9514 1404 393
Answer:
(8.49; 225°)
Step-by-step explanation:
The angle is a 3rd-quadrant angle. The reference angle will be ...
arctan(-6/-6) = 45°
In the 3rd quadrant, the angle is 45° +180° = 225°.
The magnitude of the vector to the point is its distance from the origin:
√((-6)² +(-6)²) = √(6²·2) = 6√2 ≈ 8.4859 ≈ 8.49
The polar coordinates can be written as (8.49; 225°).
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<em>Additional comment</em>
My preferred form for the polar coordinates is 8.49∠225°. Most authors use some sort of notation with parentheses. If parentheses are used, I prefer a semicolon between the coordinate values so they don't get confused with an (x, y) ordered pair that uses a comma. You need to use the coordinate format that is consistent with your curriculum materials.
Answer:
80 ounces water
60 ounces brine
Step-by-step explanation:
Let x be the amount of water
Let y be the amount of brine 35%
The goal is to have salt weight of 140(0.15) = 21 oz.
21 = 0.35y
y = 60 oz
x = 140 - 60 = 80 oz
Reference angle of -3 radians is α= - 171° 53 min 15 sec .
We know the formula for calculating circular arc
Let l=circular arc which ic according to central angle of the circle α
l=((2R π)/360)α Let l=1 radian and R=1 (unit circle with radius R=1)
1= ((2π)/360)α => α= 360/(2π)= 180/π= 57° 17 min 45sec
Angle of the 1 radian is equal to angle 57° 17min 45sec
According to this
angle of the -3 radians = -3 ( 57° 17min 45sec) = - 171° 53min 15sec
when you count in the clockwise direction.
Good luck!!!
Answer:
Find the LCD of the first two, then the LCD of that and the third one.
Step-by-step explanation:
You can do it by finding the LCD of two of the denominators, then the LCD of that and the third denominator.
Or, you can factor each of the denominators and find their LCM by multiplying the unique factors to their highest powers.
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<u>Example:</u>
1/21 + 1/35 + 1/45
The LCD of 1/21 and 1/35 is (21·35)/5 = 105. The LCD of 1/105 and 1/45 is ...
(105·45)/15 = 315
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Using factoring ...
- 21 = 3·7
- 35 = 5·7
- 45 = 3²·5
LCD = 3²·5·7 = 315
