The answer is B I believe
Answer:
√5.
Step-by-step explanation:
Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).
so cos A = adjacent / hypotenuse = 2/√5.
and sin A = opposite / hypotenuse = 1 / √5
cos A / sin A = 2/√5 / 1/ √5 = 2.
sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)
= 1 / √5 ( (√5 + 2) /√5)
= 1 / (√5 + 2)
So the answer is:
2 + 1 /(√5 + 2).
We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.
2 + 1 / (√5 + 2)
= 2(√5 + 2) + 1 / (√5 + 2 )
= { 2(√5 + 2) + 1 } / (√5 + 2)
Multiplying this by √5 - 2 / √5 - 2 we get:
(2(5 - 4) + √5 - 2) / (5 -4)
= 2 + √5 - 2 / 1
= √5.
Answer:
x = y/3 - 1/3
Step-by-step explanation:
To find the rate, first you divide 180mi/3hr to get 60mph. On the first day they were traveling at a rate of 60mph. It says that on the second day, they drove at the same rate and drove 300 miles. This means you divide 300mi/60mph to get 5hr. They drove 5hr on the second day. And finally, the question asks how long they drove total, so you add 3hr+5hr to get 8hr total.
Answer is 8hr.
Answer:
C. 2.0 < t < 2.5
Step-by-step explanation:
time = distance / speed
The circumference of the lake is given by ...
C = πd = 2π miles ≈ 6.28 miles
Then Johanna's time is ...
(6.28 mi)/(3 mi/h) ≈ 2.09 h
This time is in the interval (2, 2.5), so matches choice C.
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<em>Alternate solution</em>
If we take pi to be 3, then this boils down to ...
2×3/3 = 2 . . . hours
Pi is on the order of 5% more than 3, so her time will be on the order of 5% more than 2 hours, or just above 2, but not as great as 2.5 hours. This sort of estimating can get you to the correct answer without a calculator.
