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)
The alue of 5 is the tenths place.
The minimum and maximum number of hours the plane will travel at that speed are; at least 0.875 hours and at most 1.375 hours
<h3>How to Solve Absolute Value Inequality?</h3>
We are given that the speed of the plane is 200 miles per hour.
Now, formula for time taken is;
Time = Distance/Speed
If the speed is 225 ± 50 miles, then it means that;
Maximum distance = 275 miles
Minimum distance = 175 miles
Thus, we can say that;
Minimum number of hours = 275/200 = 1.375 hours
Maximum number of hours = 175/200 = 0.875 hours
Read more about Absolute Value Inequality at; brainly.com/question/13282457
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Answer:
6 7/24
Step-by-step explanation:
