<span>for the first part, realize that the hour and minute hands are moving at different rates; in one hour, the minute hands moves all the way around the face of the clock, and thus moves a total of 360 degrees or 2 pi radians; the hour hand moves only 1/12 away around the clock, so covers only 30 degrees or Pi/6 radians.
Now, the LINEAR distance traveled by the tip of each hand is also determined by the length of the hand. In the case of the minute hand, it sweeps out a circle of radius 10 cm, so traces out a circle of radius 10 cm. Since the circumference of a circle is 2*pi*r, the minute hand (remember it made one complete cycle) covers a distance of 2*pi*10cm=20 Pi cm
The hour hand covers only 1/12 a circle, but that circle is only 6 cm in radius, so the distance traveled by the tip of the minute hand is:
1/12 *[2 *pi*r]=1/12*[12*pi]=pi
so the difference is 19pi
for the last part, you should draw a diagram of the two hands, the minute hand is 10 cm in length, the hour hand is 6 cm in length, and they are 30 degrees apart...from that drawing, see if you can figure out the remaining leg of the triangle you can form from them
good luck</span><span>
</span>
Answer:
56 cups of water
Step-by-step explanation:
Katrina drinks 0.5 gallons of water per day
We have 7 days in a week, hence, the number of gallons of water she drinks per week is calculated as:
1 day = 0.5 gallons
7 days = x
Cross Multiply
1 day × x = 7 days × 0.5 gallons
x = 7 days × 0.5 gallons/1 day
x = 3.5 gallons
Note that 16 cups = 1 gallon
The number of cups of water she drinks per week is
1 gallon = 16 cups
3.5 gallons = x
Cross Multiply
1 gallons × x = 3.5 gallons × 16 cups
x = 3.5 gallons × 16 cups/1 gallons
x = 56 cups
Therefore, Katrina drinks 56 cups of water in a week
Answer:
66 67/100
Step-by-step explanation:
<span>5(x – 2)(x + 4) > 0
(5x-10)(x+4)>0
6x -6 > 0
+6 +6
6x >
</span>x<-4 or x>2
Answer: 1 L = 1000 mL
Step-by-step explanation:
