Answer:
#1
<u>Sum of interior angles is 180:</u>
- y = 180 - (42 + 31) = 107
<u>The law of sines:</u>
- x / sin 107 = 11 / sin 42
- x = 11 sin 107deg / sin 42deg
- x = 15.72
#2
<u>The law of cosines:</u>
- cos 76 = (6² + 17² - x² )/2(6)(17)
- 204*0.24 = 325 - x²
- x² = 325 - 48.96
- x² = 276.04
- x = √276.04
- x = 16.61
#3
<u>Same as above:</u>
- 2*9.4*10*cos 20 = (10² + 9.4² - x²)
- 176.66 = 188.36 - x²
- x² = 188.36 - 176.66
- x² = 11.7
- x = √11.7
- x = 3.42
#4
<u>Sum of interior angles is 180:</u>
<u>The law of sines:</u>
- x / sin 34 = 15 / sin 94
- x = 15 sin 34 / sin 94
- x = 8.41
A polynomial is considered prime if it cannot be factored into the standard linear form, that problem cannot be factored, making it prime
Step-by-step explanation:
Given: diameter = 16 in
hence radius, r is 16 ÷ 2 = 8 in
a) notice that the fan blades divide the circle into 3 equal sectors.
Each sector is hence 1/3 of the entire circumference of the circle
Arc Length of each sector (between blades),
= (1/3) x circumference
= (1/3) x 2πr
= (1/3) x 2 x 3.142 x 8
= 16.76 in (Answer)
b) similarly, the area between the blades
= (1/3) x πr²
= (1/3) x 3.142 x 8²
= 67.03 in² (answer)
c) The angular velocity is the radians per second that the tip moves
It is given that it moves 8π radians in 2 seconds
hence in 1 second, we expect the tip to move,
8π ÷ 2 = 4π rad/s (Answer)
That's not a good question at all. It's a lot like asking
"What are the statements for News and President Obama ?"
There are at least a hundred formulas that are useful in trigonometry.
One of the most useful is:
In a right triangle, the square of the length of the hypotenuse
is equal to the sum of the squares of the two short sides.
Pythagoras is the name of the ancient Greek mathematician who
discovered that formula. The formula is so useful that it's known
by his name, in his honor.
