It looks like you're asked to find the value of y(-1) given its implicit derivative,

and with initial condition y(2) = -1.
The differential equation is separable:

Integrate both sides:


Solve for y :



![y = -\dfrac1{\sqrt[3]{3x+C}}](https://tex.z-dn.net/?f=y%20%3D%20-%5Cdfrac1%7B%5Csqrt%5B3%5D%7B3x%2BC%7D%7D)
Use the initial condition to solve for C :
![y(2) = -1 \implies -1 = -\dfrac1{\sqrt[3]{3\times2+C}} \implies C = -5](https://tex.z-dn.net/?f=y%282%29%20%3D%20-1%20%5Cimplies%20-1%20%3D%20-%5Cdfrac1%7B%5Csqrt%5B3%5D%7B3%5Ctimes2%2BC%7D%7D%20%5Cimplies%20C%20%3D%20-5)
Then the particular solution to the differential equation is
![y(x) = -\dfrac1{\sqrt[3]{3x-5}}](https://tex.z-dn.net/?f=y%28x%29%20%3D%20-%5Cdfrac1%7B%5Csqrt%5B3%5D%7B3x-5%7D%7D)
and so
![y(-1) = -\dfrac1{\sqrt[3]{3\times(-1)-5}} = \boxed{\dfrac12}](https://tex.z-dn.net/?f=y%28-1%29%20%3D%20-%5Cdfrac1%7B%5Csqrt%5B3%5D%7B3%5Ctimes%28-1%29-5%7D%7D%20%3D%20%5Cboxed%7B%5Cdfrac12%7D)
<span>0.01388888888 is your answer
</span>
Answer:
solution given:
principal [P]=$850
time[T]=8years
rate[R]=8%
now
simple interest [S.I.]=
=$
=$544
so
Total balance=S.I.+P=$544+$850=$1394.
<u>option b.$1,394.00 is your answer</u>
Answer:
The right solution is "
".
Step-by-step explanation:
The given inequality is:
⇒ 
By solving the above expression, we get
⇒ 
⇒ 
Thus the above is the correct answer.
Answer:
You have 80 yards left to run.
Step-by-step explanation:
To solve this problem, we first must realize that if you have completed 80% of the run, that you have 20% left (this is because 100%-80% = 20%).
Next, we must find 20% of 400 yards. We must remember that in math, the word "of" represents multiplication. We also know that 20% = 20/100 = 0.2.
To find 20% of 400 yards, we can perform the following operation:
20% * 400
0.2 * 400
80
Therefore, you have 80 yards left.
Hope this helps!