Answer:
Solutions are 2, -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
or 2, -1 + 1.58 i and -1 - 1.58i
(where the last 2 are equal to nearest hundredth).
Step-by-step explanation:
The real solution is x = 2:-
x^3 - 8 = 0
x^3 = 8
x = cube root of 8 = 2
Note that a cubic equation must have a total of 3 roots ( real and complex in this case). We can find the 2 complex roots by using the following identity:-
a^3 - b^3 = (a - b)(a^2 + ab + b^2).
Here a = x and b = 2 so we have
(x - 2)(x^2 + 2x + 4) = 0
To find the complex roots we solve x^2 + 2x + 4 = 0:-
Using the quadratic formula x = [-2 +/- sqrt(2^2 - 4*1*4)] / 2
= -1 +/- (sqrt( -10)) / 2
= -1 + 0.5 sqrt10 i and -1 - 0.5 sqrt10 i
Hi there! :) :D
Step-by-step explanation:
<u><em>Undefined.</em></u>
<u><em>Therefore, the slope is -11/0</em></u>
<u><em>Final answer is -11/0</em></u>
Hope this helps!
Thanks!
Have a nice day! :)
:D
-Charlie
Convert the timing into hours only:
11:15 = 11.25h
9:45 = 9.75h
11:45 = 11.75h
7:45 = 7.75h
10:45 = 10.75h
To find the average, we need to find the middle of these timing:
11.25 + 9.75 + 11.75 + 7.75 + 10.75 = 51.25
51.25 ÷ 5 = 10.25h = 10:15 am
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Answer: The average time it docks is 10:15 am.
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Answer:
16
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality<u>
</u>
<u>Trigonometry</u>
[Right Triangles Only] Pythagorean Theorem: a² + b² = c²
- a is a leg
- b is another leg
- c is the hypotenuse<u>
</u>
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Identify variables</em>
Leg <em>a</em> = <em>a</em>
Leg <em>b</em> = 12
Hypotenuse <em>c</em> = 20
<u>Step 2: Solve for </u><em><u>a</u></em>
- Substitute in variables [Pythagorean Theorem]: a² + 12² = 20²
- Evaluate exponents: a² + 144 = 400
- [Subtraction Property of Equality] Isolate <em>a</em> term: a² = 256
- [Equality Property] Square root both sides: a = 16
Example of linear equation:
Let's have the linear equation;
<h3 /><h3>Put x=1</h3>
<h3>Put x=2</h3>
<h3>Put x=3</h3>
