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2 answers:
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Answer:
- cos(2θ) = 7/25
- tan(2θ) = -24/7
Step-by-step explanation:
Sometimes, it is easiest to let a calculator do the work. (See below)
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The magnitude of the tangent is less than 1, so the reference angle will be less than 45°. Then double the angle will be less than 90°, so will remain in the 4th quadrant, where the cosine is positive and the tangent is negative.
You can also use the identities ...
cos(2θ) = (1 -tan(θ)²)/(1 +tan(θ)²)
cos(2θ) = (1 -(-3/4)²)/(1 +(-3/4)²) = ((16-9)/16)/((16+9)/16)
cos(2θ) = 7/25
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tan(2θ) = 2tan(θ)/(1 -tan(θ)²) = 2(-3/4)/((16-9/16) = (-6/4)(16/7)
tan(2θ) = -24/7
In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
water drinking habits:
mean = 62 ounces
standard deviation = 5.2 ounces
Step 02:
normally distribution:
95% ===> 2 SD
(62 + 5.2 + 5.2) ounces = 72.4 ounces ==> + 2 SD
(62 - 5.2 - 5.2) ounces = 51.6 ounces ==> - 2 SD
The answer is:
51.6 ounces - 72.4 ounces
Answer:
Option D
Step-by-step explanation:
32). Given vertices of the triangle are M(2, -3), N(3, 1) and O(-3. 1).
Distance between two points and
is given by the expression,
Distance =
Distance between M(2, -3) and N(3, 1) will be,
MN =
=
=
Distance between M(2, -3) and O(-3, 1),
MO =
=
=
Distance between N(3, 1) and O(-3, 1),
NO =
= 6
Condition for right triangle,
c² = a² + b² [Here c is the longest side of the triangle]
By this property,
MO² = MN² + NO²
41 = 17 + 36
41 = 51
False.
Therefore, given triangle is not a right triangle.
Since, length of all sides are not equal, given triangle will be a scalene triangle.
Option D is the correct option.