Yesterday emily's bike shop sold three bikes that were priced at $200 each, and four bikes priced at $175 each. how much money d
1 answer:
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Let denote the amount of uranium-238 in the reactor at time
. As conversion to plutonium-239 occurs, the amount of uranium will decrease, so the conversion rate is negative. Because the rate is proportional to the current amount of uranium, we have
where is constant. Separating variables and integrating both sides gives
Suppose we start some amount . This means that at time
we have
, so that
We're given that after 10 years, 99.97% of the original amount of uranium remains. This means (if is taken to be in years) for some starting amount
,
The half-life is the time it takes for the starting amount
to decay to half,
:
or about 23,101 years. Notice that it doesn't matter what the actual starting amount is, the half-life is independent of that.
Answer:
Part 1: 31.4 feet
Part 2: 61 feet
Part 3: 99,000 stalks of corn
Step-by-step explanation:
<u>Part 1:</u>
Diagram attached.
You can follow the problem closely and draw a diagram like this. The RED LINE is the distance we are looking to find.
The red line is the hypotenuse of a right triangle we can create (see the dotted line). We can now use the pythagorean theorem to solve for the distance.
Pythagorean Theorem is hypotenuse^2 = leg^2 + leg^2
Let red line [what we want to find] be h and the other 2 sides are 10-5=5 ft & 25 + 6 = 31ft. So we have:
Hence Bethany has to walk 31.4 feet
<u>Part 2:</u>
See 2nd diagram attached.
The blue line is the path of Bethany and the green line is path of Ben. The RED line is what we are looking to find, the shortest distance between them.
We use Pythagorean Theorem twice on the two triangles and add up the results.
<u>Left Triangle:</u>
If we make a triangle, we have base (one leg) = 30 and the other leg is 20-10=10. So we have:
<u>RightSide triangle:</u>
two legs are 25 and 15 respectively, so we use the pythagorean theorem again:
Thus, the shortest distance = 31.62 + 29.15 = 60.77 = 61 feet (rounded to nearest whole number)
<u>Part 3:</u>
The area of the Maize MINUS the area of the path is the Area of the Corn [what we are looking for].
Area of Maze:
100 * 100 = 10,000 sq. yd.
Area of Path = 1.5 * 3000 = 4,500 sq. yd.
Area of Corn = 10,000 - 4,500 = 5,500 sq. yard of land.
Now, each sq. yd. holds 18 stalks, so 5,500 sq. yd. will hold:
18 * 5,500 = 99,000 stalks of corn
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