Answer:
Step-by-step explanation:
Given the following vectors a = (-3,4) and b = (9, -1)
|a| and |b| are the modulus of a and b respectively.
|a| = √(-3)²+4²
|a| = √9+16
|a| = √25
|a| = 5
Similarly;
|b| = √(9)²+1²
|b| = √81+1
|b| = √82
We are to find the following;
a) a + b
a+b = (-3,4) + (9, -1)
a+b = (-3+9, 4+(-1))
a+b = (6, 4-1)
a+b = (6,3)
b) 8a + 9b
8a + 9b = 8(-3,4) + 9(9, -1)
8a + 9b = (-24,32) + (81, -9)
8a + 9b = (-24+81, 32+(-9))
8a + 9b = (57, 32-9)
8a + 9b = (57, 23)
c) |a| = √(-3)²+4²
|a| = √9+16
|a| = √25
|a| = 5
d) |a − b|
To get |a − b|, we need to get a-b first
Solve for a -b
a-b = (-3,4) - (9, -1)
a-b = (-3-9, 4-(-1))
a-b = (-12, 4+1)
a-b = (-12,5)
Find modulus of a-b i.e |a − b|,
|a − b| = √(-12)²+5²
|a − b| = √144+25
|a − b| =√169
|a − b| = 13
Answer:
11 Squares are there in 11 squares
Answer:
10 1/3
Step-by-step explanation:
Convert mixed numbers into improper fractions (whole number × denominator + numerator)
25 2/3 and 15 1/3
25 × 3 + 2 = 75 + 2 = 77
Put the number over the same denominator
77/3
15 × 3 + 1 = 45 + 1 = 46
Put the number over the same denominator
46/3
77/3 - 46/3
They have common denominators so we can simply subtract the numerator values
77 - 46/3
31/3
To convert it back to a whole number, find how many times 3 fits into 31 evenly
It fits 10 times evenly with 1 remainding which looks like:
10 1/3
Hmmmm judging by the values in between integers, like 2.5, 1.5, -2.5, -3.5 and so on, those values always produce a smaller number hmm that sounds whack... lemme put it differently.
a floor() function, namely ⌊x⌋ like that, will floor the decimal values, so ⌊2.5⌋ floors to 2, because 2.5 is between 2 and 3, and the smallest is 2, the "floor", the 3 will be the "ceiling".
so for a floor function, ⌊1.5⌋ is 1, 1.5 is between 1 and 2, 1 is the smallest, ⌊-3.5⌋ is -4, recall that on the negative side, the closer to 0, the larger, so -1 is much larger than -1000.
and say ⌊-1.35⌋ is -2, -1.35 is between -2 an -1 and -2 is the smallest, the "floor".
that said
x = 2.5 ⌊ 2.5 + 3⌋ is ⌊5.5⌋ which is 5
x = 1.5 ⌊ 1.5 + 3 ⌋ is ⌊4.5⌋ which is 4
x = -2.749 ⌊ -2.749 + 3⌋ is ⌊0.251⌋ which is 0
anyway and so on, so you can pretty much see is the floor function of ⌊ x + 3⌋.
