Let, length and breadth of rectangle is L and B respectively.
It is given that :
The length rectangle is 4 cm more than 3 times the width of the rectangle.
L = 3B + 4 ......1 )
Also, area of square = area of the rectangle + 66
L² = LB + 66
Putting value of L from
L² = ( 3B + 4 )( B ) + 66
L² = 3B² + 4B + 66
( 3B + 4 )² = 3B² + 4B + 66
9B² + 16 + 24B = 3B² + 4B + 66
6B² + 20B - 50 = 0
3B² + 10B - 25 = 0
3B² + 15B - 5B -25 = 0
3B( B + 5 ) -5( B + 5 ) = 0
B = 5/3 units
L = 3( 5/3 ) + 4
L = 5 + 4 = 9 units
Hence, this is the required solution.
Answer:
(A) The population's growth rate in equation form is y = (0.016t * 7652) + 7652
(B) y = (0.016t * 7652) + 7652 =
y = (0.016(8) * 7652) + 7652 =
y = (0.128 * 7652) + 7652 =
y = 979.456 + 7652 =
y = 8631.456 (Or About) 8631
Step-by-step explanation:
(A) Y = the total population of the town. 0.016 is 1.6% just in its original form. T = the year in which were trying to find the town's total population. 7652 is the total population of the town in 2016. With this information, the equation reads, The total population of the town (Y) is equal to 16% (0.016) of the current year's population (T) added to 2016's population of 7652. (This last sentence can also be read what is 1.6% of the towns population in the year were trying to find. Because the population is always growing, 1.6% gets multiplied as to scale with the total population in year T)
(B) We just substitute (T) for 2024, or 8 years after 2016 (2024-2016) and simplify the equation we made.
