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)
Answer:
Option D. 5x + 12y + 4z is the corrct one.
Remark
It looks like all you want is question 6. If that is the case, there are two ways to do it.
Algebra
<u>First answer</u>
abs(b - 22) = 5 Equate to + 5
b - 22 = 5 Add 22 to both sides.
b = 5 + 22
b = 27
<u>Second Answer</u>
Equate to - 5
b - 22 = -5
b = 22 - 5
b = 17
Method Two
<u>Graph the question</u>
The graph y = abs(b - 22) is shown below in red.
The values of y when y =5 are shown in blue.
Answer:
width = 10 units and length = 20 units
Step-by-step explanation:
Let the width be w
so Length will be 2w
using the rectangle formula:





Find length:


