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

Answers

Answer 1
Answer:

17 cubic units.

Step-by-step explanation:

The volume (V) of a parallelepiped with one vertex at the origin is given by the absolute value of the scalar vector product of the vectors at the adjacent vertices.

V = |(a x b) · c|

In this case,

a = (1,4,0) = i + 4k + 0j

b = (-2,-5,2) = -2i -5j + 2k

c = (-2,2,1) = -2i + 2j + k

First, let's calculate the cross product of vectors a and b. i.e a x b as follows:

(i) Arrange the vectors in a matrix form

a x b = | i        j         k |

          | 1       4        0 |

          | -2    -5        2 |

(ii) Calculate the determinant of the matrix

a x b = i(8 - 0) -j(2-0) + k(-5+8)

a x b = i(8) -j(2) + k(3)

a x b = 8i - 2j + 3k

Secondly, calculate the scalar product of the cross product found above and the vector c as follows;

(a x b) . c = (8i - 2j + 3k) · (-2i + 2j + k)

Multiply like terms

(a x b) . c = (8 * -2)(i.i) + (-2 * 2)(j.j) + (3 * 1)(k.k)             [i.i = j.j = k.k = 1]

(a x b) . c = (-16) + (-4) + (3)

(a x b) . c = -16 - 4 + 3

(a x b) . c = -17

Thirdly, find the absolute value of the result found above. i.e

|(a x b) . c| = |-17|

|(a x b) . c| = 17

Therefore, the volume of the parallelepiped is 17 cubic units.


Related Questions

if someone can explain this it would really help.​

Answers

Answer:

6

Step-by-step explanation:

KL = 26-(11+9) = 26-20 =6

Answer:

KL is 6

Step-by-step explanation:

IL is 26, IJ = 9 JK= 11

IL= IJ + JK + KL

26= 9 + 11 + KL

Rearrange

KL= 9 + 11 - 26

    = 6

resuelve la siguiente ecuación
x2+40=100

Answers

pregunta:x2+40=100

resultado:x=30

Step-by-step explanation:

the anwer is x=30......

Type the correct answer in each box. Use numerals instead of words.
Consider function h.

Answers

Answer:

33

Step-by-step explanation:

Value-Mart had 2,371 customers last week. Each customer donated $2 to the food bank. How much money did Value-Mart raise for the food bank? *

Answers

9514 1404 393

Answer:

  $4,742

Step-by-step explanation:

The total of donations is the product of the number of donations and the amount of each.

  (2371 customers) × ($2/customer) = $(2371×2) = $4742

Value-mart raised $4,742 for the food bank last week.

_____

You could find the total donated by adding the 2371 donations. Multiplication was invented to make repeated addition easier. When the sum consists of 2371 instances of $2, we can find the total by multiplying $2 × 2371.

Find the surface area of the
prism.

Answers

Answer:

D. 464 ft²

Step-by-step explanation:

Area of trapezoidal prism = h(b + d) + l(a + b + c + d)

Where,

h = 4 ft

a = 5 ft

b = 6 ft

c = 5 ft

d = 12 ft

l = 14 ft

Plug in the values into the formula

Area of trapezoidal prism = 4(6 + 12) + 14(5 + 6 + 5 + 12)

= 4(18) + 14(28)

= 72 + 392

= 464 ft²

SIX is a right triangle with the measure of X = 60° and the measure of I = 90° IF IX = 5. find the length of SX​

Answers

Answer:

10

Step-by-step explanation:

Given the following

<X = 60°

I = 90°

IX = 5(Adjacent)

Required

SX (HYPOTENUSE

According to SOH CAH TOA

Cos theta = adj/hyp

Cos 60 = 5/SX

SX = 5/cos 60

SX = 5/(1/2).

SX =5×2

SX = 10

A roundabout is a one-way circular intersection.
About how many feet would a car travel if it drove
once around the roundabout? Round to the
nearest foot.

Answers

Answer:

[tex]471\:\mathrm{ft}[/tex]

Step-by-step explanation:

In one full rotation around the roundabout, the car is travelling a distance equal to the circumference, or the perimeter, of the circle. The circumference of a circle with radius [tex]r[/tex] is given by [tex]C=2r\pi[/tex]. In the diagram, the diameter is labelled 150 feet. By definition, the radius of a circle is exactly half of the diameter of the circle. Therefore, the radius must be [tex]\frac{150}{2}=75[/tex] feet. Thus, the car would travel [tex]2\cdot 75\cdot \pi=471.238898038=\boxed{471\:\mathrm{ft}}[/tex]

a walking path across a park is repersented by the equation y=-2x-7. A new path will be built perpendicular to this path the paths will intercept at the point (-2,-3) identify the equation that represents the new path

Answers

Answer:

y + 3 = (1/2)(x + 2)

Step-by-step explanation:

The slope of the original path is -2.  Any new path perpendicular to this one will have a slope which is the negative reciprocal of -2, which here is 1/2.

