Answer:
Step-by-step explanation:
Answer:
9 1/6 miles
Step-by-step explanation:
Add the mixed number by the improper fraction.
1 + 1/3 + 35/6
Solve the fractions first.
In order to have both of the fractions have the same denominator, find the Least Common Multiple of both of the fractions.
1/3 = 2/6
2/6 + 35/6 = 37/6
Turn the improper fraction into a mixed number by dividing the the numerator by the denominator. When you get your quotient, use the remainder as the new numerator over the denominator.
37/6 = 6 1/6
Now, add the 1.
6 1/6 + 1 = 7 1/6
Now, add the 2 miles that Carol walked on Wednesday.
7 1/6 + 2 = 9 1/6
So, Carol walked about 9 1/6 miles on Monday, Tuesday, and Wednesday all together.
R= diameter/2
answer: 8 units
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
Answer:
(3,4)
Step-by-step explanation:
