It is given to us that Tatenda takes t seconds to mow a square meter of lawn and Ciara takes c seconds to mow a square meter of lawn.
It is also given to us that Tatenda mows 700 square meters of lawn per week and Ciara mows 750 square meters of lawn per week.
Thus, if Tatenda mows 700
in a week, then that means he took
seconds to complete the mowing.
Likewise, if Ciara mows 750
in a week, then that means she took
seconds to complete the mowing.
Answer:
125
Step-by-step explanation:
Answer:
-3.4 = (-17
/5) = -3 2/5
Step-by-step explanation:
No solution exists for -3x+y=-18 and -3x+y=-6
Let
![T(t)](https://tex.z-dn.net/?f=T%28t%29)
be the temperature of the body
![t](https://tex.z-dn.net/?f=t)
hours after 1:30 PM. Then
![T(0) = 32.5](https://tex.z-dn.net/?f=T%280%29%20%3D%2032.5)
and
![T(1) = 30.3](https://tex.z-dn.net/?f=T%281%29%20%3D%2030.3)
.
Using Newton's Law of Cooling,
![\dfrac{dT}{dt} = k(T - T_s)](https://tex.z-dn.net/?f=%5Cdfrac%7BdT%7D%7Bdt%7D%20%3D%20k%28T%20-%20T_s%29)
, we have
![\dfrac{dT}{dt} = k(T-20)](https://tex.z-dn.net/?f=%5Cdfrac%7BdT%7D%7Bdt%7D%20%3D%20k%28T-20%29)
. Now let
![y = T - 20](https://tex.z-dn.net/?f=y%20%3D%20T%20-%2020)
, so
![y(0) = T(0) - 20 = 32.5 - 20 = 12.5](https://tex.z-dn.net/?f=y%280%29%20%3D%20T%280%29%20-%2020%20%3D%2032.5%20-%2020%20%3D%2012.5)
, so
![y](https://tex.z-dn.net/?f=y)
is a solution to the initial value problem
![dy/dt = ky](https://tex.z-dn.net/?f=dy%2Fdt%20%3D%20ky)
with
![y(0) = 12.5](https://tex.z-dn.net/?f=y%280%29%20%3D%2012.5)
.
By separating and integrating, we have
![y(t) = y(0)e^{kt} = 12.5e^{kt}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20y%280%29e%5E%7Bkt%7D%20%3D%2012.5e%5E%7Bkt%7D)
.
![y(1) = 30.3 - 20\ \Rightarrow\ 12.5e^{k(1)} = e^{k} = \frac{10.3}{12.5}\ \Rightarrow \\ k = \ln \frac{10.3}{12.5} ](https://tex.z-dn.net/?f=y%281%29%20%3D%2030.3%20-%2020%5C%20%5CRightarrow%5C%20%2012.5e%5E%7Bk%281%29%7D%20%3D%20e%5E%7Bk%7D%20%3D%20%5Cfrac%7B10.3%7D%7B12.5%7D%5C%20%5CRightarrow%20%5C%5C%0Ak%20%3D%20%5Cln%20%5Cfrac%7B10.3%7D%7B12.5%7D%0A)
![y(t) = 37 - 20\ \Rightarrow\ 12.5e^{kt} = 17\ \Rightarrow\ e^{kt} = \frac{10.3}{12.5} \ \Rightarrow \\ \\ kt = \ln \frac{10.3}{12.5}\ \Rightarrow\ t = \left( \ln \frac{17}{12.5} \right)/ \frac{10.3}{12.5} \approx -1.588 \mathrm{\ h}](https://tex.z-dn.net/?f=y%28t%29%20%3D%2037%20-%2020%5C%20%5CRightarrow%5C%2012.5e%5E%7Bkt%7D%20%3D%2017%5C%20%5CRightarrow%5C%20e%5E%7Bkt%7D%20%3D%20%5Cfrac%7B10.3%7D%7B12.5%7D%20%5C%20%5CRightarrow%20%5C%5C%20%5C%5C%0Akt%20%3D%20%5Cln%20%5Cfrac%7B10.3%7D%7B12.5%7D%5C%20%5CRightarrow%5C%20t%20%3D%20%5Cleft%28%20%5Cln%20%5Cfrac%7B17%7D%7B12.5%7D%20%20%5Cright%29%2F%20%5Cfrac%7B10.3%7D%7B12.5%7D%20%20%5Capprox%20-1.588%20%5Cmathrm%7B%5C%20h%7D)
≈ 95 minutes. Thus the murder took place about 95 minutes before 1:30 PM, or 11:55 AM.