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:
y = 5x - 21
Step-by-step explanation:
Since we already know the slope, all we need to do is plug the values of x and y into the equation.
y = 5x + b
-1 = 5(4) + b
-1 = 20 + b
-21 = b
The equation is y = 5x - 21.
Answer:
Kidneys,nephrons
Step-by-step explanation:
Everyone got a calculator.....each weighed 16 oz.......gave them to 20 students.....20 * 16 = 320 total oz
16 oz = 1 lb
320/16 = 20 lbs <==
or, if u just think about it...u gave 16 oz to each student.....16 oz = 1 lb...so u gave 1 lb to each student....20 students = 20 lbs
<span>Michael bought 0.44 pound of sliced turkey.
Now, we need to find what digit is in the value of hundredths.
Note, that the place value is hundredths with ths. Thus, the value is in the
decimal points.
And the value that Michael bought is a decimal number as well.
Not, let us find the value of hundredths.
=> 0.44 pounds
=> .4 = tenths
=> 0.04 = hundredths.
Thus the value of hundredths is 4 or 0.04 or 4/100 in fraction form.
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