(a) By the fundamental theorem of calculus,
<em>v(t)</em> = <em>v(0)</em> + ∫₀ᵗ <em>a(u)</em> d<em>u</em>
The particle starts at rest, so <em>v(0)</em> = 0. Computing the integral gives
<em>v(t)</em> = [2/3 <em>u</em> ³ + 2<em>u</em> ²]₀ᵗ = 2/3 <em>t</em> ³ + 2<em>t</em> ²
(b) Use the FTC again, but this time you want the distance, which means you need to integrate the <u>speed</u> of the particle, i.e. the absolute value of <em>v(t)</em>. Fortunately, for <em>t</em> ≥ 0, we have <em>v(t)</em> ≥ 0 and |<em>v(t)</em> | = <em>v(t)</em>, so speed is governed by the same function. Taking the starting point to be the origin, after 8 seconds the particle travels a distance of
∫₀⁸ <em>v(u)</em> d<em>u</em> = ∫₀⁸ (2/3 <em>u</em> ³ + 2<em>u</em> ²) d<em>u</em> = [1/6 <em>u</em> ⁴ + 2/3 <em>u</em> ³]₀⁸ = 1024
None, the equation 6x - 2 = 6x + 7 does not have any solutions.
<h3>What is an algebraic equation? </h3>
An algebraic equation is an equation that consists of numbers and variables. To solve the variables, there is a need to make use of some or all of the arithmetic operations such as:
- Addition
- Subtraction
- Division, and
- Multiplication
From the given equation:
6x - 2 = 6x + 7
Collect like terms
6x - 6x -2 - 7 = 0
0 - 9 = 0
Since there is no variable to solve for in the equation, we can conclude that the equation does not have any solutions.
Learn more about algebraic equations here:
brainly.com/question/4344214
Answer:
15/34
Step-by-step explanation:
Edited with the correct answer, sorry I made a mistake
Number four is 8.0596 and number 5 is 1.98102
If you would like to know the value of x in the solution to the system of equations, you can find this using the following steps:
6x + 3y = 13
3x - y = 4 ... y = 3x - 4
___________
<span>6x + 3y = 13
</span>6x + 3 * (3x - 4) = 13
6x + 9x - 12 = 13
15x = 13 + 12
15x = 25
x = 25/15
x = 5/3
The correct result would be 5/3.
