which is the explicit formula for the sequence above?

Given:

The two vectors are:

[tex]\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}[/tex]

[tex]\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}[/tex]

To find:

The value of [tex]|\overrightarrow{a}\times \overrightarrow{b}|[/tex].

Solution:

We have,

[tex]\overrightarrow{a}=2\hat{i}-\hat{j}+\hat{k}[/tex]

[tex]\overrightarrow{b}=\hat{i}-3\hat{j}+5\hat{k}[/tex]

The cross product of these two vectors is:

[tex]\overrightarrow{a}\times \overrightarrow{b}=\begin{vmatrix}\hat{i}&\hat{j}&\hat{k}\\2&-1&1\\1&-3&5\end{vmatrix}[/tex]

[tex]\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[(-1)(5)-(1)(-3)]-\hat{j}[(2)(5)-(1)(1)]+\hat{k}[(2)(-3)-(-1)(1)][/tex]

[tex]\overrightarrow{a}\times \overrightarrow{b}=\hat{i}[-5+3]-\hat{j}[10-1]+\hat{k}[-6+1][/tex]

[tex]\overrightarrow{a}\times \overrightarrow{b}=-2\hat{i}-9\hat{j}-5\hat{k}[/tex]

Now the magnitude of the cross product is:

[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{(-2)^2+(-9)^2+(-5)^2}[/tex]

[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{4+81+25}[/tex]

[tex]|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{110}[/tex]

Therefore, the value of [tex]|\overrightarrow{a}\times \overrightarrow{b}|[/tex] is [tex]\sqrt{110}[/tex].

Answer:

The answer is B

Step-by-step explanation:

Triangle ABC was reflected across the y-axis and then translated 7 units down.

Answer:

The length of diagonal TU is 102 units

Step-by-step explanation:

Mathematically, the diagonals of a parallelogram bisect each other

This means that the lengths on either of the either of the sides are equal

Mathematically, we have it that;

7x + 2 = 6x + 9

7x - 6x = 9-2

x = 7

The diagonal TU has the measure of ;

(7x + 2) + (6x + 9)

7x + 6x + 2 + 9

= 13x + 11

substituting the value of x, we have

13(7) + 11

= 102

Answer:

2/8

Step-by-step explanation:

I think, I am not sure

The volume of the cube is 4,913 cubic millimeters. In order to find out the value of V, we must find the cube root of 4913, which is 17 = V.

V = 17

Answer:

65 degrees

Step-by-step explanation:

I recently answered a question in detail that was similar to this one. Feel free to look at my answered questions for it.

For this one, the easiest way to think about it is this. The line on which both angle 4 and angle 1 sit is a straight line, that makes them supplementary angles which is just a fancy word that means if you add them together they equal 180.

(angle 4) + (angle 1) = 180

And if (angle 1) = 115, then that means

(angle 4) = 180 - 115

(angle 4) = 65

Step-by-step explanation:

the answer is 3 following triangle law

Answer:

No

Step-by-step explanation:

While both legs of the triangle are similar with a ratio of 3:4, the hypotenuses of the triangles have a ratio of 8:11

Answer:

Step-by-step explanation:

that vector is in the 4th quadrent. This means that it will be between 270 and 360 degrees.

setting up directions over the graph (like a compass), the vector would be between East and South  

using the diagram below it would most likly be south of east and 350 degrees

Answer:

I dont understand spanish!

Step-by-step explanation:

Answer:

x2 + 7y = -64 (if x = -5 and y = -8)

Step-by-step explanation:

x2 + 7y

(-5 × 2) + (7 × -8)

-10 + -54 which is the same as -10 - 54

-64

The value of expression x² + 7y at x = - 5 and y = - 8 is, - 31.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

We have to given that;

The expression is,

⇒ x² + 7y

And, x = - 5 and y = - 8

Now, Substitute the value of x and y in the expression, we get;

⇒ x² + 7y

⇒ (-5)² + 7×- 8

⇒ 25 - 56

⇒ - 31

Thus, The value of expression is, - 31.