Use the point-slope formula y - k = m(x - h):

y - (-3) = (1/2)(x - (-2)), or

y + 3 = (1/2)(x + 2)  represents the new path.

Please help!!☺️☺️
Will mark brainilest!!

Answers

Answer:

C

Step-by-step explanation:

The graph of the absolute value function y = | x | has its vertex at the origin and has the shape V

The graph here is the absolute value translated vertically 3 units down, so

y = | x | - 3 → C

Hi there!  

»»————- ★ ————-««

I believe your answer is:  

[tex]c) |x| - 3[/tex]

»»————- ★ ————-««  

Here’s why:  

The graph given is an absolute value function. This eliminates options A and B, since they are not absolute value functions.  The graph shows the parent function of f(x) = |x| that is shifted 3 units down. This can be written as f(x) = |x| - 3.

⸻⸻⸻⸻

Option C should be the correct answer.  

»»————- ★ ————-««  

Hope this helps you. I apologize if it’s incorrect.  

PLZ Help
what is the surface area of this cylinder

Answers

Answer:

188.5)

Step-by-step explanation:

2 x 3.14 x 4 x 3.5 + 2 x 3.14 x 4 x 2

=2πrh+2πr2

Note:

Pls notify me if my answer is correct for the other users that will see this response.

-kiniwih426

PLEASE HELP !! Whoever gets it right gets brainliest

Answers

Answer:

21

Step-by-step explanation:

4x-2=3x+19

4x-3x=19+2

x=21

Answer:

x = 21

Step-by-step explanation:

These are opposite angles and are therefore equal.

Equate the two angles to solve for x.

4x-2 = 3x+19

subtract 3x-2 from either side (i.e. numbers on the left, and variables on the right)

4x-2 -(3x-2) = 3x+19 - (3x-2)

x = 21

check: 4x-2= 82, 3x+19=82, so solution is good.

A 6-digit PIN number is selected. What it the probability that there are no repeated digits?
The probability that no numbers are repeated is
Write your answer in decimal form, rounded to the nearest thousandth.
Submit Question

Answers

Mark Brainliest please

Answer: 0.1512

So I know that there are 10 possible digits that can be selected, each time the pool of selected digits gets smaller.

The first digit cannot be zero therefore there are 9 possibilities for this digit. Then, seeing as the order doesn't matter, but repeats do, so I thought a permutation would be the correct method to apply.

9 * ((9!)/(9-5!)) = 136,080 (<-- total number of 6 digit numbers)

Without repeats and no 0 as first digit

Total number of 6 digit numbers = 10^6

Therefore the probability of this scenario happening is:

(139,080/10000000) = 0.13608

Answer:

we got 10 digits to choose from for the first digit, 9 for the second and so on

[tex]10 \times 9 \times 8 \times 7 \times 6 \times 5[/tex]

scenarios that got no repeated digits.

the total number of possible PINs with 6 digits is

[tex]10 \times 10 \times 10 \times 10 \times 10 \times 10[/tex]

or just 10⁶

so the fraction we are looking for is the number of valid states decided by all possible states.

[tex] \frac{10 \times 9 \times 8 \times 7 \times 6 \times 5}{ {10}^{6} } [/tex]

=0.1512

rounded to the nearest thousandth it's

0.151

(actually, I didn't expect the probability to be around 15 percent)

hope it helps. asked question whenever you like

kind regards

Alex

factorize,
m
[tex] {m }^{2} - 40 + 6m[/tex]

Answers

Answer:

Step-by-step explanation:

m^2-40+6m

=m^2+6m-40

=m^2-(10-4)m-40

=m^2-10m+4m-40

=m(m-10)+4(m-10)

=(m+4)(m-10)

Kareem's rectangular flower bed measures 3ft long and 2ft wide. He wants to cover the flower bed in mulch. He knows the area each bag of mulch covers, but only in square centimeters

Answers

Hey buddy I am here to help!

Area of flower bed = 3 x 2 = 6ft

1 ft = 30.48cm

6 x 30.48 = 182.88cm2

HPC Education
Year 5* 6 Problem Solving Questions
10. Megan and Olivia had some money. They made a donation of $100 together. Megan donated of
her money. After donating $24, Olivia found that she had $32 more than Megan. What was the
sum of money both of them had at first

Answers

I’ll pay anyone to do my 7 math assignments(no scams no bs) Hmu asap

A man leaves the town of Elmsville at 8:00 am and drives to Oak City at a constant rate of 50 miles per hour. Two hours later, a woman leaves Elmsville following the same route to Oak City. The man and woman arrive in Oak City at 3:00 p.m. What was the rate of the woman

Answers

Answer: 70 mph

Step-by-step explanation:

Given

A man leaves the town of Elmsville at 8:00 am and reach oak city at 3 Pm

Rate of driving is 50 miles per hour

time taken by man [tex]t=7\ hr[/tex]

Woman leaves 2 hour later and reach by 3 Pm, so time taken is [tex]5\ hr[/tex]

Distance traveled by both the person is same

[tex]\therefore 50\times 7=v\times 5\quad[v=\text{rate of woman}]\\\\\Rightarrow v=\dfrac{50\times 7}{5}\\\\\Rightarrow v=70\ mph[/tex]

Thus , the rate of woman is 70 miles per hour.

