582.74 square inches of glass is required to construct the tank
Step-by-step explanation:
Base dimensions= 22 x 12 inches
Volume of the fish tank = 3960 cubic inches
Volume = l x w x h
3960 = 22 x 12 x h
h = 3960 /(22 x 12)
h = 3960/462
h = 8.57 inches
The glass used = lateral surface area of the rectangular prism
= 2(lh + wl)
= 2(188.57 + 102.8)
= 2(291.37)
= 582.74 square inches
582.74 square inches of glass is required to construct the tank
Mohamed decided to track the number of leaves on the tree in his backyard each year. the first year, there were 500 leaves. each year thereafter, the number of leaves was 40% more than the year before. let f(n) be the number of leaves on the tree in Mohamed's backyard in the n^th year since he started tracking it. f is a sequence. what kind of sequence is it?
Number of leaves on the tree in first year = 500
The number of leaves was 40% more than the year before.
So rate of increase is 40/100 = 0.4
We use exponential growth formula,
f(n) = a(1+r)^n
Where a is the initial number, r is the rate of growth, n is the number of years
We know a= 500, r= 0.4
f(n) = 500(1+0.4)^n
f(n) = 500(1.4)^n
Plug in n=1,2,3...
f(1) = 500
f(2) = 500 * 1.4^1
f(3) = 500 * 1.4^2 and so on
From this we can see that the common ratio is 1.4
Hence it is a Geometric sequence.
Answer:
12 12 12 12 12 12 12 12 12 1 2 12 12
1 foot = 12 inches
12 * 5 = 60 and 8 * 12 = 96
Therefore, 60 inches is a shorter length than 8 feet.
Steps:
1. calculate the values of y at x=0,1,2. using y=5-x^2
2. calculate the areas of trapezoids (Bottom+Top)/2*height
3. add the areas.
1.
x=0, y=5-0^2=5
x=1, y=5-1^2=4
x=2, y=5-2^2=1
2.
Area of trapezoid 1 = (5+4)/2*1=4.5
Area of trapezoid 2 = (4+1)/2*1=2.5
Total area of both trapezoids = (4.5+2.5) = 7
Exact area by integration:
integral of (5-x^2)dx from 0 to 2
=[5x-x^3/3] from 0 to 2
=[5(2-0)-(2^3-0^3)/3]
=10-8/3
=22/3
=7 1/3, slight greater than the estimation by trapezoids.
