The key is Esther travelled the same distance - x - in both her morning and evening commute.
45(time she took in the morning, or p) = x
30(time she took in the evening, or q) = x
Therefore 45(p) = 30(q), or divide both sides by 5 and get 9(p) = 6(q). I know you can divide it further, but these numbers are small enough and it's not worth the time.
Since the whole trip took an hour, (p + q) = 60min, and so, p = 60-q.
Therefore 9(60-q) = 6q or 540-9q = 6q. So 540 = 15q, which makes q = 36. If q = 36, then by (p+q)=60, p (the time she took in the morning) must equal 24.
45 miles per hour, her speed in the morning, times (24/60) hours, her time, makes 18 miles travelled in the morning. If you check, 30 miles per hour times (36/60) hours also makes 18 miles in the evening.
<span>Hope that makes a little sense. And I also hope it's right</span>
The tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
<em>Lets simplify the problem,</em>
Let assume the "tens" digit be x
Then the "units" difference = (x-1), according to the condition.
Hence, the number itself is N = 10x + (x-1).
Then the number N+8 is 10x + (x-1) + 8 = 10x + x + 7 = 11x + 7.
From the last statement of the problem, we have this equation
Simplify and find "x"
.
Thus the tens digit is 3; the units digit is 3-1 = 2; and the number itself is 32.
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Answer:
theta = 9/19 radians or approximately .4737 radians
Step-by-step explanation:
The formula for arc length is
S = r theta
where theta is in radians. Lets put in what we know. The radius would be 1.9 since the ropes would be the radius.
.9 = 1.9 theta
Divide by 1.9 on each side.
.9/1.9 = theta
theta = 9/19 radians
or in decimal form it is approximately .4737 radians
9514 1404 393
Answer:
(d) Infinitely Many Solutions
Step-by-step explanation:
Each point of intersection between the lines is a solution. When the lines lie on top of each other, there are infinitely many points of intersection, hence ...
Infinitely Many Solutions
