Explanation:
The Law of Sines is your friend, as is the Pythagorean theorem.
Label the unmarked slanted segments "a" and "b" with "b" being the hypotenuse of the right triangle, and "a" being the common segment between the 45° and 60° angles.
Then we have from the Pythagorean theorem ...
b² = 4² +(2√2)² = 24
b = √24
From the Law of Sines, we know that ...
b/sin(60°) = a/sin(θ)
y/sin(45°) = a/sin(φ)
Solving the first of these equations for "a" and the second for "y", we get ...
a = b·sin(θ)/sin(60°)
and ...
y = a·sin(45°)/sin(φ)
Substituting for "a" into the second equation, we get ...
y = b·sin(θ)/sin(60°)·sin(45°)/sin(φ) = (b·sin(45°)/sin(60°))·sin(θ)/sin(φ)
So, we need to find the value of the coefficient ...
b·sin(45°)/sin(60°) = (√24·(√2)/2)/((√3)/2)
= √(24·2/3) = √16 = 4
and that completes the development:
y = 4·sin(θ)/sin(φ)
Answer:
184800 times
Step-by-step explanation:
The first step is to find out how many times the wheels turn in one foot. The ratio of rotations per minute is 20:140. This can be simplified to 1:7, meaning there is 1/7 of a rotation for every 1 foot.
Next, we need to find out how many times they turn in one mile. The ratio is 1:7, and the 1 needs to become 5280. To do this, multiply both sides of the ratio by 5280. You will get 5280:36960, meaning there is 36960 rotations every mile (the ratio of miles to rotations is 1:36960).
Now, multiply 1:36960 by 5 to get the amount of rotations per every 5 miles. You will get 184800.
Final answer: the wheels turn 184800 times in 5 miles.
Robyn bakes 4 pies because if she has 8 total cups of flour and each pie needs 2 cups of flour then all you need to do its divide. Hope this made sense and helped.
Answer:
42 1/2>42.500
Step-by-step explanation:
Answer:
Step-by-step explanation:
line <em>l</em>
