Can you give a detailed example of a specific scenario, outside of pure math, where eigenvectors are useful? I know about lots of general applications (image processing, differential equations, etc) but I want something specific.
No answer take the points.

Answer:

The answer is below

Step-by-step explanation:

The Freeman family barbecued veggie burgers, corn cobs, and mushroom caps. 3/8 of the items barbecued are veggie burgers, and 1/3 of the items barbecued are corn cobs.

Let the total number of berbecued items be x. Therefore:

x = barbecued veggie burgers + barbecued corn cobs + barbecued mushroom caps

Barbecued veggie burgers = (3/8)x, barbecued corn cobs = (1/3)x, Let barbecued mushroom caps be y

Substituting:

x = (3/8)x + (1/3)x + y

Multiply through by 24

24x = 9x + 8x + 24y

24x = 17x + 24y

24y = 24x - 17x

24y = 7x

y = (7/24)x

barbecued mushroom caps = (7/24) of items

7/24 of the items barbecued are mushroom caps

Using fractions, it is found that the fraction of barbecued items that are mushroom caps is of \(\frac{7}{24}\).

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Thus:

\(\frac{3}{8} + \frac{1}{3} + x = 1\)

Then:

\(\frac{3\times3 + 8\times1 + 24x}{24} = 1\)

\(\frac{17 + 24x}{24} = 1\)

\(17 + 24x = 24\)

\(24x = 7\)

\(x = \frac{7}{24}\)

The fraction of barbecued items that are mushroom caps is of \(\frac{7}{24}\).

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Reflection across the line y=x transforms the point (x, y) into (y, x). Then,

P(1, 2) → P'(2, 1)

Q(4,3) → Q'(3, 4)

The new coordinates are P'(2, 1) and Q'(3, 4)

The area of the rectangular basement carpeting carvers'  family need is :Area = 56  sq. ft.

An object with a rectangle's four sides, four corners, and four right angles is a 2D shape. In a rectangle, the opposite sides are equal in length, with one pair substantially longer compared to the opposite pair.

An equiangular quadrilateral is another name for a rectangle. The reason for this is that a rectangle is now a quadrilateral form (4-sided shape) with parallel sides that are equal to one another and four corners with 90o angles.

A rectangle can also be referred to as an equiangular quadrilateral because all of the angles are 90 degrees.

The given dimensions of the rectangular carvers' basement:

length 8 ft and width 7 ft.

Area =  length x width

Area =   8 ft x 7 ft.

Area = 56  sq. ft.

Thus, the area of the rectangular basement carpeting carvers'  family need is :Area = 56  sq. ft.

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The complete questions:

The Carvers' basement has the dimensions shown below.

The family plans to have wall-to-wall carpeting installed.

Dimension: length 8 ft and width 7 ft.

How many square feet of carpeting will the family need?

Show your work.

22 ft²

56 ft²

48 ft²

10 ft²

Answer:

In the equation y = 2 cos(5x + 3) - 6, we can ignore the coefficients 2 and -6 for the purposes of calculating the period because they do not change the period. They only change the amplitude (2) and vertical shift (-6) of the function.

The coefficient 5 in front of x inside the cosine function affects the period of the function. It is a horizontal compression/stretch of the graph of the function.

The period of the basic cosine function, y = cos(x), is 2π. When there is a coefficient (let's call it b) in front of x, such as y = cos(bx), the period becomes 2π/b.

So, in your case, b = 5, so the period T of the function y = 2 cos(5x + 3) - 6 is:

T = 2π / 5

This is the simplest form for the period of the given function.

Answer:

WE reject the Null and conclude that the mean coefficient of restitution exceeds 0.82

Step-by-step explanation:

This is a one sample t test :

The hypothesis :

H0 : μ = 0.82

H0 : μ > 0.82

Given the sample data:

0.8411 0.8191 0.8182 0.8125 0.8750

0.8580 0.8532 0.8483 0.8272 0.7983

0.8042 0.8730 0.8282 0.8359 0.8660

Sample size, n = 15

Sample mean = ΣX / n = 0.837

Sample standard deviation, s = 0.0246 (from calculator)

The test statistic :

T = (xbar - μ) ÷ (s/√(n))

T = (0.837 - 0.82) ÷ (0.0246/√(15))

T = 2.676

The critical value at α = 0.05

df = n - 1 ; 15 - 1 = 14

Tcritical(0.05, 14) = 1.761

Reject H0 if Test statistic > Tcritical

Since, 2.676 > 1.761 ; WE reject the Null and conclude that the mean coefficient of restitution exceeds 0.82

Answer:

y = 2x - 3.

