The law of cosines is
c= square root of a^2 + b^2 - 2ab cos c
the law of sines is
a = b(sin a /sin b)
Answer:
a =
and b =
Step-by-step explanation:
As we know, the radius of the unit circle is 1 unit (it is the hypotenuse in the right triangle, the blue line)
We use trigonometric formulas to find out a and b
- Sin(45) = opposite side / hypotenuse
<=> Sin(45) = b / 1
<=> b= Sin(45)*1 =
- Cos(45) = adjacent side / hypotenuse
<=> Cos(45) = a / 1
<=> a = Cos(45)*1 = 
So: a =
and b =
Answer:
The mass of the grains = 120 ± 1 g
Step-by-step explanation:
we are given the following:
Total mass of container + grains = 185 grams
Mass of container = 65 grams
Therefore, mass of grains is calculated as follows:
Mass of grains = ( Mass of container + grains) - mass of container
= 185 - 65 = 120 grams.
since the scale has an absolute uncertainty of 1 g, the mass of the grains is written as 120 ± 1 g
Answer:
Step-by-step explanation:
2 coins are 0.25 = 50 cents. That leaves 92-50 = 42 cents and 5 coins to go.
The only way to get 2 cents is to have 2 pennies. That leaves 40 cents and 3 coins to go.
The only way to get 40 cents with 3 coins is 1 quarter, 1 dime, and 1 nickel.
So you have 3 quarters = 75 cents.
2 pennies = 2 cents.
1 dime = 10 cents.
1 nickel = 5 cents.
92 cents total and 7 coins.The only way to get 40 cents
A number line consists only of one axis, conventionally a horizontal axis. Just create a line, and scale it according to practicality and your preference. Usually, it has an interval of 1 unit. But for this case, since it is in fraction form, the interval should be smaller so that you can see clearly where it is located.
In decimal form, 13/17 is equal to 0.7647058824. Let's just round this off to 0.764, that can suffice already. So, you would expect it to be between 0.7 and 0.8 on the number line. Just estimate visually where it is located. Since, it is more than 0.75, the dot would be just slightly closer to 0.8 than 0.7. The exact location is shown in the attached picture.