Change in y over the change in x
-1-7=-8
1- -3=4
-8 divided by 4
Slope=-2
Answer: The required solution is
Step-by-step explanation: We are given to solve the following differential equation :
Let us consider that
be an auxiliary solution of equation (i).
Then, we have
Substituting these values in equation (i), we get
![m^2e^{mt}+10me^{mt}+25e^{mt}=0\\\\\Rightarrow (m^2+10y+25)e^{mt}=0\\\\\Rightarrow m^2+10m+25=0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~[\textup{since }e^{mt}\neq0]\\\\\Rightarrow m^2+2\times m\times5+5^2=0\\\\\Rightarrow (m+5)^2=0\\\\\Rightarrow m=-5,-5.](https://tex.z-dn.net/?f=m%5E2e%5E%7Bmt%7D%2B10me%5E%7Bmt%7D%2B25e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%5E2%2B10y%2B25%29e%5E%7Bmt%7D%3D0%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B10m%2B25%3D0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~%5B%5Ctextup%7Bsince%20%7De%5E%7Bmt%7D%5Cneq0%5D%5C%5C%5C%5C%5CRightarrow%20m%5E2%2B2%5Ctimes%20m%5Ctimes5%2B5%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20%28m%2B5%29%5E2%3D0%5C%5C%5C%5C%5CRightarrow%20m%3D-5%2C-5.)
So, the general solution of the given equation is
Differentiating with respect to t, we get
According to the given conditions, we have
and
Thus, the required solution is
Answer:
0.500 hour
Step-by-step explanation:
Givens
<em><u>Distance</u></em>
- Total Distance on the highway = 3hr * 60 miles / hr = 180 miles
- Distance in the city = 20 miles
- Total Distance = 180 + 20 = 200 miles
<em><u>Time</u></em>
- Time on the highway = 3 hours
- Time in the city = x
Formula
d /t = r
Solution
- Average rate = 57.14
- Total Distance / Total Time = average rate
- 200 / (3 + x) = 57.14 Multiply both sides by 3 + x
- 200 = 57.14 * (3 + x) Remove the brackets
- 200 = 57.14*3 + 57.14x Multiply the factors on the right
- 200 = 171.42 + 57.14x Subtract 171.42 from both sides.
- 200 - 171.42 = 171.42 - 171.42 + 57.14x So the subtraction
- 28.58 = 57.14x Divide by 57.14
- 28.57/57.14 = x
- x = 0.500 hour Answer
45 dogs and 52 cats because 5+7=12 so 45+7=52
