Answer:
Area = 10025.66 square units
Step-by-step explanation:
We are given the following in the question:
The birth rate of a population:
The death rate of a population:
The area between the curve for 0 ≤ t ≤ 10, is given by:
![\displaystyle\int_0^{10}b(t) - d(t)~ dt\\\\\displaystyle\int_0^{10} 2300e^{0.024t}-1450e^{0.019t}~dt\\\\= \Bigg[\frac{2300e^{0.024t}}{0.024}\Bigg]_0^{10}-\Bigg[\frac{1450e^{0.019t}}{0.019}\Bigg]_0^{10}\\\\= \Bigg[\frac{2300e^{0.24}}{0.024}-\frac{1450e^{0.19}}{0.019}\Bigg]-\Bigg[\frac{2300}{0.024}-\frac{1450}{0.019}\Bigg]\\\\= 29543.2058565 - 19517.5438596 \approx 10025.6](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cint_0%5E%7B10%7Db%28t%29%20-%20d%28t%29~%20dt%5C%5C%5C%5C%5Cdisplaystyle%5Cint_0%5E%7B10%7D%202300e%5E%7B0.024t%7D-1450e%5E%7B0.019t%7D~dt%5C%5C%5C%5C%3D%20%5CBigg%5B%5Cfrac%7B2300e%5E%7B0.024t%7D%7D%7B0.024%7D%5CBigg%5D_0%5E%7B10%7D-%5CBigg%5B%5Cfrac%7B1450e%5E%7B0.019t%7D%7D%7B0.019%7D%5CBigg%5D_0%5E%7B10%7D%5C%5C%5C%5C%3D%20%5CBigg%5B%5Cfrac%7B2300e%5E%7B0.24%7D%7D%7B0.024%7D-%5Cfrac%7B1450e%5E%7B0.19%7D%7D%7B0.019%7D%5CBigg%5D-%5CBigg%5B%5Cfrac%7B2300%7D%7B0.024%7D-%5Cfrac%7B1450%7D%7B0.019%7D%5CBigg%5D%5C%5C%5C%5C%3D%2029543.2058565%20-%2019517.5438596%20%5Capprox%2010025.6)
Width =3.5, length = 4
Let's make a few equations to summarize what we know.:
a = 14
l = 2w -3
a = wl
Now let's substitute the expression for l into the expression for area and solve.
a = w(2w - 3)
a = 2w^2 - 3w
14 = 2w^2 - 3w
0 = 2w^2 - 3w - 14
which factors into
(2w - 7) (w + 2)
Solving for w
2w - 7 = 0
2w = 7
w = 3.5
w+2 = 0
w = -2
So w can be either 3.5 or -2. Since a negative width doesn't make sense, w = 3.5
Let's verify
w = 3.5
l = 2w - 3
l = 2*3.5 - 3
l = 7 - 3
l = 4
a = wl
a = 3.5 * 4
a = 14
So the width is 3.5 and the length is 4.
Y=2x-1
y=-3x+14
First you would substitue one of the y's for the other so
2x-1=-3x+14
no you would solve for x...
add one on both sides
2x=-3x+15
now add 3x to both sides which becomes
5x=15
divide 5 on both sides which gives you x=3
now to solve for y plug into any one of the equations(doesn't matter which one) from before 3 for x and solve
y=2(3)-1
y=6-1
y=5
And that is you answer y=5
Answer:
28
Step-by-step explanation:
