Determine the volume of the parallelepiped with one vertex at the origin and the three vertices adjacent to it at (2, â1, â1), (2, 4, â2), and (2, â6, 1).

Answers

Answer 1

Answer:

23

Step-by-step explanation:

Here is the complete question

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1, 0, -3), (1, 2, 4), and (5, 1, 0).

Solution

We find the volume of the parallelepiped by making a 3 × 3 column matrix whose columns are the corresponding coordinates of the vertices of the parallelepiped.

So, (1, 0, -3), (1, 2, 4)  and (5, 1, 0)

[tex]A = \left[\begin{array}{ccc}1&1&5\\0&2&1\\-3&4&0\end{array}\right][/tex]

The determinant of A is the volume of the parallelepiped. So,

detA = 1(2 × 0 - 4 × 1) - 1(0 × 0 - (-3) × 1) + 5(0 × 4 - (-3) × 2)

= 1(0 - 4) - 1(0 + 3) + 5(0 + 6)

= 1(-4) - 1(3) + 5(6)

= -4 - 3 + 30

= 23

So the volume of the parallelepiped is 23


Related Questions

Find the coefficient of x^2 y^3 in the expansion of (-4x+y)^5. Give your answer as an integer.

Answers

Coefficients are the numbers in front of the variables therefore The coefficient of x^2 y^3 would be (-4)x and 1(y). Anytime there isn’t a coefficient shown in front of a variable the coefficient will always be 1. I hope this helped :)

what is the product in simplest form? -8/9 times 5/6 All the ANSWERS:
-1
-13/15
-20/27
-1/5

Answers

C -20/27 because 5x-8= -40 and 9x6= 54 and u divide both numbers by two and get C

Write the quadratic function in vertex form, then identify the vertex

h(x)=x^2+20x+90

h(x)=

Vertex:

I need this answered ASAP please !

Answers

Answer:

vertex = (- 10, - 10 )

Step-by-step explanation:

The equation of a quadratic in vertex form is

y = a(x - h)² + k

where (h, k ) are the coordinates of the vertex and a is a multiplier

To obtain this form use the method of completing the square.

Given

h(x) = x² + 20x + 90

add/subtract ( half the coefficient of the x- term )²

h(x) = x² + 2(10)x + 100 - 100 + 90

      = (x + 10)² - 10 ← in vertex form

with (h, k ) = (- 10, - 10 )

What of the following lines is perpendicular to the line passing across the points (1,1) and (-5,-6)?

y = 6/7x + 1

y = -6/7x + 1

y = -6/7x - 1

y = 6/7x - 1

Answers

First find slope
(-6-1)/(-5-1) = -7/-6 = 7/6
Perpendicular = opposite sign and reciprocal slope
Slope would be -6/7
It would be anything with slope of -6/7

2х + y = 4
у = 3х – 1

Answers

its 2 because 2plus is 2

In metrics, the meter is the standard unit of: mass distance volume length

Answers

Answer: Length because A unit of length refers to any arbitrarily chosen and accepted reference standard for measurement of length.

Find the slope of the line containing the two given points.

(9,-5) and (6,8)

Answers

Answer:

13/-3

Step-by-step explanation:

Answer:

-13/3

Step-by-step explanation:

The slope is rise over run.

From the first point to the other, the line goes 13 units up and -3 units to the right.

Putting it in the form of rise over run we have:

13/-3 which is the same as -13/3

What is the volume of a cylinder, in cubic feet, with a height of 5 feet and a base
diameter of 10 feet? Round to the nearest tenths place

Answers

Answer: 392.7

Step-by-step explanation:

PLEASE SHOW FULL SOLUTIONS!! Will Mark Brainliest for the best answer. The radius of a spherical balloon is 3.5 cm. What is the volume of air in the balloon? Show your answer in terms of pi or round your answer to one decimal place.

THANKS

Answers

9514 1404 393

Answer:

  343π/6 cm³ ≈ 179.6 cm³

Step-by-step explanation:

The formula for the volume of a sphere is one of the volume formulas worth memorizing. It is ...

  V = (4/3)πr³

For r = 3.5 cm, the volume is ...

