Answer:
a. 59049
b. 15120
Step-by-step explanation:
<u>a. If digits can be repeated:</u>
- There are 9 possible numbers for each digit
That is: possible 5-digit pass codes are 9×9×9×9×9=
=59049
<u>b. If digits cannot be repeated.</u>
There is
- 9 possibility for the first digit,
- 8 possibility for the second digit
- 7 possibility for the third digit
- 6 possibility for the fourth digit
- 5 possibility for the fifth digit
That is: possible 5-digit pass codes are 9×8×7×6×5=15120
No because 280 is 21 numbers away from 301
Refer to the diagram shown below.
In order for the airplane to maintain a heading of 65° west of north, it actually heads at (65° +x) west of north at a speed of 750 km/h, to compensate for the wind blowing from west t east at 60 km/h.
The actual speed of the airplane relative to the ground is V km/h.
From geometry, obtain the triangle shown.
The speed of 750 km/h is opposite an angle of 155°, and the unknown angle x is opposite the wind speed of 60 km/h.
From the Law of Sines, obtain
The heading that the pilot should take is 65 + 1.937 = 66.94° west of north.
The third angle of the triangle is 180 - (155 + 1.937) = 23.063°.
Use the Law of Sines to calculate V.
Answer:
The pilot heads approximately 67° (nearest integer) west of north.
The speed of the airplane relative to ground is 695.2 km/h (nearest tenth)
