Answer:
6 miles north and 3 miles west
Step-by-step explanation:
If you picture these miles on a graph, you start at (0,0). Then you go 8 miles south (0, -8). Then 3 miles east (3, -8). Finally, 2 miles north (3, -6). You are 3 miles east and 6 miles south, so you go the opposite directions.
Answer:
A. C (3,5)
Step-by-step explanation:
This makes the most sense because of the position point C is at on the coordinate plane. It is above point D, which has a x-axis of 3. Option A is the only one that has an x-axis of 3.
Hope it helps!
Answer:
the following studies may fail to yield the desired information because
(a) i. some of the students might have died before 2015.
ii. Some people might lie based on the questionnaire sent.
So based on the two factors above the desired information might be altered or incorrect.
(b) i. individuals may be unwilling to provide accurate answers during the survey.
Step-by-step explanation:
Information may be altered when individuals are asked about their income or spending in other to show off to friends or the person asking the questions.
By definition of tangent,
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
Recall the double angle identities:
sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)
cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1
where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):
sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))
and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.
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We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get
sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5
Then
tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)
tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)
tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)
tan(2<em>θ</em>) = 24/7