Step-by-step explanation:

The slope  is 2 and the y-intercept is at y = -3

Answer:

z=2

Step-by-step explanation:

56-35z+17=3

73-35z=3

-35z=-70

z=2

Answer:

13 - 6 x

Step-by-step explanation:

Answer:

x-7x+5

Step-by-step explanation:

4+x-7x+1

x-7x+5

Answer:

2. y = 4x+7; y=-7x+5

Step-by-step explanation:

The Volume of the box is 12 cubic unit.

We have,

Height = 1 unit

Width = 2 unit

Length = 6 unit

So, Volume of box

= l w h

= 1 x 2 x 6

= 12 cubic unit

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Answer:

64,765

Step-by-step explanation:

multiplicas porque dice que uno cuesta 315 entonces si hay 205 hay 64,765

Answer:

\(274\,\text{in}^3\)

Step-by-step explanation:

\(V=\pi r^2h=\pi(3.75)^2(6.21)\approx274\,\text{in}^3\)

Answer:

What is the question?

Step-by-step explanation:

If its how much will it cost to get ____ gallons

Just multiply the number of gallons you want and 3.50 (the price)

Again, I don't really know what your question is, but I'm saying this so that if what I put up there is actually what your question was, you don't have to make another one. (I'm not sure if you can edit questions or not.)

Answer:

80 degrees

Step-by-step explanation:

Answer:

(1, 7/2)

Step-by-step explanation:

the formula for midpoint is  \((\frac{X1 + X2}{2}\), \(\frac{Y1 + Y2}{2})\)

Answer:

\(\boxed{15 \ dime \ and \ 10 \ nickel \ coins}\)

Step-by-step explanation:

1 dime = 10 cents

1 nickel = 5 cents

So,

If there are 15 dimes

=> 15 dimes = 15*10 cents

=> 15 dimes = 150 cents

=> 15 dimes = $1.5

Rest is $0.5

So, for $0.5 we have 10 nickels coins

=> 10 nickels = 10*5

=> 10 nickels = 50 cents

=> 10 nickel coins = $0.5

Together it makes $2.00

Answer: 3x + 3

Step-by-step explanation:

Answer: 2/3πx³

Step-by-step explanation:

Let the radius of the cone be represented by x.

Since the height of the cone is twice the radius of its base, the height will be: = 2x

Volume of a cone = 1/3πr²h

where,

r = x

h = 2x

Volume of a cone = 1/3πr²h

= 1/3 × π × x² × 2x

= 1/3 × π × x² × 2x

= 1/3 × π × 2x³

= 2/3πx³

Therefore, the correct answer is 2/3πx³.

Answer:

the perimeter in unites of abc with 3, -3 is a

Answer:

18 Units

Step-by-step explanation:

According to the calculator

SOLUTION

A non-negative integer is either positive or zero. It's the union of the natural numbers and the number zero.

A prime number is a number with only two factors, which are 1 and the number itself

Let consider the number

1) It satisfies the first statement

M is prime

2 is prime

2) M+3 is prime

since

Hence

The second statement is satisfied

The third statement says

Hence the third statement is satisfied

M=2

Since exactly 3 of the 4 statements is satisfied

From the second condition,

All prime numbers except 2 are odd numbers

Also,

The sum of two odds is even

from the second condition,

M+3 is prime

Hence

There is no other prime number that satisfies exactly three of the four conditions above

Therefore,

The number of non-negative integers that satisfy exactly three of the four conditions is 1

There is only one non-negative integer M which is 2 that satisfy the condition 1,2,3 above

Answer:

\( \frac{1}{2} \times 8 \times 16 \\ = 64\)

The answer you are looking for is 64 m².

Solution/Explanation:

First, setting up the formula for the area of a triangle,

A=1/2bh

Next, substituting the given values of the base and the height,

A=1/2(8)(16)

Now, simplifying it to get to the final answer,

A=64 m²

So, therefore, the final answer is 64 m².

