1/4t + 3/5= 2/5 - t
Is it
(1/4)t or 1/(4t)?
(1/4)t
d/dx(sinx+cosx)
(1/4)t + 3/5= 2/5 - t
=> (5/4)t + 3/5 = 2/5
=> (5/4)t = -1/5
=> t/4 = -1/25
=> t = -4/25
Strictly the equation should read
(d/dx)(sin(x) + cos(x))
=> (d/dx)sin(x) + (d/dx)cos(x)
=> cos(x) - sin(x)
The differentials of sin and cos should be learned. You can demonstrate the results by differentiating their respective series
To solve the equation 1/4t + 3/5 = 2/5 - t, we can follow these steps:
Step 1: Simplify the equation by finding a common denominator for the fractions involved. The common denominator for 4, 5, and 5 is 20. Multiply each fraction by the necessary value to achieve this common denominator:
(1/4t) * 5/5 + (3/5) * 4/4 = (2/5) * 4/4 - t
(5/20)t + (12/20) = (8/20) - t
Step 2: Distribute and simplify further:
(5t/20) + (12/20) = (8/20) - t
5t + 12 = 8 - 20t
Step 3: Combine like terms by moving all the terms with "t" to one side of the equation and all the constant terms to the other side:
5t + 20t = 8 - 12
25t = -4
Step 4: Solve for "t" by dividing both sides of the equation by 25:
(25t)/25 = (-4)/25
t = -4/25
So, the solution to the equation is t = -4/25.