At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 2 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 2 feet high?

For any square matrix A, if it is invertible, its inverse is given by

[tex]A^{-1} = \dfrac1{\det(A)} \mathrm{adj}(A)[/tex]

where adj(A) is the so-called adjugate matrix, which is the transpose of the cofactor matrix of A. If you don't know what that is, that's not terribly important. What is important is that the inverse does not exist if the determinant, det(A), is zero.

We have

[tex]A=\begin{bmatrix}6&7\\-6&7\end{bmatrix} \implies \det(A) = 6\times7-7\times(-6)=84 \neq 0[/tex]

so the inverse does indeed exist. (And we eliminate D as an answer.)

From the given choices, it's quite clear that C must the correct answer, since we know det(A) = 84, and we can easily confirm that

[tex]\begin{bmatrix}7&-7\\6&6\end{bmatrix} \begin{bmatrix}6&7\\-6&7\end{bmatrix} = \begin{bmatrix}84&0\\0&84\end{bmatrix}[/tex]

so that multiplying by 1/84 recovers the identity matrix.

We are given with a square matrix and we are asked to find it's inverse if it exists . So , let's recall some important points first :-

Now , in this question let's assume that [tex]{\sf A=\begin{bmatrix}6 & 7 \\ -6 & 7\end{bmatrix}}[/tex]

Now , Calculating det(A) :-

[tex]{:\implies \quad \sf det(A)=\begin{vmatrix}6 & 7 \\ -6 & 7 \end{vmatrix}}[/tex]

[tex]{:\implies \quad \sf det(A)=42-(-42)}[/tex]

[tex]{:\implies \quad \sf det(A)=42+42}[/tex]

[tex]{:\implies \quad \sf det(A)=84}[/tex]

As , det(A) ≠ 0 . So , [tex]{\bf A^{-1}}[/tex] exists . Now , we need to find the matrix of cofactors first , but let's find cofactors first , so here ;

[tex]{\blacktriangleright \sf C_{11}=7,\: C_{12}=6,\: C_{21}=-7,\: C_{22}=6}[/tex]

Now , let's assume that matrix of cofactors is C , so putting the cofactors as elements of the matrix , C will be ;

[tex]{:\implies \quad \sf C=\begin{bmatrix}7 & 6 \\ -7 & 6\end{bmatrix}}[/tex]

Now , adj(A) will be found by interchanging it's rows by columns and vice versa.

[tex]{:\implies \quad \sf adj(A)=\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex]

Now as [tex]{\sf A^{-1}}[/tex] is given by [tex]{\bf{A^{-1}=\dfrac{1}{adj(A)}det(A)}}[/tex]

[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{A^{-1}=\dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}}}[/tex]

Hence , Option C) [tex]{\sf \dfrac{1}{84}\begin{bmatrix}7 & -7 \\ 6 & 6\end{bmatrix}}[/tex] is correct :D

Answer: See below

Step-by-step explanation:

Event 1:

There are 13 diamond cards in total

A standard deck of cards has a total of 52 cards

Probability = 13/52

P = 1/4 or 25%

Event 2:

There are a total of 6 sides on a standard dice

Probability = 4/6

P = 2/3 or 66.67%

Event 3:

There are 3 blue marbles in a bag of 18 marbles

Probability = 3/18

P = 1/6 or 16.67%

Answer: a) 1/4     b) 2/3     c) 1/6

Step-by-step explanation:

All of these are probability problems. They have this trick.

First, the trick. The chance of taking an x amount of blue marbles out of a bag of y marbles is x/y. Now using this…

a) there are 13 diamonds and 52 total. 13 is x, and 52 is y. It is 13/52 = 1/4

b) There are 4 numbers you need to get, and 6 in total. Therefore; there is a 4/6 chance which simplifies to 2/3.

c) There are 3 marbles you need, and 18 of them in total. It is 3/18 which is 1/6.

I once struggled on these problems, for they can be difficult.

