What is the solution to the equation?t
1 answer:
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Answer:
y = 10.5x - 37
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
Equality Properties
Slope Formula:
Slope-Intercept Form: y = mx + b
- m - slope
- b - y-intercept
Step-by-step explanation:
<u>Step 1: Define</u>
Point (-4, 47)
Point (2, -16)
<u>Step 2: Find slope </u><em><u>m</u></em>
- Substitute:
- Subtract/Add:
- Simplify:
<u>Step 3: Find y-intercept </u><em><u>b</u></em>
- Define: y = 21/2x + b
- Substitute: -16 = 21/2(2) + b
- Multiply: -16 = 21 + b
- Isolate <em>b</em>: -37 = b
- Rewrite: b = -37
<u>Step 4: Write linear equation</u>
<em>Combine all parts.</em>
y = 21/2x - 37
y = 10.5x - 37
And we have our final answer!
Answer:
The general solution of the equation is y = + 5
Step-by-step explanation:
Since the differential equation is given as y'(t) = 3y -5
The differential equation is re-written as
dy/dt = 3y - 5
separating the variables, we have
dy/(3y - 5) = dt
dy/(3y - 5) = dt
integrating both sides, we have
∫dy/(3y - 5) = ∫dt
∫3dy/[3(3y - 5)] = ∫dt
(1/3)∫3dy/(3y - 5) = ∫dt
(1/3)㏑(3y - 5) = t + C
㏑(3y - 5) = 3t + 3C
taking exponents of both sides, we have
exp[㏑(3y - 5)] = exp(3t + 3C)
3y - 5 =
3y - 5 =
3y = + 5
dividing through by 3, we have
y = + 5
So, the general solution of the equation is y = + 5