The quotient of a number y squared and 6 is greater than or equal to 20
y^2/6 >= 20
The quotient of twenty-three and a number y is greater than or equal to six
Well, well, well, it seems like we have a mathematical inequality on our hands! Let's break it down together.
The quotient of a number y squared and 6 is greater than or equal to 20. So if we write it out, it looks like this:
y^2 / 6 ≥ 20
Now, how can we solve this in a hilarious way? Let's see...
Imagine y is so square that it needs to be divided by 6. And guess what, even after being divided by 6, it still ends up being greater than or equal to 20! That's one ambitious square, I must say.
But how do we find the value of y? Well, let me tell you a secret. The square root of a number stays hidden between the lines. So if we square root both sides of the inequality, we get:
√(y^2 / 6) ≥ √20
Now, my friend, we have:
y / √6 ≥ √20
But hold on tight, because we don't want any square roots in the denominator. We can multiply both sides by √6 to clear things up:
y ≥ √20 * √6
And to simplify further, we can multiply those square roots together:
y ≥ √(20 * 6)
And doing some quick math, we get:
y ≥ √120
But don't forget that square roots can be negative too! So the final solution can take the form:
y ≥ ± √120
Well, that's one way to clown around with numbers and inequalities. I hope that brought a smile to your face!
To solve the inequality, we can set up the equation:
y^2 / 6 ≥ 20
To isolate y^2, we can multiply both sides of the inequality by 6:
6 * (y^2 / 6) ≥ 6 * 20
This simplifies to:
y^2 ≥ 120
To solve for y, we can take the square root of both sides of the inequality (since we're dealing with squared terms):
√(y^2) ≥ √120
This simplifies to:
|y| ≥ √120
Since we're dealing with an absolute value inequality, we need to consider both the positive and negative roots. Therefore, the solution set for the inequality is:
y ≥ √120 or y ≤ -√120
To solve this inequality, we need to isolate the variable y. Let's break down the steps:
1. Start with the given inequality: y^2 / 6 ≥ 20.
2. Multiply both sides of the inequality by 6 to eliminate the fraction: (y^2 / 6) * 6 ≥ 20 * 6. This gives us y^2 ≥ 120.
3. Take the square root of both sides of the inequality to solve for y: √(y^2) ≥ √120. Since y^2 is always positive, we can remove the square root and simplify it as y ≥ √120.
4. Find the square root of 120: √120 = √(4 * 30) = 2√30.
5. Therefore, the solution to the inequality is y ≥ 2√30 or approximately y ≥ 10.95.
To summarize, the quotient of a number y squared and 6 is greater than or equal to 20 if y is greater than or equal to approximately 10.95.