1/3 (2^4 + 2). This question is designed to test your intelligence.
1 answer:
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The Amanda's house is 6.7 km far from her school.
<u>Step-by-step explanation:</u>
From the given information,
- The Amanda's school is due west of her house forms the base.
- The school is due south of the Shereen's house forms the height.
- The straight-line distance between Amanda's house and Shereen's house forms the hypotenuse.
Therefore, It can be determined that it forms the right angle triangle.
It is given that,
The distance between the school and Shereen's house is 2 kilometers.
That is, the height of the triangle = 2 km
The straight-line distance between Amanda's house and Shereen's house is 7 kilometers.
That is, the hypotenuse of the triangle = 7 km
Now, the distance between the Amanda's house and her school is the base of the triangle.
<u>To find the base :</u>
Base =
⇒
⇒
⇒
⇒ 6.7 km
Therefore, the Amanda's house is 6.7 km far from her school.
4) (a) For these problems, you should take time to familiarize yourself with common fractions that appear on the unit circle. does not appear in the unit circle unless you take the quotient 1/2 divided by sqrt(3)/2 which gives you 1/sqrt(3) which is the same as sqrt(3)/3. So our numerator is 1/2 and our denominator is sqrt(3)/2.
And remember tangent is just sin/cos. So what degree has sinx as 1/2 and and cosx as sqrt(3)/2? Well, 30 degrees does, but 30 degrees is not within the range we are given. That means they are looking for a sinx that gives us -1/2 and a cosx that gives us -sqrt(3)/2 and that is 210 degrees.
And 210 degrees in radians is 7pi/6.
I hoped that made sense.
(b) This is a lot easier. What angle gives us a cos x of -sqrt(3)/2? According to the unit circle, 150 degrees and 210 degrees does. They usually want these in radians, so the answer is 5pi/6 and 7pi/6, respectively.
5) What quadrant is radian measure 5 in?
Well 2pi or roughly 6.28 is a full circle. And 5 is slightly less than 6.28, so it is probably in quadrant IV.
But to be sure let's change 5 radian to degrees:
5 * 180/pi = 900/pi = 286.48 degrees
286.48 degrees is definitely in Q4, so we are correct.