Answer:
6
Step-by-step explanation:
1. Let a and b be coefficients such that
Combining the fractions on the right gives
so that
2. a. The given ODE is separable as
Using the result of part (1), integrating both sides gives
Given that y = 1 when x = 1, we find
so the particular solution to the ODE is
We can solve this explicitly for y :
![\ln|y| = \ln\left|\sqrt[3]{\dfrac{5x}{2x+3}}\right|](https://tex.z-dn.net/?f=%5Cln%7Cy%7C%20%3D%20%5Cln%5Cleft%7C%5Csqrt%5B3%5D%7B%5Cdfrac%7B5x%7D%7B2x%2B3%7D%7D%5Cright%7C)
![\boxed{y = \sqrt[3]{\dfrac{5x}{2x+3}}}](https://tex.z-dn.net/?f=%5Cboxed%7By%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B5x%7D%7B2x%2B3%7D%7D%7D)
2. b. When x = 9, we get
![y = \sqrt[3]{\dfrac{45}{21}} = \sqrt[3]{\dfrac{15}7} \approx \boxed{1.29}](https://tex.z-dn.net/?f=y%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B45%7D%7B21%7D%7D%20%3D%20%5Csqrt%5B3%5D%7B%5Cdfrac%7B15%7D7%7D%20%5Capprox%20%5Cboxed%7B1.29%7D)
Given Equations :
✿ 2x + y = 20 ------------------ [1]
✿ 6x - 5y = 12 ----------------- [2]
Multiplying Equation [1] with 5, We get :
⇒ 5(2x + y) = 5(20)
⇒ 10x + 5y = 100 -------------- [3]
Adding Equations [2] and [3], We get :
⇒ (10x + 5y) + (6x - 5y) = 100 + 12
⇒ 16x = 112
⇒ x = 7
Substituting x = 7 in Equation [1], We get :
⇒ 2(7) + y = 20
⇒ 14 + y = 20
⇒ y = 20 - 14
⇒ y = 7
So, The Solution for the Given System of Equations is : (x , y) = (7 , 7)
Where is the question located?
<span>The acceleration of an object as produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object.</span>
