The answer is 16 if you solve it, because the square root of 64 is 8 and 2 * 8 = 16
Answer:
Quadrants I and II.
O: (-2, 2)
N: (-2, 4)
M: (1, 4)
P: (1, 2)
Step-by-step explanation:
When rotating about the origin 90 degrees in a counterclockwise direction, focus on the coordinates of one point on the preimage at a time. So, the x-coordinate on the image will be the opposite of the y-coordinate of the preimage, and the y coordinate of the image will be the x-coordinate of the preimage. That sounds complicated so here is an example from the problem.
O is a point on the preimage. Its coordinates are (2, 2). To find the x-coordinate, take the opposite of the image's y-coordinate. The y-coordinate is 2, so it will be a -2 x-coordinate on the image. To find the y-coordinate on the image, take the x-coordinate of the preimage (O). The x-coordinate of O is 2, so the y-coordinate of the image will be 2. Combine those together and after a 90 degree counterclockwise rotation, you get a point of (-2, 2)
Answer:
Limit=0
Converges
Absolutely converges
Step-by-step explanation:
If 
then
.
Let's rewrite
a little.
I'm going to hone in on (3(n+1)+4)! for a bit.
Distribute: (3n+3+4)!
Combine like terms (3n+7)!
I know when I have to find the limit of that ratio I'm going to have to rewrite this a little more so I'm going to do that here. Notice the factor (3n+4)! in
. Some of the factors of this factor will cancel with some if the factors of (3n+7)!
(3n+7)! can be rewritten as (3n+7)×(3n+6)×(3n+5)×(3n+4)!
Let's go ahead and put our ratio together.

The second factor in this just means reciprocal of
.
Insert substitutions:

Use the rewrite for (3(n+1)+4)!:

Let's go ahead and cancel the (3n+4)!:

Use 2^(n+1)=2^n × 2 with goal to cancel the 2^n factor on top and bottom:


Use (n+1)!=(n+1)×n! with goal to cancel the n! factor on top and bottom:


Now since n approaches infinity and the degree of top=1 and the degree of bottom is 3 and 1<3, the limit approaches 0.
This means it absolutely converges and therefore converges.
Answer:
6 Km / hour
Step-by-step explanation:
Convert distance to Km ( 1 Km = 1000 m )
150 m = 150 ÷ 1000 = 0.15 Km
Convert 1.5 mins to hours ( 1 hour = 60 minutes )
1.5 = 1.5 ÷ 60 = 0.025 hours
average speed =
=
= 6 Km / hour
Answer:
Step-by-step explanation:
<u>Equation:</u>
- sin 35 = 18/x
- x = 18/sin 35deg
- x = 31.4 (rounded to the nearest tenth)