Answer:
Step-by-step explanation:
We have plane 1 flying SW for 4 hours at a rate of 415 mph. The distance he covers using the d = rt formula for distance, is 415(4) = 160 miles.
We also have plane 2 flying directly east (along the x-axis) for 4 hours at 327 mph. The distance he covers using the d = rt formula for distance, is 327(4) = 1308 miles. The angle in between them at this point is 135 degrees, and what we need to find is the length of the vector connecting the 2 planes. IF this was right triangle trig that distance would be the hypotenuse and we could solve for it using Pythagorean's Theorem. BUT it is NOT a right triangle, so we have to find some other means with which to solve for that length. We will use the Law of Cosines to do this.
which simplifies a bit to
If you add all of that together, you'll get
and you'll take the square root of that to get that the distance between the 2 planes after 4 hours is
2745 miles
You need to find "dollars per hour". So you need to know the total dollars and the total hours.
You already know the total dollars ... it's 54.
What are the total hours ? 2-1/2 plus 4-1/4 . Can you add those ?
Once you add up the total hours, divide ($54) divided by (total hours).
The quotient is the number of dollars she earns for each hour she works.
Answer:
x = 11
Step-by-step explanation:
Properties of a square,
1). Diagonal of a square bisect the opposite angles.
2). All interior angles of a square measure 90°.
From these properties,
m∠PQR = 90°
Since, diagonal QS bisects angle PQR,
m∠PQS = m∠RQS = 45°
(6x - 21)° = 45°
6x = 45 + 21
6x = 66
x = 11
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