Answer:
1.94 x , 1.25 x , 6 x , 8.1 x
Step-by-step explanation
the highest negative power is the least and then the greatest is the highest positive power. so is the least and is the greatest.
Critical points is where the derivative (slope) is zero or does not exist. So to do this we have to find the derivative of our function:
So we apply chain rule:
=
Set our first derivative to zero and solve for x:
3(x^2 - 1) * 2x = 0
So we can see that (by plugging in) 0, -1 and 1 makes our solution true
So our critical value is x = 0, x = -1, x = 1
1. 20%
2. 12
3. 90%
4. 48
BRANLIEST? :)
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
<u>Calculus</u>
Antiderivatives - Integrals
Integration Constant C
Integration Rule [Reverse Power Rule]:
Integration Property [Multiplied Constant]:
Integration Property [Addition/Subtraction]:
Step-by-step explanation:
*Note:
Velocity is the derivative of Position, and Acceleration is derivative of Velocity.
↓
Velocity is integration of Acceleration, Position is integration of Velocity.
<u>Step 1: Define</u>
a(t) = 4t m/s²
s(0) = 9 m
v(0) = 16 m/s
<u>Step 2: Find Velocity Function</u>
<em>Integration Pt. 1</em>
- [Velocity] Set up integral:
- [Velocity] Substitute in function:
- [Velocity] Rewrite [Integration Property - Multiplied Constant]:
- [Velocity] Integrate [Integration Rule - Reverse Power Rule]:
- [Velocity] Multiply:
<em>Finding C</em>
- [Velocity] Substitute in initial condition:
- [Velocity] Substitute in function value:
- [Velocity] Evaluate exponents:
- [Velocity] Multiply:
- Rewrite:
Velocity Function:
<u>Step 3: Find Position Function</u>
<em>Integration Pt. 2</em>
- [Position] Set up integral:
- [Position] Substitute in function:
- [Position] Rewrite [Integration Property - Addition]:
- [Position] Rewrite [Integration Property - Multiplied Constant]:
- [Position] Integrate [Integration Rule - Reverse Power Rule]:
- [Position] Multiply:
<em>Finding C</em>
- [Position] Substitute in initial condition:
- [Position] Substitute in function value:
- [Position] Evaluate exponents:
- [Position] Multiply:
- [Position] Divide:
- [Position] Rewrite:
Position Function:
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Integration
Book: College Calculus 10e
The final velocity is 13.5m/s
The formula of velocity is given as:
And the parameters are given as:
- the initial velocity, u = 3 m/s
- the acceleration, a = 1.5 m/s²
- the time, t = 7 seconds
So, we have:
Hence, the final velocity is 13.5m/s
Read more about velocity at:
brainly.com/question/4931057