<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>
Substitute y=4x to the second equation:
x^2 + (4x)^2 = 17
x^2 + 16x^2 = 17
17x^2 = 17
x^2 = 17/17
x^2 = 1
x = 1 and -1
When x=1, y=4(1) = 4
When x=-1, y=4(-1) = -4
Thus the solutions would be (1,4) and (-1,-4). That would correspond to D. and A.
Answer:
A, 3/4(4/3)x=-6(4/3)
Step-by-step explanation:
Multiplying each side of the equation by 4/3 isolates x and solves the equation in one step.
Answer:
Step-by-step explanation:
As per diagram, the two triangles are similar, as all angles are congruent (one is vertical, one is right, one is the
Let the distance across the river be x.
<u>The ratio of corresponding sides is same. Find x using ratios:</u>
- x/45 = 75/60
- x = 45*75/60
- x = 56.25 feet
