Answer:
Step-by-step explanation:
When a question asks for the "end behavior" of a function, they just want to know what happens if you trace the direction the function heads in for super low and super high values of x. In other words, they want to know what the graph is looking like as x heads for both positive and negative infinity. This might be sort of hard to visualize, so if you have a graphing utility, use it to double check yourself, but even without a graph, we can answer this question. For any function involving x^3, we know that the "parent graph" looks like the attached image. This is the "basic" look of any x^3 function; however, certain things can change the end behavior. You'll notice that in the attached graph, as x gets really really small, the function goes to negative infinity. As x gets very very big, the function goes to positive infinity.
Now, taking a look at your function, 2x^3 - x, things might change a little. Some things that change the end behavior of a graph include a negative coefficient for x^3, such as -x^3 or -5x^3. This would flip the graph over the y-axis, which would make the end behavior "swap", basically. Your function doesn't have a negative coefficient in front of x^3, so we're okay on that front, and it turns out your function has the same end behavior as the parent function, since no kind of reflection is occurring. I attached the graph of your function as well so you can see it, but what this means is that as x approaches infinity, or as x gets very big, your function also goes to infinity, and as x approaches negative infinity, or as x gets very small, your function goes to negative infinity.
Well -5/8 as a decimal would be -0.625.
So, the order would be -0.615 -0.62(0) and then -5/8 (or -0.625).
You could easily search up 5/8 as a decimal :)
The Answer Is 21.6 repeating
Answer:
csc²(x)
Step-by-step explanation:
csc(x) = 1/sin(x)
sin²(x) + cos²(x) = 1
=> cos²(x) = 1 - sin²(x)
cos(2x) = cos²(x) - sin²(x) = (1 - sin²(x)) - sin²(x) =
= 1 - 2×sin²(x)
=> 2×sin²(x) = 1 - cos(2x)
sin²(x) = 1/2×(1-cos(2x))
=> 1 - cos(2x) = 2×(1/2×(1-cos(2x)) = 2×sin²(x)
=> 2 / (1-cos(2x)) = 2 / (2×sin²(x)) = 1/sin²(x) =
= 1/sin(x) × 1/sin(x) = csc(x)×csc(x) = csc²(x)
Answer:
Sorry this is late and I think this is right.
They are both parallel, they have the same slope, and do <em>not </em>intersect. If you were to draw a slope out for it, you would find this to be true.
For example: Say the question called for you to explain why there aren't any solutions to these system of inequalities:
<em>y < - 1/2x -3</em>
<em>y > 1/2x + 2</em>
<em>y= -x/2 -3</em> and <em>y= -x/2 + 2 </em>have the same exact slope, are parallel, and never intersect. The first line is 5 units below the second line when x = 0. Because the lines are parallel, it is always below the second line. The solutions of y < - x/2 -3 are the points in the plane below the first line. The solutions of y > 1/2 + 2 are points above the second line.
I hope this helps you. Good luck on whatever you're working on and stay safe! Please let me know if this helped you or didn't.