The rectangle shown as a perimeter of 70 cm and the given area. It’s length is 8 more than twice it’s width. Write and solve a system of equations to find the dimensions of the rectangle. The length of the rectangle is ___cm and the width of the rectangle is ___cm.
Answers
width of the rectangle = b = x
length of the rectangle = l = 8 + 2x
Perimeter of the rectangle = 70cm
Also, perimeter of the rectangle = 2(l + b)
70 = 2[x + (8 + 2x)]
70 = 2(x + 8 + 2x)
70 = 2(3x + 8)
70 = 6x + 16
70 - 16 = 6x
54 = 6x
54/6 = x
9 = x
Therefore, b = x
b = 9cm
l = 8 + 2x
I = 8 + 2×9
I = 8 + 18
I = 26cm
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The annual growth rates for each factor are:
1. the land required to grow a unit of food, -1% (due to greater productivity per unit of land)
2. the amount of food grown per calorie of food eaten by a human, +0.5%
3. per capita calorie consumption, +0.1%
4. the size of the population, +1.5%.
Required:
At these rates, how long would it take to double the amount of cultivated land needed? At that time, how much less land would be required to grow a unit of food?
Answers
Answer:
Kindly check explanation
Step-by-step explanation:
Given the following annual growth rates:
land/food = - 1%
food/kcal = 0.5%
kcal/person = 0.1%
population = 1.5%
Σ annual growth rates = (-1 + 0.5 + 0.1 + 1.5)% = 1.1% = 0.011
Exponential growth in Land :
L = Lo * e^(rt)
Where Lo = Initial ; L = increase after t years ; r = growth rate
Time for amount of cultivated land to double
L = 2 * initial
L = 2Lo
2Lo = Lo * e^(rt)
2 = e^(0.011t)
Take the In of both sides
In(2) = 0.011t
0.6931471 = 0.011t
t = 0.6931471 / 0.011
t = 63.01 years
Land per unit of food at t = 63.01 years
L = Fo * e^(rt)
r = growth rate of land required to grow a unit of food = 1% = 0.01
L/Fo = e^(-0.01* 63.01)
L/Fo = e^(−0.6301)
= 0.5325385 = 0.53253 * 100% = 53.25%
Land per unit now takes (100% - 53.25%) = 46.75%
working today?
Answers