Answer:

[tex]x=\frac{1}{2}[/tex]

Step-by-step explanation:

equation of a circle:  [tex](x - h)^2+(y-k)^2=r^2[/tex]

where (h, k) = center and r = radius

From inspection, we can see that the center of the circle = (0, 0)

and the radius = 1

[tex]\implies (x - 0)^2+(y-0)^2=1^2[/tex]

[tex]\implies x^2+y^2=1[/tex]

Substitute [tex]y=\frac{\sqrt{3}}{2}[/tex]  into  [tex]x^2+y^2=1[/tex]  and solve for [tex]x[/tex]:

[tex]\implies x^2+(\frac{\sqrt{3}}{2})^2=1[/tex]

[tex]\implies x^2+\frac{3}{4}=1[/tex]

[tex]\implies x^2=\frac{1}{4}[/tex]

[tex]\implies x=\pm \sqrt{\frac{1}{4}}[/tex]

[tex]\implies x=\pm\frac{1}{2}[/tex]

As point P is in quadrant 1, [tex]x[/tex] is positive, so [tex]x=\frac{1}{2}[/tex]

Answer:

6

Step-by-step explanation:

the least common denominator of 3 and 6 is 6

THATS how I got six

Hopped this helped <3

The slope of the line will be -2/3. And the coordinates will be A(-35/4, 6) and B(9, -34/6).

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = -2/3 x + 1/6

The slope of the line is - 2/3.

At y = 6, the value of 'x' is calculated as,

6 = -2/3 x + 1/6

35/6 = -2/3 x

x = -35 / 4

At x = 9, the value of 'y' is calculated as,

y = -2/3 (9) + 1/6

y = -6 + 1/6

y = -35/6

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Answer:

0.25

Step-by-step explanation:

11/12 = 0.917

2/3 = 0.667

0.917 - 0.667 = 0.25

Answer:

75200 x 1/100= 752

hope this helps!

Answer:

1/1

Step-by-step explanation:

22/22 =1

The possible outcomes are the sample space of the game

The number of possible outcomes in the game is 3

The number of games is given as:

n = 5 i.e. 5 games to finish the season

In each game, the soccer team can either win, lose or tie.

So, we have the outcome of each game to be:

Outcome = {Win, Lose, Tie}

Count the outcomes

Count = 3

Hence, the number of possible outcomes in the game is 3

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Answer:

(0, -3)

Step-by-step explanation:

It will help to graph it out.

Also is the phase shift negative or is it just to the right? Im assuming its just right pi over 4

Answer: 0

Step-by-step explanation:

2pi/4 does not equal pi, it equals half of pi. 2pi/2 equals pi. Regardless here's my answer, since it also checks out for a similar function that was confirmed to have a phase shift of pi/2:

The formula for this is asin(bx - c) + d, where

|a| = amplitude

period = 2pi/b

and phase shift = c/b

The amplitude is 3

3sin(bx - c) + d

Phase shift is c/b, in this case, pi/4

3sin(4x - pi) + d  

d is vertical shift

(phase shift, c, is also known as horizontal shift)

We don't see any d here so graph on Desmos as follows....

Graph 3sin(4x - pi)

Looks like the y-intercept is 0

Check by substituting 0 for x:

3sin(4x - pi)

3sin(4(0) - pi)

3sin(-pi) = 0

The answer is 0, checks out.

Answer:

58

Step-by-step explanation:

the way of the parts of the question

Answer:

March 25, 2021, Mrs. Chaues balance is _____

Step-by-step explanation:

Mrs. Chauke balance in words is Eighteen thousand five hundred eighty-two and seven hundredths

From the complete question, we have the following highlights:

When 18,582,07 is expressed In words, it is:

Eighteen thousand five hundred eighty-two and seven hundredths

Hence, Mrs. Chauke balance on the 25 March 2021 in words is Eighteen thousand five hundred eighty-two and seven hundredths

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Step-by-step explanation:

f'(x)=-2sin(x)+2cos(2x)=0

as cos(2x)=2sin(x)cos(x),

-2sin(x)+4cos(x)sin(x)=0

sin(x)-2cos(x)sin(x)=0

(sin(x))(1-2cos(x))=0

-> x = 0, pi/3

testing these values along with the end points of the interval,

f(0)=2

f(pi/3)=1+(0.5sqrt(3))

f(pi/2)=0

so the min is 0 and the max is 2.

