Answer:
As we get closer to x=-3, the limit is approaches -1, on both sides of -3 so this is a good limit so c is 8.
Step-by-step explanation:
In order for a limit to exists, the left side limit must exist and right side limit must exist and on top of that, they must be equal to each other.
In this case, this a piece wise function and by definition of a limit that exist, the limit of this piece wise function as x approaches 3 from either side, must be equal.
We let x=-3 for the top equation.
So we set the second equation equal to -1.
So the value of c is 8. We can prove this by graphing as well.
<h3>
Answer: Choice D. 8m, 9m, 10m</h3>
==================================
Explanation:
If a = 8 and b = 9 are the two legs of a triangle and c = 10 is the hypotenuse, then
a^2 + b^2 = c^2
8^2 + 9^2 = 10^2
64 + 81 = 100
145 = 100
We get a false equation as 145 and 100 are two different values. So the original equation is false when (a,b,c) = (8,9,10)
By the converse of the pythagorean theorem, we have proven that this particular triangle is not a right triangle
-------------
Contrast this with something like choice A where we have a = 3, b = 4, c = 5 leading to
a^2 + b^2 = c^2
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25
we get a true equation so a triangle with sides 3,4,5 is a right triangle. Choices B and C follow a similar path.
The intersection between the curves are
3, 0
0, 3
The volume of the solids is obtained by
V = ∫ π [ (4 - (y-1)²)² - (3 - y)²] dy with limits from 0 to 3
The volume is
V = 108π/5 or 67.86
6 < 3b or 3b + 12 < 9
2< b Or 3b < -3 You can only change the sign should you multiply or divide the negative number.
<span>2 < b or b < 1 that means b > 2
Hope this helps :)</span>
Answer:
Step-by-step explanation:
The distance between point (x1,y1) and (x2,y2) on a coordinate plane is given by expression 
In the problem given coordinate points are
(0, a) and (a, 0).
Thus, distance between these points are given by
Thus , expression gives the distance between point (0, a) and point (a, 0) on a coordinate grid.
