The height, h, in feet of the tip of the hour hand of a wall clock varies from 9 feet to 10 feet. Which of the following equatio
2 answers:
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Given equation is
It gives approx world population in billions for t years since 2004.
Answer(a):
Compare with growth formula P=a(b)^t, we get:
growth factor b = 1.0126
We know that if r is the percent rate of growth then
1+r=b
1+r=1.0126
r=0.0126
Hence the yearly percent rate of growth of the world population is 0.0126 or 1.26%.
Answer(b):
To find worlds population in 2004, plug t=0 because year is counted from 2004.
Hence answer is 6.40 billion.
To find worlds population in 2018, plug t=2018-2004=14 because year is counted from 2004.
Hence answer is approx 7.63 billion.
Answer(c):
Average rate of change of the world population between 2004 and 2018 is given by:
Hence answer is approx 0.0878571428571 billion per year.
To convert it into millions, multiply by 1000
So we get 0.0878571428571*1000 = 87.8571428571
Which is approx 88 to the nearest integer
Hence final answer is approx 88 millions per year.
Answer: 58 ft × 58 ft
Step-by-step explanation:
Let the length of the region = x feet
And, the width of the region = y feet
Since, the perimeter of the region = 234 feet ( Given )
⇒
⇒
⇒
Again the area of the region, A = xy
⇒
⇒
By differentiating the above equation with respect to x,
⇒
For maxima or minima,
Again differentiating equation A'(x) with respect to x,
We get, A''(x) = -2
Hence, For x = 58.5 A''(x) = negative
⇒ For x = 58.5 feet the area A(x) is maximum,
⇒ The length of the region having maximum area = x = 58.5 feet
And, the width of the region having maximum area = y = 117-x= 117 - 58.5=58.5 feet,
⇒ The dimension of the region having the maximum area = 58.5 ft × 58.5 ft