The lengths of the bases are: 4cm and 12cm.

Since the area of a trapezoid is given by the formula;

Where a and b are the lengths of the bases and h is the height of the trapezoid.

Hence, in this case scenario; it follows that;

a = x = 4cm

b = 3x = 12cm.

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Answer:

1.

Step-by-step explanation:

The greatest common factor is the largest positive integer that divides evenly into all numbers with zero remainder.

So, let's factor each number:

12w⁴: To factor it, factor 12 and w⁴ separately.

12: 1, 2, 3, 4, 12

w⁴: 1, w, w², w³, w⁴

So, the factor of 12w⁴ is all the combinations of the factor of 12 and w⁴.

1, 2, 3, 4, 12, 1w, 2w, 3w, 4w, 12w, 1w², 2w², ..., 12w⁴

5y³: To factor it, factor 5 and y³ separately.

5: 1, 5

y³: 1, y, y², y³

So, the factors of 5y³ are all the combinations of the factor of 5 and y³.

1, 5, 1y, 5y, 1y², ... , 5y³

The only factor that 12w⁴ and 5y³ have in common is 1.

Answer: 1.

Answer:Given a normal distribution with μ = 62 and σ = 4., calculate the 68-95-99.7 rule, or three-sigma rule, or empirical rule ranges

Calculate Range 1:

Range 1, or the 68% range, states that 68% of the normal distribution values lie within 1 standard deviation of the mean

68% of values are within μ ± σ

μ ± σ = 62 ± 4.

62 - 4. <= 68% of values <= 62 + 4.

58 <= 68% of values <= 66

Calculate Range 2:

Range 2, or the 95% range, states that 95% of the normal distribution values lie within 2 standard deviations of the mean

95% of values are within μ ± 2σ

μ ± 2σ = 62 ± 2(4.)

62 - 2 x 4. <= 95% of values <= 62 + 2 x 4.

62 - 8 <= 95% of values <= 62 + 8

54 <= 95% of values <= 70

Calculate Range 3:

Range 3, or the 99.7% range, states that 99.7% (virtually ALL) of the normal distribution values lie within 3 standard deviations of the mean

99.7% of values are within μ ± 3σ

μ ± 3σ = 62 ± 3(4.)

62 - 3 x 4. <= 99.7% of values <= 62 + 3 x 4.

62 - 12 <= 99.7% of values <= 62 + 12

50 <= 99.7% of values <= 74

Step-by-step explanation:

The probability that a data value is between 56 and 64 is,

= 64.7%

The term probability refers to the likelihood of an event occurring. Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.

Given that :

Mean (m) = 62

Standard deviation (s) = 4

Hence, Probability that a data value is between 56 and 64

P(56 < x < 64)

Using the relation :

(x - m) / s

P(x < 56) : (56 - 62) / 4

              = - 1.5

P(Z < - 1.5) = 0.10565

( Z probability calculator)

P(x < 64) :

(64 - 62) / 4 = 0.75

P(Z < 0.75) = 0.77337 (Z probability calculator)

Hence, We get;

P(Z < 0.75) - P(Z < - 1.25)

0.77337 - 0.10565

= 0.64772

= 64.7%

Thus, the probability that a data value is between 56 and 64 is,

= 64.7%

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Answer:

57/6   60/6    22/6   26/6

Step-by-step explanation:

So the answers for the blanks are 57, 60, 22, 26.

Let me know if I am incorrect.

