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Find the volume of this object.

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:

z=20

Step-by-step explanation:

(2z + 16) +124 =180

2z + 16 +124

2z +  140 = 180

2z     -140 -140

2z        =  40

z           =  20

Step-by-step explanation:

the answer is 3 following triangle law

Answer:

Median since the numbers are arranged in an ascending order.

Answer:

x=5cm

Step-by-step explanation:

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

Answer:

102

Step-by-step explanation:

All angles added together=180

180-13-65

180-78

102

Answer:

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

Step-by-step explanation:

Answer:

r= 2.90%

Step-by-step explanation:

delta math

Answer:

-4(3c + 4)(c + 1)

Step-by-step explanation:

Reorder the expression

-12c² - 28c - 16

Divide it by -4

3c² + 7c + 4

Factor it by multiplying a (3) and c (4), then finding 2 factors that add up to b (7)

Two factors of 12 that add up to 7 are 4 and 3.

Use 4c and 3c to substitute for 7c in the expression, and simplify

3c² + 7c + 4

3c² + 3c + 4c + 4

3c(c + 1) + 4(c + 1)

(3c + 4)(c + 1)

Since we factored out a -4 in the beginning, add this in front

-4(3c + 4)(c + 1)

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:

The answer is B

Step-by-step explanation:

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

Answer:

D) x - 7 + 3

Step-by-step explanation:

gave sister = subtract

aunt gave = addition

Equation:

x - 7 + 3

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:

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.

south side of town? I think

Answer: north

Step-by-step explanation:

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:

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:

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:

16 play only basketball

5 play only baseball

19/29 + 5/29 = 24/.29

Step-by-step explanation:

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:

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:

15

Step-by-step explanation:

Answer:

1) 4x^2-x+1

2) -4x^2+3x

3) 6r^3 - 15r

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:

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 answer is 140

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

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