Adriana sold 50 shares of a company’s stock through a broker. The price per share on that day was $22.98. The broker charged her a 0.75% commission. What was Adriana’s real return after deducting the broker’s commission?

A.
$8.62
B.
$229.80
C.
$1,140.38
D.
$1,149.00

Answers

Answer:
C $1,140.38
Step-by-step explanation:
We are given that Adriana sold 50 shares and that the price per share was $22.98
This means that:
Total value = 50 * 22.98 = $1149
Now, we know that the broker charged 0.75% commission on the total value
This means that:
Broker's charge = 0.75% * 1149 = 0.0075 * 1149 = $8.6175
Therefore,
Adriana's return = Total value - broker's charge
Adriana's return = 1149 – 8.6175 = $1,140.38

.....................................:.

Answers

Answer:

..........................................................................................................................................................................

Answer:

um..BG should also be equal to 12 I guess

What is 9x + 5= 32 described as

Answers

Answer:

9x + 5= 32

9x=27

x=3

x + 2∕5 = 1∕3 for x.

Answers

Answer:

?

Step-by-step explanation:

?

which statement is true?

Answers

Answer:

The slope of function A is greater than the slope of function B

hope it is helpful to you

Function a is greater than the function b

A) Abdul invests 400$ at 6.05% per year simple interest, calculate how much interest Abdul receives

B) Samia receives 400$ for 2 years at 6% per year compound interest, give your answer in 2 decimal places

Answers

Answer:

$24.20

amount invested = $356

Interest = $44

Step-by-step explanation:

Samia receives a total amount of 400$ for 2 years at 6% per year compound interest, give your answer in 2 decimal places

Simples interest = amount invested x time x interest rate

400 x 0.065 x 1 = $24.20

b. interest = amount received - amount invested

Amount invested = amount received / (1 + r)^n

r = interest rate

n = number of years

400 / (1.06)^2 = 356

Interest = 400 - 356 = $44

Answer this question for points

Answers

Djbdbdndhdb did d d d s. DNAs

Answer:

kjhgfdcxcfvghj

Step-by-step explanation:

A number that has both a whole number and a fraction is called a(n)

O A) improper fraction
OB) mixed number
OC) whole fraction
OD) combined number​

Answers

Answer:

mixed number <3

Step-by-step explanation:

vause it is

Question 7
Find the volume.

Answers

Answer:

A: 686π≈2,156

Step-by-step explanation:

First, you need to find the area of the circle then times that by 14.

π[tex]r^{2}[/tex]         Formula for the area of a circle

π[tex]7^{2}[/tex]          r stands for radius, so you divide the diameter by 2 and get 7.

π49        This is the area of the circle

π49×14    Now multiply by 14

=686π      This is your answer.

=2155.13256     When you times it by pi this is what you get

=2156               This is your answer if you want it rounded up

Can someone help me?

Answers

Answer:

The slope is 2

Step-by-step explanation:

Slope formula:

m=(y2-y1)/(x2-x1)

Given:

y2 = -10

y1 = -6

x2 = 2

x1 = 4

Work:

m=(y2-y1)/(x2-x1)

m=(-10 + 6)/(2 - 4)

m= (-4)/(-2)

m = 2

What is the length of sides of the square shown below? 45 2 90 A. 2sqrt(2) B. 4sqrt(2) C. 1 OD. sqrt(2) E. 4 F. 2

Answers

Answer:

Uh oh! It looks like your question is missing some crucial information.

Step-by-step explanation:

There is no " square shown below"

f(x+k) what is the value of k

Answers

Answer:

k = -3

Hope this helps!

Answer:

Step-by-step explanation:

f(x+k) is a horizontal shift of -k units.

Since the vertex went from 1 to -2, k = 3.

Will mark brainlest!
formula of (x+1)cube

Answers

Answer:

(x+1)^3=x^3+3x^2+3x+1

Answer:

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

Step-by-step explanation:

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

[tex](A+B)^{3} = A^{3} + 3A^{2}B+3AB^{2} + B^{3}[/tex]

What is the area of the parallelogram shown

Answers

9514 1404 393

Answer:

  60 square units

Step-by-step explanation:

The area is given by the formula ...

  A = bh

The base of this parallelogram is 15 units, and its height is 4 units. The area is ...

  A = (15 u)(4 u) = 60 u²

The area is 60 square units.

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