Collinear vectors are the vectors which lie on the same line or parallel lines. In order to find if two vectors are collinear, their ratio is found. If the ratio is same for all unit vectors then the vectors are collinear.

Given

$a = (a_1, a_2) = (3,2)\\b = (b_1, b_2) = (9,n)$

The ratio of first unit vectors is:

$\frac{a_1}{b_1} = \frac{3}{9} = \frac{1}{3}$

In order for the vectors to be collinear the other ratio should also be 1/3

$\frac{a_2}{b_2} = \frac{1}{3}$

Writing it mathematically

$\frac{2}{n} = \frac{1}{3}\\2*3 = n\\n = 6$

Hence,

For n=6, the given vectors will be collinear.

8 0

3 years ago

Can someone please help me solve 4 & 5? I'll love you forever

marusya05 [52]

Based on my little knowledge of statistics
4.
It's 8!/4!= 1680
(the exclamation point is basically the number of probabilities in the combination)
5.
(speculation) It's 10!-6!= 3,628,080
plus
8!-6!=39,600
equals
(3,628,080 + 39,600) / 6! = 5094
(the 6! is the amount of drink combinations you are limited to)
FYI- you can use the exclamation mark on your phone calculator, either swipe to side or press the ''extras'' button

4 0

3 years ago

Read 2 more answers

The speed limit is 55 minutes per hr. write an inequalit to represent the speed limit.

anygoal [31]

Answer: Either $x \le 55$ or $0 \le x \le 55$ depending on your teacher's preference. See the note at the bottom for more info.

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Let x be the speed limit. It is simply a placeholder. Think of it as a box with the number inside. We don't know what the number is, but we know that the largest it can be is 55. It cannot be larger than 55.

So x can be equal to 55 or it can be smaller

Put another way, x is less than or equal to 55 which is written as $x \le 55$ (on the keyboard you would type " x <= 55 " without quotes).

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Note: since negative speeds make no sense, we also must imply that x can't be negative. Your teacher may want you to write this in to clearly state it. If so, then you would also have $x \ge 0$ which when combined with the first inequality, you get this compound inequality $0 \le x \le 55$ (basically saying "x is some speed between 0 and 55 mph"). This very clearly states the boundaries on what x can be. Though your teacher may want you to stick to the first format as its simpler.

5 0

3 years ago

(PLEASE HELP) I need help on the left overs​

(PLEASE HELP) I need help on the left overs