  V = (4/3)π(3.5 cm)³ = 343π/6 cm³ ≈ 179.6 cm³

The volume of air in the balloon is about 179.6 cm³.

Express 76.5% as a decimal and a fraction

Answers

as a decimal it’s 0.765 and as a fraction is 76.5/100

HELP PLEASE.............

Answers

I'm pretty sure it is the fourth answer.

PLEASE HELP ME QUICK
A serving dish has a parabolic surface with the vertex (0, 0) at the center of the dish. When the width of the dish is 6 inches, the depth of the dish is 3 inches. The equation that models the shape of the serving dish is y = ax2. What is the value of a?

1/12
1/3
1/2
1

Answers

Answer:

B

Step-by-step explanation:

1/3

The required value of a is 1/3 for parabola [tex]y = 1/3x^2[/tex].

A parabolic dish with vertex (0,0) at the center, width is 6 inches and depth is 3 inches. y = ax² where a is to be determined.


What is a parabola?

A parabola is a cross-section cut out of the cone and represented by an equation [tex]y=4ax^2[/tex].

Here,  
Vertex is at the center of the parabolic plate (0,0),
with the help of the width and depth coordinate of the one corner is(3,3).
Now put these coordinates in y = ax²  
3 = a3²
a = 3/3²
a = 1/3

Thus, The required value of a is 1/3 for the parabola [tex]y = 1/3x^2[/tex].

Learn more about parabola here:

brainly.com/question/4074088

#SPJ5



Given f(x) = 5(2-x), what is the value of f(-3) ?

Answers

Answer:

f(-3) = 25

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Function Notation

Step-by-step explanation:

Step 1: Define

f(x) = 5(2 - x)

f(-3) is x = -3

Step 2: Evaluate

Substitute:                    f(-3) = 5(2 - -3)Simplify:                        f(-3) = 5(2 + 3)Add:                              f(-3) = 5(5)Multiply:                        f(-3) = 25

What is the quotient of 1/10 and 9/10

Answers

Answer:

1/9 = 0.1111111

Step-by-step explanation:

Select the correct answer

Answers

Answer:

Option B

Step-by-step explanation:

Domain of a function is represented by the set input values or x-values

Range of the function is represented by the set of output values or y-values.

From the graph attached,

y-values are varying from y = - 9 to y = 8.

Therefore, range of the function from the given graph will be,

-9 ≤ y ≤ 8

Option B will be the correct option.

a rental car company charges drivers a flat fee to rent a car plus $0.25 for each mile they drive. If a drivers pays $100 drives 160 miles , which equation can he use to find his total cost y in terms of the number of miles driven ?

Answers

ANSWER

y = 100 + 0.25(160) - equation

y = 140 - if you needed the answer

Please give me the correct answer ​

Answers

Your answer would be: 3 x 10^-5

Hope this helps and happy holidays!!

Zelda rode her bike at a steady rate of 12 miles per hour for 3

Answers

Answer:

36miles

Step-by-step explanation:

Given parameters:

Rate  = 12mph

Time  = 3hr

Unknown:

Distance = ?

Solution:

The given rate amount is the speed. Speed is the distance divided by the time.

It is mathematically expressed as:

         Speed  = [tex]\frac{distance}{time}[/tex]  

    Distance  = Speed x time

    Distance  = 12 x 3  = 36miles

Please give me the correct answer ​

Answers

Answer:

the first one; 3*1/10^-4

Step-by-step explanation:

10^-4 can be ocnverted into a fraction: 1/10^4

Answer:

3 times 1/10,000

Step-by-step explanation:

Does this scatter plot show a positive trend, a negative trend, or no trend?​

Answers

it shows a negative trend

Answer:

no trend

a positive trend would start in the bottom left and go toward the top right

a negative trend would start at the top left and go town the bottom right

this is an example of no trend

Step-by-step explanation:

a "trend" shows an increasing or decreasing relationship between the x and y values, in this they don't have any sort of relationship. you can tell by the repeating y values for multiple different x-values, or the repeating x-values for multiple different y-values.

