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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:

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

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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:

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:

D) x - 7 + 3

Step-by-step explanation:

gave sister = subtract

aunt gave = addition

Equation:

x - 7 + 3

Answer:

15

Step-by-step explanation:

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:

I dont understand spanish!

Step-by-step explanation:

Answer: i think its alternate interior

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:

x=5cm

Step-by-step explanation:

[tex]\sqrt{4^{2}+3^{2} } =5[/tex]

Answer:

The answer is 140

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

Step-by-step explanation:

the answer is 3 following triangle law

Answer:

r= 2.90%

Step-by-step explanation:

delta math

Answer:

1) 4x^2-x+1

2) -4x^2+3x

3) 6r^3 - 15r

Step-by-step explanation:

south side of town? I think

Answer: north

Step-by-step explanation:

Line graphs allow us to see overall trends such as an increase or decrease in data over time. Bar graphs are used to compare facts. The bars provide a visual display for comparing quantities in different categories or groups. ... Circle Graphs are used to compare the parts of a whole.

Answer:

1. B.

2. A, E.

3. D.

Step-by-step explanation:

1. 8.225 ÷ 5 = 1.645

2. 892 ÷ 8 = 111.5

8920 ÷ 80 = 111.5

894 ÷ 10 = 89.4

89.2 ÷ 0.08 = 1115

8.92 ÷ 0.8 = 11.15

0.892 ÷ 0.008 = 111.5

3. 4367 ÷ 0.004 = 1,091,750

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 chances of rolling a 3 are 1/6

the changes of not doing it is 5/6

Answer:

In 5 hours he would have 7.5 inches of snow JUST from the snowstorm but the question says that he already had 5 inches in his lawn so that would make 12.5 inches of snow in 5 hours.

The second one says t, it doesn't state a number so lets assume the number is ten. So that's 5 more hours of constant snowfall, this makes our total be the sum of 12.5+7.5. This is equal to 20.

10 hours into the snowstorm Nathaniel had 20 inches of snow in his lawn.

Consider a brainliest if it helps :)

Answer:

Snow after 5 hours = 12.5

Show after t hours= 1.5t+5

Step-by-step explanation:

Answer:

The answer is B

Step-by-step explanation:

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

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:

z=20

Step-by-step explanation:

(2z + 16) +124 =180

2z + 16 +124

2z +  140 = 180

2z     -140 -140

2z        =  40

z           =  20

Answer:

11/8 and if you need percentage its about 61%

Step-by-step explanation:

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:

102

Step-by-step explanation:

All angles added together=180

180-13-65

180-78

102

Answer:

x=−2

y=−4

Step-by-step explanation:

−2x+2y=−4

3x+3y=−18

In order to solve by elimination, coefficients of one of the variables must be the same in both equations so that the variable will cancel out when one equation is subtracted from the other.

−2x+2y=−4,3x+3y=−18

To make −2x and 3x equal, multiply all terms on each side of the first equation by 3 and all terms on each side of the second by −2.

3(−2)x+3×2y=3(−4),−2×3x−2×3y=−2(−18)

Simplify.

−6x+6y=−12,−6x−6y=36

Subtract −6x−6y=36 from −6x+6y=−12 by subtracting like terms on each side of the equal sign.

−6x+6x+6y+6y=−12−36

Add −6x to 6x. Terms −6x and 6x cancel out, leaving an equation with only one variable that can be solved.

6y+6y=−12−36

Add 6y to 6y.

12y=−12−36

Add −12 to −36.

12y=−48

Divide both sides by 12.

y=−4

Substitute −4 for y in 3x+3y=−18. Because the resulting equation contains only one variable, you can solve for x directly.

3x+3(−4)=−18

Multiply 3 times −4.

3x−12=−18

Add 12 to both sides of the equation.

3x=−6

Divide both sides by 3.

x=−2

The system is now solved.

x=−2,y=−4