| x-3 | < x-3 can someone give a step by step process on how to do this?
1 answer:
Answer:
There are no solutions to the inequality.
Step-by-step explanation:
|x - 3| < x – 3
1. Separate the inequality into two separate ones.
(1) x – 3 < x – 3
(2) x – 3 < -(x – 3)
2. Solve each equation separately
(a) Equation (1)
(b) Equation (2)
For example, if x = 0, we get
|0 - 3| < 0 - 3 or
3 < -3
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The extraneous solution of the given radical equation is x = 3
<h3>Finding the extraneous solution:</h3>
Here we have the radical equation:
We want to get the extraneous solution, to get it, we first need to square both sides of the equation, so we get:
Now we got a quadratic equation, we can rewrite it as:
To solve this we use Bhaskara's formula, we will get:
Then the two solutions are:
x = (15 + 9)/2 = 12
x = (15 - 9)/2 = 3
<h3>Which one is the extraneous solution?</h3>Let's evaluate both solutions in our original equation and let's see which is the one that does not work:
for x = 12 we have:
This is true.
For x = 3 we have:
This is false, so the extraneous solution is x = 3.
If you want to learn more about extraneous solutions, you can read:
Answer:
-0.69 feet per second
Step-by-step explanation:
We have dx/dt = 2 ft/sec, and we want to determine dy/dt.
x and y are related by the Pythagorean Theorem.
x²+y²=16²
Differentiate both sides of this equation with respect to t to get
Divide both sides by 2y
When x = 5 ft, we have
x²+y²=16²
5²+y²=256
y²=256-25=231
therefore
y=
=-0.69
The top of the ladder is sliding down (because of the negative sign in the result) at a rate of -0.69 feet per second.