I hope this helped you find your answer. Enjoy your day, and take care!

The trigonometric equations has the following solutions: x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

In this problem we find the case of a trigonometric equation, whose solutions on the interval [0, 2π] must be found. This can be done by both algebra properties and trigonometric formulae. First, write the entire expression:

tan² x · sec² x + 2 · sec² x - tan² x = 2

Second, use trigonometric formulas to reduce the number of trigonometric functions:

tan² x · (tan² x + 1) + 2 · (tan² x + 1) - tan² x = 2

Third, expand the equation:

tan⁴ x + tan² x + 2 · tan² x + 2 - tan² x = 2

tan⁴ x + 2 · tan² x = 0

Fourth, factor the expression:

tan² x · (tan² x - 2) = 0

tan² x = 0 or tan² x = 2

tan x = 0 or tan x = ± √2

Fifth, determine the solutions to trigonometric equation:

x = 0 + j · π or x = 0.352π + j · π or x = - 0.352π + j · π, where j is a non-negative whole number.

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To find the total time it takes for the airplane to travel from Mumbai to Tokyo via Seoul, we need to add the time taken for the Mumbai-Seoul leg and the Seoul-Tokyo leg.

The airplane takes 3.2 hours to fly from Mumbai to Seoul.

The airplane takes 1 1/3 hours to fly from Seoul to Tokyo, which is equivalent to 1.33 hours.

To find the total time, we add the two durations:

3.2 hours + 1.33 hours = 4.53 hours

Therefore, it takes approximately 4.53 hours for the airplane to travel from Mumbai to Tokyo if it flies through Seoul.

Answer: C) local maximum at x = -3; local minimum at x = 1/3

Step-by-step explanation:

Given the function:

f(x) = x^3 + 4x^2 - 3x - 4

Set f'(x) = 0

f'(x) = 3x² + 8x - 3

f'(x) = 0

3x² + 8x - 3 = 0

Using the quadratic function calculator :

x = - 3 or x = 1/3

Critical points = - 3 ; 1/3

To find the maximum and minimum points :

f''(x) = 6x + 8

Substitute the values of X in

At x = - 3

6(-3) + 8

-18 + 8 = - 10

At x = 1/3

6(1/3) + 8

2 + 8 = 10

Value of f''(x) at - 3 is negative, hence - 3 is the maximum point

Value of f''(x) at 1/3 is positive , hence 1/3 is the minimum point

Answer:

B) 1/2

Step-by-step explanation:

Note that pi=180.

Then we have 180/3=60 and so 5*60=300.

Thus cos 300=1/2.

Therefore, cos 5pi/3=1/2.

Answer: B

Step-by-step explanation:

The expression that is equivalent to StartRoot \(8 x^7 y^8\) EndRoot is (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2.

To understand why this is the case, let's break down each expression and simplify them step by step:

StartRoot \(8 x^7 y^8\) EndRoot:

We can rewrite 8 as \(2^3\), and since the square root can be split over multiplication, we have StartRoot \((2^3) x^7 y^8\) EndRoot. Applying the exponent rule for square roots, we get StartRoot \(2^3\) EndRoot StartRoot \(x^7\) EndRoot StartRoot \(y^8\) EndRoot.

Simplifying further, we have 2 StartRoot \(2 x^3 y^4\) EndRoot StartRoot \(2^2\) EndRoot StartRoot \(x^2\) EndRoot StartRoot \(y^4\) EndRoot. Finally, we obtain 2 \(x^3 y^4\) StartRoot 2 x EndRoot, which is the expression in question.

(\(2 x y^2\) StartRoot 8 x^3 EndRoot)^2:

Expanding the expression inside the parentheses, we have \(2 x y^2\)StartRoot \((2^3) x^3\) EndRoot. Applying the exponent rule for square roots, we get \(2 x y^2\) StartRoot \(2^3\) EndRoot StartRoot \(x^3\) EndRoot.

Simplifying further, we have \(2 x y^2\) StartRoot 2 x EndRoot. Squaring the entire expression, we obtain (\(2 x y^2\) StartRoot 2 x EndRoot)^2.

Therefore, the expression (\(2 x^3 y^4\) StartRoot 2 x EndRoot)^2 is equivalent to StartRoot \(8 x^7 y^8\) EndRoot.

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