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2 years ago

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Find the value of n for which the vectors a⃗ =(3,2)a→=(3,2) and b⃗ =(9,n)b→=(9,n) are collinear.

1 answer:

Makovka662 [10]2 years ago

8 0

Answer:

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

Step-by-step explanation:

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.

You might be interested in

Find the indicated sum of each sequence S8 of -2,-13,-24,-35

valentina_108 [34]

Answer:

The sum of the arithmetic sequence is $S_{8}=-324$ .

Step-by-step explanation:

A sequence is a set of numbers that are in order.

In an arithmetic sequence the difference between one term and the next is a constant. In other words, we just add the same value each time infinitely.

If the first term of an arithmetic sequence is $a_1$ and the common difference is d, then the nth term of the sequence is given by:

$a_{n}=a_{1}+(n-1)d$

For the sequence

$-2,-13,-24,-35,...$

The pattern is continued by adding -11 to the last number each time.

An arithmetic series is the sum of an arithmetic sequence. We find the sum by adding the first, $a_1$ and last term, $a_n$ , divide by 2 in order to get the mean of the two values and then multiply by the number of values, <em>n</em>

<em> </em> $S_{n}=\frac{n}{2}(a_{1}+a_{n})$ <em />

The sum of the arithmetic sequence is

$a_{8}=-2+(8-1)(-11)=-2-77=-79$

$S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324$

3 0

3 years ago

I NEED HELP PLEASEEE! <br> thank you :)

Artemon [7]

Answer:

70°

Step-by-step explanation:

The tangent- chord angle is one half the measure of the intercepted arc.

intercepted arc = 360° - 220° = 140°, thus

inscribed angle = 0.5 × 140° = 70°

5 0

3 years ago

Read 2 more answers

Pls help:Find all the missing elements:

Yuliya22 [10]

Answer:

<h3>B = 48.7° , C = 61.3° , b = 12</h3>

Step-by-step explanation:

In order to find B we must first angle C

To find angle C we use the sine rule

That's

$\frac{ |a| }{ \sin(A) } = \frac{ |c| }{ \sin(C) }$

From the question

a = 15

A = 70°

c = 14

So we have

$\frac{15}{ \sin(70) } = \frac{14}{ \sin(C) }$

$\sin(C) = \frac{14 \sin(7 0 ) }{15}$

$C = \sin^{ - 1} ( \frac{14 \sin(70) }{15} )$

C = 61.288

<h3>C = 61.3° to the nearest tenth</h3>

Since we've found C we can use it to find B.

Angles in a triangle add up to 180°

To find B add A and C and subtract it from 180°

That's

A + B + C = 180

B = 180 - A - C

B = 180 - 70 - 61.3

<h3>B = 48.7° to the nearest tenth</h3>

To find b we can use the sine rule

That's

$\frac{ |a| }{ \sin(A) } = \frac{ |a| }{ \sin(B) }$

$\frac{15}{ \sin(70) } = \frac{ |b| }{ \sin(48.7) }$

$|b| = \frac{15 \sin(48.7) }{ \sin(70) }$

b = 11.9921

<h3>b = 12.0 to the nearest tenth</h3>

Hope this helps you

6 0

3 years ago

Sixty percent (60%) of those who attended the soccer game were parents. There were 120 people who

IrinaVladis [17]

Answer:

72

Step-by-step explanation:

<u>Given:</u>

There were 120 people in total.

60% were parents.

<u>To find:</u>

Number of parents attended.

Solution:

1. 60% of 120

It can also be written as:

$\frac{60}{100}\times \frac{120}{1}$

Simplify

Cancel zeros

$\frac{60}{100}\\\\=\frac{6}{10}$

Divide by common factor (2)

$\frac{6\div2}{10\div2}=\frac{3}{5}$

2. $\bold{\frac{3}{5}\times \frac{120}{1}}$

Multiply

$\frac{3\times120}{5\times1} = \frac{360}{5}$

Divide

$\frac{360}{5}= 360\div5=72$

Therefore, 72 parents attended the game.

4 0

2 years ago

Karla is ordering a pizza. The cost of the pizza is $8.99, plus she must pay $1.50 for each additional topping. Write an equatio

icang [17]

Answer:

8.99+1.50t

Step-by-step explanation:

hope this helps

3 0

3 years ago

Read 2 more answers