Edmund made a scale drawing of the rectangular floor of his kitchen. In the scale
drawing, 1 inch represents 2.5 feet. The measurements of the scale drawing are
shown in the diagram.
6.4 in.
4.8 in.
what is the perimeter of the actual kitchen floor in feet?

Answers

2.5*6.4=16, 2.5*4.8=12. 12+12+16+16=56

Answer:

324

Step-by-step explanation:

Evaluate the surface integral.
S(x + y + z) dS, S is the parallelogram with parametric equations
x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.

Answers

Answer:

[tex]\frac{115\sqrt{14} }{2}[/tex]

Step-by-step explanation:

∫∫ ( x + y + z ) ds

where :

x = u + v ,  y = u - v ,  z = 1 + 2u + v ,  

0 ≤ u ≤ 5,  

0 ≤ v ≤ 1

R ( u,v ) = < u+v , u-v , 1 + 2u +v >   next we have to differentiate

attached below is a detailed solution

The surface integral S(x + y + z) dS, where S is the parallelogram is [tex]115\sqrt{14} /2[/tex] and this can be determined by integrating the given expression.

Given :

The surface integra S(x + y + z) dS, S is the parallelogram with parametric equations  x = u + v, y = u − v, z = 1 + 2u + v, 0 ≤ u ≤ 7, 0 ≤ v ≤ 3.

The following calculation can be used in order to determine the surface integral.

[tex]\rm R_u\times R_v = <3,1,-2>[/tex]

[tex]\rm ||R_u\times R_v|| = \sqrt{14}[/tex]

Now, evaluate the surface integral.

[tex]\rm I = \rm \int\int_s(x+y+z)dr[/tex]

[tex]\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)||R_u\times R_v||dA[/tex]

[tex]\rm I = \int^5_{u=0}\int^1_{v=0}(u+v+u-v+1+2u+v)\sqrt{14} \;du\;dv[/tex]

[tex]\rm I = \sqrt{14} \int^5_0(v+4uv+\dfrac{v^2}{2})^1_0\;du[/tex]

[tex]\rm I = \sqrt{14} (\frac{3}{2}u+4\frac{u^2}{2})^5_0[/tex]

Simplify the above expression.

[tex]\rm I = \dfrac{115\sqrt{14} }{2}[/tex]

The surface integral S(x + y + z) dS, where S is the parallelogram is [tex]115\sqrt{14} /2[/tex]

For more information, refer to the link given below:

https://brainly.com/question/22008756

K mola ofkg o okdgmbo9k

Answers

Answer: c

Step-by-step explanation:

C because the hour each have 25 more added to it

What is the slope of the line graphed below

Find the equation of the line above. Write the equation in slope intercept form.

Answers

Slope is 1/3

Equation of the line is:

y = 1/3x - 8

Question is in the image​

Answers

Answer:

4.

Step-by-step explanation:

y = -2x + 3

-1 = -2(2) + 3

-1 = -4 + 3

-1 = -1

y = x - 3

-1 = 2 - 3

-1 = -1

jerry's softball team is made up of 15 players,and 9 of them are boys.On the team,what is ratios to boys to girls?

Answers

Answer:

9:6

Step-by-step explanation:

boys= 9 teammates

girls= 6 teammates

Ava plays on the softball team at her school. The team won 8 of its first 12 games. At that rate, how many games will Ava's team win if it plays 60 games in all?

Answers

Answer:

She wins 40 games

Step-by-step explanation:

I'm not the best at explaining but 5x12=60 so then we multiply 8 by 5 aswell and bam we have 40.

Identify the following parasite provided and draw a large labelled diagram of each
specimen​

Answers

Answer:

Spiced eye gonna flush my toilet now ;)

Answer:

hes right

Step-by-step explanation:

The sum of x and y equals 26.

If x= 17, which equation can be used to find the value of the y?

Answers

26-17=9
which means y=9

WILL MARK BRAINLIEST
please help geometry problem in the picture

Answers

(x-6, y+8)

Count how many units horizontally and vertically from one green corner and see how many units it takes to get the blue corner.

You minus 6 from x because it is going in the left direction. You add 8 to the y because it is moving upwards which is a positive direction
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