Learn more about the mathematical expression visit:

brainly.com/question/1859113

#SPJ2

Answer:

x = 25

angle measure = 55

Step-by-step explanation:

The two angles are supplementary

2x+5+5x = 180

7x+5 = 180 subtract 5 from both sides

7x = 175 divide both sides by 7

x = 25 to find the angle with the star replace x with 25

25*2 + 5 = 55

Answer:

15

Step-by-step explanation:

Answer:

a): 68

b): 32

Step-by-step explanation:

In a triangle, there is a total of 180 degrees

We are given 2 out of the 3 angles, 54 and 58 degrees

180-54-58= 68 degrees

In the other angle, both lines form a 90-degree angle

We are given 58 degrees, so the rest must be 32.

Answer:

The arc length is 9.75 pi units

Step-by-step explanation:

Mathematically, we use the formula below to get the length of an arc

Length of an arc is;

theta/360 * 2 * pi * r

where theta is the central angle

for 3pi/4 ; let us convert to degrees

The degree measure is 180 degrees for pi

so 3pi/4 will be (3 * 180)/4 = 135 degrees

So we have the arc length as follows;

135/360 * 2 * pi * 13 = 9.75 pi unit

Answer:

The first one.

Step-by-step explanation:

The symbol that you are comparing the numbers with is equal two or greater than and you have to be 48 inches or taller.

Answer: i think its alternate interior

Answer:

D) x - 7 + 3

Step-by-step explanation:

gave sister = subtract

aunt gave = addition

Equation:

x - 7 + 3

Answer:

D)

A = x(x + 4)

Step-by-step explanation:

Area of a rectangular map = width × length

Length of the rectangular map = (x + 4) miles

Width of the rectangular map = x miles

Area of a rectangular map = width × length

= x(x + 4)

= x² + 4x

D)

A = x(x + 4)

Answer:

the chances of rolling a 3 are 1/6

the changes of not doing it is 5/6

Answer:

The answer is 140

The yellow part which is shaded is 14x10 which equals 140

Answer:

C

Step-by-step explanation:

The question is asking which one is equal to the absolut value of 12. The absolute value of -12 equals 12, so it is the same as the absolute value of 12.

Answer:

Propiedad distributiva de la multiplicación sobre la suma

Step-by-step explanation:

Spanish

Propiedad distributiva de la multiplicación sobre la suma

2 × (4 + 7)

Aquí vemos que el número 2 se multiplica por 4 y 7

2 se distribuye a 4 y 7

= 2 × 4 + 2 × 7

Después de la multiplicación se suman ambos

= 8 + 14 = 22

Esta propiedad se llama propiedad distributiva de la multiplicación sobre la suma.

English

No development of multiplication 2 × (4 + 7) = 2 × 4 + 2 × 7 = 8 + 14 = 22, which property was used?

Distributive property of multiplication over addition

2 × (4 + 7)

Here we see that the number 2 is multiplied with both 4 and 7

2  is distributed  to both 4 and 7

= 2 × 4 + 2 × 7

After multiplication both are added

= 8 + 14 = 22

This property is called distributive  property of multiplication over addition.

Given:

The expression are:

[tex]3x^2+7x-6[/tex]

[tex]2x^2+7x+3[/tex]

To find:

The HCF of the given expression.

Solution:

We have,

[tex]3x^2+7x-6[/tex]

[tex]2x^2+7x+3[/tex]

The factor form of given expressions are:

[tex]3x^2+7x-6=3x^2+9x-2x-6[/tex]

[tex]3x^2+7x-6=3x(x+3)-2(x+3)[/tex]

[tex]3x^2+7x-6=(x+3)(3x-2)[/tex]

Similarly,

[tex]2x^2+7x+3=2x^2+6x+x+3[/tex]

[tex]2x^2+7x+3=2x(x+3)+1(x+3)[/tex]

[tex]2x^2+7x+3=(x+3)(2x+1)[/tex]

From the factor forms it is clear that the factor [tex](x+3)[/tex] is common.

Therefore, the HCF of given expressions is [tex](x+3)[/tex].

9514 1404 393

Answer:

  g(f(x)) = 6x^2 -2

Step-by-step explanation:

Evaluate the expression using the given argument value.

  g(f(x)) = g(2x^2 +1) = 3(2x^2 +1) -5

  = 6x^2 +3 -5 = 6x^2 -2

__

  g(f(x)) = 6x^2 -2

Answer:

D

Step-by-step explanation:

You multiply each coordinate by 1/4 to get the new coordinates of the triangle

I hope this helps you

Answer:

1) 4x^2-x+1

2) -4x^2+3x

3) 6r^3 - 15r

Step-by-step explanation: