If the inequality symbol is ≤ or ≥ , then the region includes the parabola, so it should be graphed with a solid line. Otherwise, if the inequality symbol is < or > , the parabola should be drawn with a dotted line to indicate that the region does not include its boundary. Example: Graph the quadratic inequality.
Factor the following:
2 x^2 - 32 y^2
Factor 2 out of 2 x^2 - 32 y^2:
2 (x^2 - 16 y^2)
x^2 - 16 y^2 = x^2 - (4 y)^2:
2 (x^2 - (4 y)^2)
Factor the difference of two squares. x^2 - (4 y)^2 = (x - 4 y) (x + 4 y):
Answer: 2 (x - 4 y) (x + 4 y)
By using the arc length formula, we will see that the length of the curve is L = 1.48
<h3>
How to use the arc length formula?</h3>
Here we have the curve:
y = 2 - x^2 with 0 ≤ x ≤ 1
And we want to find the length of the curve.
The arc length formula for a curve y in the interval [x₁, x₂] is given by:

For our curve, we have:
dy/dx = -2x
And the interval is [0, 1]
Replacing that we get:

This integral is not trivial, using a table you can see that this is equal to:

evaluated from x = 1 to x = 0, when we do that, we will get:

That is the length of the curve.
If you want to learn more about curve length, you can read:
brainly.com/question/2005046
Answer:
H. 1/9.
Step-by-step explanation:
The area of a circle is calculated by solving for π
.
The smallest circle has an area of π
= π * 1 = π.
The middle ring will then have an area of π
- π = π * 4 - π = 4π - π = 3π.
The largest ring will then have an area of π
- π
= 9π - 4π = 5π.
5π + 3π + π = 9π
So, the probability of hitting the innermost circle will be π / 9π = 1 / 9.
Your answer is H. 1/9.
Hope this helps!
Answer: B. -2/3 the amount of water decreases every 3 minutes!
Step-by-step explanation:
B because it starts with 14 gallons with 0 minutes and the slope goes go down 2 and run 3 so therefore, the answer is B because from 14 gallons and 0 minutes it goes to 3 minutes 12 gallons and 6 minutes and 10 gallons so it decreases 2 gallons everything 3 minutes!
Hope this helps please give brainliest!
and here is the equation if you would need it
y=-2/3x+14