Answer:
X=the smaller
y=the larger
The bigger of two numbers is four more than the smaller, then:
y=x+4
one more than twice the smaller is the same as the larger, then
1+2x=y
We have the following system of equations:
y=x+4
y=2x+1
We solve this system by equal values method:
x+4=2x+1
x-2x=1-4
-x=-3
x=3
We find the value of "y"now:
y=x+4
y=3+4
y=7
the values of x and y are:
x=3
y=7
Step-by-step explanation:
The pairs that are equivalent to each other are 40/1000 and 40%, 6/5 and 120%, 1/8 and 12.5% . They are the correct answers because if we divide for example 6/5 , we would get 1.2 and to turn a decimal into a percent we have to move the decimal point 2 times to the right meaning that the percentage would be 120% and you just do that for all! I hope this helped :)!!
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
