinate axes can be translated to rectangular coordinates by
displacement*(cos(angle), sin(angle))
Angles can be measured in the conventional way—from the positive x-axis. A direction of southeast will be +315° or -45°. A direction of southwest will be +225° or -135°.

Then the sum of the displacements in rectangular coordinates is ...
= (7, -3) + 3*(cos(-45°), sin(-45°)) + 4*(cos(-135°), sin(-135°))
= (7, -3) + ((√2)/2)*((3, -3) + (-4, -4))
= (7, -3) + 0.707107*(-1, -7)
= (6.2929, -7.9497)
Then the Pythagorean theorem is used to find the direct distance from home to this displaced location.
d = √(6.2929² +(-7.9497)²) ≈ √102.7990
d ≈ 10.1390 . . . . miles