Answer:
Step-by-step explanation:
Substitution method = plug in the slope and the (x, y) point values into y = mx + b, then solve for b. ...
Point-slope form = y − y 1 = m ( x − x 1 ) , where ( x 1 , y 1 ) is the point given and m is the slope given.
Answer:
y = 5/3 x + 4
Step-by-step explanation:
To find the inverse, interchange the x and y variables and solve for y. (that might sound a bit confusing, but don't worry! :)
Our current function is f(x) = 3/5 (x-4). Let's make f(x) = y, so the function is y = 3/5 (x - 4).
Now, switch the x and y variables. x = 3/5 (y - 4).
Now, just solve for y!
x = 3/5 y - 12/5
5x = 3y - 12
5x + 12 = 3y
3y = 5x + 12
y = 5/3 x + 4
hope this helps! <3
Answer:
44 Minutes
Step-by-step explanation:
If he takes for minutes per lap than some easy multiplication will do the job to find out how long 11 laps will take.
If he keeps running a lap in 4 minutes for every lap up, until the 11th lap, that means we multiply 11 times 4.
<em>Another example being, if I run 1 lap in 1 minute then if I ran 2 laps it would take me 2 minutes, because 1 times 2 is 2, and so fourth for each lap. So if I ran 11 laps it would take me 11 minutes because 11 times 1 is 11.</em>
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Algebra I</u>
- Exponential Rule [Powering]:
<u>Calculus</u>
Derivatives
Derivative Notation
Derivative of a constant is 0
Implicit Differentiation
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
eˣ Derivative:
Step-by-step explanation:
<u>Step 1: Define</u>
<u>Step 2: Differentiate</u>
- Rewrite [Exponential Rule - Powering]:
- Implicit Differentiation:
- [Derivative] eˣ derivative:
- [Derivative] Basic Power Rule:
- [Derivative] Simplify:
- [Derivative] [Subtraction Property of Equality] Subtract 7 on both sides:
- [Derivative] [Division Property of Equality] Divide 5 on both sides:
- [Derivative] Rewrite:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Derivatives - Implicit Differentiation
Book: College Calculus 10e