Y=-4x-7 in standard form
1 answer:
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You know that 
so 
.
Area of a shaded region is:
![$A=\int\limits_0^k\dfrac{y^2}{4}\,dy=\frac{1}{4}\int\limits_0^ky^2\,dy=\frac{1}{4}\left[\frac{y^3}{3}\right]_0^k=\frac{1}{4}\left[\frac{k^3}{3}-\frac{0^3}{3}\right]=\frac{1}{4}\cdot\dfrac{k^3}{3}=\boxed{\frac{k^3}{12}}](https://tex.z-dn.net/?f=%24A%3D%5Cint%5Climits_0%5Ek%5Cdfrac%7By%5E2%7D%7B4%7D%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cint%5Climits_0%5Eky%5E2%5C%2Cdy%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7By%5E3%7D%7B3%7D%5Cright%5D_0%5Ek%3D%5Cfrac%7B1%7D%7B4%7D%5Cleft%5B%5Cfrac%7Bk%5E3%7D%7B3%7D-%5Cfrac%7B0%5E3%7D%7B3%7D%5Cright%5D%3D%5Cfrac%7B1%7D%7B4%7D%5Ccdot%5Cdfrac%7Bk%5E3%7D%7B3%7D%3D%5Cboxed%7B%5Cfrac%7Bk%5E3%7D%7B12%7D%7D%20)
so k:
![\dfrac{k^3}{12}=\dfrac{9}{4}\\\\\\k^3=\dfrac{9\cdot12}{4}\\\\\\k^3=9\cdot3\\\\k^3=3^3\quad|\sqrt[3]{(\ldots)}\\\\\boxed{k=3}](https://tex.z-dn.net/?f=%5Cdfrac%7Bk%5E3%7D%7B12%7D%3D%5Cdfrac%7B9%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D%5Cdfrac%7B9%5Ccdot12%7D%7B4%7D%5C%5C%5C%5C%5C%5Ck%5E3%3D9%5Ccdot3%5C%5C%5C%5Ck%5E3%3D3%5E3%5Cquad%7C%5Csqrt%5B3%5D%7B%28%5Cldots%29%7D%5C%5C%5C%5C%5Cboxed%7Bk%3D3%7D)
Area of a shaded region is:
so k:
Answer:
The population of the city in 2020 is 3,839,832
Step-by-step explanation:
Given:
Population at 2000 = 315,000
Rate at which the population increases = 2%
To Find:
The Population in the city after 2020 = ?
Solution:
The population in the city after 2020 can be found by using Exponential growth function.
Exponential growth occurs when a quantity increases by the same factor
Exponential growth function is
Where
y is the final amount
a is the initial amount
r is the rate of increase
t is the time period.
Now substituting the values ,
In 2020 i.e., after 10 years
y = 3,839,832.42