sin(<em>θ</em>) + cos(<em>θ</em>) = 1
Divide both sides by √2:
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = 1/√2
We do this because sin(<em>x</em>) = cos(<em>x</em>) = 1/√2 for <em>x</em> = <em>π</em>/4, and this lets us condense the left side using either of the following angle sum identities:
sin(<em>x</em> + <em>y</em>) = sin(<em>x</em>) cos(<em>y</em>) + cos(<em>x</em>) sin(<em>y</em>)
cos(<em>x</em> - <em>y</em>) = cos(<em>x</em>) cos(<em>y</em>) - sin(<em>x</em>) sin(<em>y</em>)
Depending on which identity you choose, we get either
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = sin(<em>θ</em> + <em>π</em>/4)
or
1/√2 sin(<em>θ</em>) + 1/√2 cos(<em>θ</em>) = cos(<em>θ</em> - <em>π</em>/4)
Let's stick with the first equation, so that
sin(<em>θ</em> + <em>π</em>/4) = 1/√2
<em>θ</em> + <em>π</em>/4 = <em>π</em>/4 + 2<em>nπ</em> <u>or</u> <em>θ</em> + <em>π</em>/4 = 3<em>π</em>/4 + 2<em>nπ</em>
(where <em>n</em> is any integer)
<em>θ</em> = 2<em>nπ</em> <u>or</u> <em>θ</em> = <em>π</em>/2 + 2<em>nπ</em>
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We get only one solution from the second solution set in the interval 0 < <em>θ</em> < 2<em>π</em> when <em>n</em> = 0, which gives <em>θ</em> = <em>π</em>/2.
Answer: 502.654825 cm3
Step-by-step explanation: The formula for the volume of a cylinder is height x π x (diameter / 2)2, where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius2. Visual in the figure below:
Step 1: -12x - 2y ≥ -42
Step 2: -2y ≥ -12 - 42
Step 3: y ≤ -6x + 21
So the answer is
D) <span>y ≤ -6x + 21</span>
1*3=3
6*7=42
3/42 can be simplifyed
to 1/14
Answer:
The guard should be positioned at the safe
Step-by-step explanation:
The night watchmen should be positioned to guard whichever place gives the highest expected value to the thief.
The expected value of robbing the safe is:
The expected value of robbing the cash register is:
Therefore, the guard should be positioned at the safe since it yields a higher expected value to the thief in case he tries to rob it.
