The distance formula is:
We are given two points in the form (x,y), so plug in the values to the distance formula:
Next we can simplify. We know that 12-12 is 0, so we can drop it from the equation, as it will not affect our answer. Also, we know that -10-15 is -25:
The square and square root cancel each other out leaving us with 25.
The answer is 25.
ANSWER
$1,413.81
EXPLANATION
The compound interest formula is given by:
Where P=900 is the balance in the account, t=10 is the number of years and r=0.0462 is the rate.
We substitute the values in to the formula to get:
This simplifies to:
Therefore $1413.81 will be in the account after 10 years.
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
Let x be the amount of cement and y be the amount of sand. If <span>the ratio of cement to sand for mortar is 1:3, then
and y=3x.
</span>
So, if <span>Sandy puts in x=7 shovels of cement, then she puts
shovels of sand.
</span><span>
</span><span>
Answer: 21 shovels of sand.
</span>
Answer:
your slope is 1/1 and your y-intercept is 7. you have to plot this on a graph.
Step-by-step explanation:
