Answer:
The angle has a measure of
radians.
Step-by-step explanation:
According to the statement, an angle centered at the center of the circle covers an arc of
units, the arc is a portion of the circunference. We include a figure representing the circle below.
Where:
- Radius, measured in units.
- Arc, measured in units.
- Angle of the arc, measured in radians.
From Geometry, we can calculate the length of the arc by means of this equation:
(1)
If we know that
and
, then the angle of the arc is:
![\alpha = \frac{s}{R}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7Bs%7D%7BR%7D)
![\alpha = \frac{\frac{25\pi}{6} }{5}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B%5Cfrac%7B25%5Cpi%7D%7B6%7D%20%7D%7B5%7D)
![\alpha = \frac{25\pi}{30}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B25%5Cpi%7D%7B30%7D)
![\alpha = \frac{5\pi}{6}\,rad](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cfrac%7B5%5Cpi%7D%7B6%7D%5C%2Crad)
The angle has a measure of
radians.
Answer:
(3) x ≥ -3
(4) 2.5 gallons
(4) -12x + 36
Step-by-step explanation:
<em>Hey there!</em>
1)
Well its a solid dot meaning it will be equal to.
So we can cross out 1 and 2.
And it's going to the right meaning x is greater than or equal to -3.
(3) x ≥ -3
2)
Well if each milk container has 1 quart then there is 10 quarts.
And there is 4 quarts in a gallon, meaning there is 2.5 gallons of milk.
(4) 2.5 gallons
4)
16 - 4(3x - 5)
16 - 12x + 20
-12x + 36
(4) -12x + 36
<em>Hope this helps :)</em>
<u>Part A
</u><u />To estimate this, we should first look at our fractions and see if they can be combined to form a whole number. In this case,
![\frac{3}{5}](https://tex.z-dn.net/?f=%20%5Cfrac%7B3%7D%7B5%7D%20)
and
![\frac{2}{3}](https://tex.z-dn.net/?f=%20%5Cfrac%7B2%7D%7B3%7D%20)
equal approximately 1. We can add this "1" to the other to full gallons to estimate that the painter needs about
3 gallons.
<u>Part B
</u><u /><u />To find the exact amount, we should first change the mixed numbers to improper fractions. We do this by multiplying the denominator by the whole number, adding the numerator, and placing that value over the denominator.
![1 \frac{3}{5} \\ \\ (5*1)+3 =8 \\ \\ \frac{8}{5} \\ \\ \\ \\ 1 \frac{2}{3} \\ \\ (3*1)+2=5 \\ \\ \frac{5}{3} ](https://tex.z-dn.net/?f=1%20%5Cfrac%7B3%7D%7B5%7D%20%5C%5C%20%5C%5C%20%20%285%2A1%29%2B3%20%3D8%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B8%7D%7B5%7D%20%20%5C%5C%20%20%5C%5C%20%20%5C%5C%20%5C%5C%20%201%20%5Cfrac%7B2%7D%7B3%7D%20%5C%5C%20%20%5C%5C%20%283%2A1%29%2B2%3D5%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B5%7D%7B3%7D%20%20%0A)
Now, we need to find the least common denominator. This is the lowest value that both denominators will divide evenly into. In this case, that number is 15.
Next, we should multiply both fractions so that the denominator is that number. Remember that we must also multiply the numerator for the fraction to remain equivalent to its original value.
![\frac{8}{5} *3 = \frac{24}{15} \\ \\ \frac{5}{3} *5 = \frac{25}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B8%7D%7B5%7D%20%2A3%20%3D%20%20%20%5Cfrac%7B24%7D%7B15%7D%20%5C%5C%20%20%5C%5C%20%20%5Cfrac%7B5%7D%7B3%7D%20%2A5%20%3D%20%20%5Cfrac%7B25%7D%7B15%7D%20%20%20%20)
Now, we can simply add our numerators.
![25+24=49](https://tex.z-dn.net/?f=25%2B24%3D49)
We know that he needs
![\frac{49}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B49%7D%7B15%7D%20)
gallons of paint, but this is not in the most simplified format. To simplify, we need to turn our improper fraction back to a mixed number. To do this, we need to divide our numerator by the denominator to create our whole number, and the remainder becomes our new numerator.
![\frac{49}{15} \\ \\ 49 / 15 = 3(Remainder: 4) \\ \\ 3\frac{4}{15}](https://tex.z-dn.net/?f=%20%5Cfrac%7B49%7D%7B15%7D%20%5C%5C%20%20%5C%5C%2049%20%2F%2015%20%3D%203%28Remainder%3A%204%29%20%5C%5C%20%20%5C%5C%20%203%5Cfrac%7B4%7D%7B15%7D%20%20%20)
Using that logic, we can see that the painter needs exactly
gallons of paint.
Equal to because 12 yards equals 36 feet