The rabbit population in a certain area is 500% of last year's population. There are 700 rabbits this year. How many were the
1 answer:
For this case we have the following data:
700 rabbits that represent 500% of the population of last year. So, to obtain the rabbit population of last year, we developed a rule of three:
700 -----------> 500%
x ---------------> 100%
Where x represents the rabbit population of last year.
Clearing x we have:
rabbits
In this way, last year there was a population of 140 rabbits.
Answer:
140 rabbits
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The equation of the hyperbola with directrices at x = ±2 and foci at (5, 0) and (−5, 0) is
The given parameters are:
- Directrices at x = ±2
- Foci at (5, 0) and (−5, 0)
The foci of a hyperbola are represented as:
Foci = (k ± c, h)
The center is:
Center = (h,k)
And the directrix is:
Directrix, x = h ± a²/c
By comparison, we have:
k ± c = ±5
h = 0
h ± a²/c = ±2
Substitute h = 0 in h ± a²/c = ±2
0 ± a²/c = ±2
This gives
a²/c = 2
Multiply both sides by c
a² = 2c
k ± c = ±5 means that:
k ± c = 0 ± 5
By comparison, we have:
k = 0 and c = 5
Substitute c = 5 in a² = 2c
a² = 2 * 5
a² = 10
Next, we calculate b using:
b² = c² - a²
This gives
b² = 5² - 10
Evaluate
b² = 15
The hyperbola is represented as:
So, we have:
Evaluate
Hence, the equation of the hyperbola is
Read more about hyperbola at:
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Step 1
Given;
Required; To find the difference in interest between the two periods.
Step 2
State the formula for simple interest
Step 3
Find the interest when the rate is 8%
Therefore the interest is given as;
Step 4
Find the interest in 1980 with a 20% rate
The interest is given as;
Step 5
Find the difference in interest between the two rates.
Hence, the difference in interest between the two rates = $11095.89