The answer is 29. Hope this helps.
Hi there!
From this problem we can pull out some key information and remove any excess.
- The trail is 1/4 of a mile long.
- Angelo rode around the trail 8 times.
- Angelo claims he rode 8/4 miles.
- Teresa claims he rode 2 miles.
From that we know that if Angelo rode around the trail 8 times and the trail is 1/4 a mile, he in total rode 8/4 of a mile.
However, Teresa claims he rode 2 miles!
And the answer is... they're both correct!
Angelo did indeed ride 8/4 miles however that is equivalent to 2 miles so they are both in the right.
Separate the vectors into their <em>x</em>- and <em>y</em>-components. Let <em>u</em> be the vector on the right and <em>v</em> the vector on the left, so that
<em>u</em> = 4 cos(45°) <em>x</em> + 4 sin(45°) <em>y</em>
<em>v</em> = 2 cos(135°) <em>x</em> + 2 sin(135°) <em>y</em>
where <em>x</em> and <em>y</em> denote the unit vectors in the <em>x</em> and <em>y</em> directions.
Then the sum is
<em>u</em> + <em>v</em> = (4 cos(45°) + 2 cos(135°)) <em>x</em> + (4 sin(45°) + 2 sin(135°)) <em>y</em>
and its magnitude is
||<em>u</em> + <em>v</em>|| = √((4 cos(45°) + 2 cos(135°))² + (4 sin(45°) + 2 sin(135°))²)
… = √(16 cos²(45°) + 16 cos(45°) cos(135°) + 4 cos²(135°) + 16 sin²(45°) + 16 sin(45°) sin(135°) + 4 sin²(135°))
… = √(16 (cos²(45°) + sin²(45°)) + 16 (cos(45°) cos(135°) + sin(45°) sin(135°)) + 4 (cos²(135°) + sin²(135°)))
… = √(16 + 16 cos(135° - 45°) + 4)
… = √(20 + 16 cos(90°))
… = √20 = 2√5
Alright,
So LCM stands for "least common multiple"
While GCF is "greatest common factor"
Let's look at your number 1 (3&6)
3,6,9,12
6,12,18,24
Both times table has 6 in them making 6 the LCM
To find the GCF we need to know what can go into 3 equally. Since 3 is prime the greatest factor for 3 is....3. 6 goes into 3 two times so 3 is the GCF.
LCM:6
GCF:3
Lets do number 10 (40&4)
For LCM you see whats the smallest number that is in both times tables
4,8,12,16,20,24,28.......40
40,80, 160....
40 is the LCM because 40 is what's the smallest number between the two
GCF?
4 times 1 equals 4. Nothing bigger than 4 can make 4 (if your multiplying). That makes 4 automatically the GCF. :)
The <u>circle</u> is best described as all the points that are the same distance from a single point as its center.
distance between the midpoint and the border of circle are called <u>radius of circle.</u>
because a circle is special type of ellipse
