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3 years ago

1. Find the number of different

Mathematics

1 answer:

irakobra [83]3 years ago

8 0

Answer:

1. 40320 numbers of different arrangements of the letters of the word ogbogoro.

2. 24 is the permutation.

Step-by-step explanation:

Permutation Formula:

n!/(n-r)!

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Find two vectors in R2 with Euclidian Norm 1<br> whoseEuclidian inner product with (3,1) is zero.

alina1380 [7]

Answer:

$v_1=(\frac{1}{10},-\frac{3}{10})$

$v_2=(-\frac{1}{10},\frac{3}{10})$

Step-by-step explanation:

First we define two generic vectors in our $\mathbb{R}^2$ space:

$v_1 = (x_1,y_1)$
$v_2 = (x_2,y_2)$

By definition we know that Euclidean norm on an 2-dimensional Euclidean space $\mathbb{R}^2$ is:

$\left \| v \right \|= \sqrt{x^2+y^2}$

Also we know that the inner product in $\mathbb{R}^2$ space is defined as:

$v_1 \bullet v_2 = (x_1,y_1) \bullet(x_2,y_2)= x_1x_2+y_1y_2$

So as first condition we have that both two vectors have Euclidian Norm 1, that is:

$\left \| v_1 \right \|= \sqrt{x^2+y^2}=1$

and

$\left \| v_2 \right \|= \sqrt{x^2+y^2}=1$

As second condition we have that:

$v_1 \bullet (3,1) = (x_1,y_1) \bullet(3,1)= 3x_1+y_1=0$

$v_2 \bullet (3,1) = (x_2,y_2) \bullet(3,1)= 3x_2+y_2=0$

Which is the same:

$y_1=-3x_1\\y_2=-3x_2$

Replacing the second condition on the first condition we have:

$\sqrt{x_1^2+y_1^2}=1 \\\left | x_1^2+y_1^2 \right |=1 \\\left | x_1^2+(-3x_1)^2 \right |=1 \\\left | x_1^2+9x_1^2 \right |=1 \\\left | 10x_1^2 \right |=1 \\x_1^2= \frac{1}{10}$

Since $x_1^2= \frac{1}{10}$ we have two posible solutions, $x_1=\frac{1}{10}$ or $x_1=-\frac{1}{10}$ . If we choose $x_1=\frac{1}{10}$ , we can choose next the other solution for $x_2$ .

Remembering,

$y_1=-3x_1\\y_2=-3x_2$

The two vectors we are looking for are:

$v_1=(\frac{1}{10},-\frac{3}{10})\\v_2=(-\frac{1}{10},\frac{3}{10})$

5 0

3 years ago

Adult tickets to a basketball game cost $5. Student tickets cost $1. A total of $2,546 was collected on the sale of 1,082 ticket

vova2212 [387]

Answer:

adult tickets sold: 407

student tickets sold: 839

Step-by-step explanation:

5 0

3 years ago

The corner market sold 24 prints on monday and 18 prints on tuesday how many prints did the market sell on those two days

NISA [10]

Answer:Number of prints sold on these two days =42 Prints

Step-by-step explanation:

Number of prints sold on Monday = 24

Number of prints sold on Tuesday= 18

Number of prints sold on these two days =Number of prints sold on Monday +Number of prints sold on Tuesday= 24+ 18 = 42 Prints

5 0

3 years ago

1+1

Stells [14]

The answer would be more likely 2

3 0

4 years ago

Read 2 more answers

Simplify x^2+2x+1 divided by x+1

baherus [9]

The quotient is x+1.

<h3>What Long division method?</h3>

Long division is a method for dividing one large multi digit number into another large multi digit number.

Given:

f(x)= x²+2x+1

g(x)= x+1

The steps to divide the polynomial is :

Divide the leading term of the dividend by the leading term of the divisor: x²/x=x.
Multiply it by the divisor: x(x+1)=x²+x.
Subtract the dividend from the obtained result: (x²+2x+1)−(x²+x)=x+1.
Divide the leading term of the obtained remainder by the leading term of the divisor: x/x=1.
Multiply it by the divisor: 1(x+1)=x+1.
Subtract the remainder from the obtained result: (x+1)−(x+1)

Learn more about long division method here:

brainly.com/question/10532559

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3 0

2 years ago