Answer:

[tex]6x-7x^{2}[/tex]

Step-by-step explanation:

o= 4x [tex]x[/tex] 2 +7x -3

0= 8x +7x -3

0= 15x -3

- 15x =-3

x= [tex]\frac{1}{5}[/tex]

x= 0.2  , x =[tex]x^{-1}[/tex]

[tex](f+g)(2)[/tex]

[tex]18 - 7x -5-7 \\6-7x\\[/tex]

Answer:

380,460

Step-by-step explanation:

x copies have been sold to date

so 8.7% * x = 33,100

x = 33,100/0.087 = 380,460

Answer:

Rectangle is the closed shaped polygon with 4 sides. Opposite sides of the rectangle are equal. when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.Given-The length of the sandbox is 10.The width of the sandbox is 6.a) The percent of change in the perimeter.Perimeter of the rectangleThe perimeter of the rectangle is the twice of the sum of its side.The perimeter P of the sandbox is,When the length and the width of the sandbox are doubled the perimeter of the box is,Percentage  change in the perimeter,b) The percent of change in the area.Area of the rectangleThe area of the rectangle is the product of its side.The area A of the sandbox is,When the length and the width of the sandbox are doubled the area  of the box is,Percentage  change in the area,Thus when the length and the width of the sandbox are doubled the percent of change in the perimeter is 100 percent and the percent of change in the area is 300 percent.

This would be the average value of R(x) between 10 m and 50 m :

[tex]\displaystyle \frac1{50\,\mathrm m - 10\,\mathrm m} \int_{10\,\rm m}^{50\,\rm m} kx^2 \, dx[/tex]

The average intensity of radiation between 10 meters and 50 meters from the source is 1033.33 k.

It is the reverse of differentiation.

The intensity of radiation at a distance x meters from a source is modeled by the function given by

R(x)=kx²

where k is a positive constant.

The average intensity of radiation between 10 meters and 50 meters from the source will be

[tex]\rm Average \ intensity = \dfrac{1}{50 - 10} \int_{10}^{50} \ kx^2 \ dx\\\\\\Average \ intensity = \dfrac{k}{50 - 10} [ \dfrac{x^3}{3} ]_{10}^{50}\\\\\\Average \ intensity = \dfrac{k}{40} [ \dfrac{50^3}{3} - \dfrac{10^3}{3} ]\\\\\\Average \ intensity =1033.33k[/tex]

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Prioritize meeting basic needs and invest in education and skill development, while supporting community projects for a fair distribution of funds.

Prioritize basic needs: I would recommend ensuring that everyone's basic needs are met first, such as food, shelter, and healthcare. This promotes fairness by addressing essential requirements for survival and well-being.

Invest in education and skill development: Allocating funds towards education and skill development programs can empower individuals to improve their future prospects and contribute to society. It promotes fairness by providing equal opportunities for personal growth and advancement.

Support community projects: Encouraging investments in community projects, infrastructure development, and social initiatives can benefit a broader range of people. It promotes fairness by aiming to uplift the community as a whole, rather than focusing solely on individual interests.

By following these principles, the recommended approach for spending money can ensure fairness by addressing basic needs, fostering personal development, and benefiting the community at large. Ultimately, the specific allocation of funds would depend on the context, priorities, and values of the individuals involved.

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Answer:

Letter a is 6:38 and letter b is 2:17

Hope this helps!

Let's make a system of equations:

144/x=y

168/(x+5)=y

So,

144/x=168/(x+5)

Solving using cross multiplication,

x=30

So, her average speed for driving 144 miles was 30 miles per hour.

-Hunter

Answer:

No.

Step-by-step explanation:

For there to be a equal sign, it will mean that both sides will have to have the same exact amount. If it is expressions on both sides, then the expressions must, when combined, equal to each other.

In this case, there is not given operation that will allow for both numbers to equal each other, and 17.8 is 10 less than 18.8, therefore it is not reasonable.

17.8 ≠ 18.8

The number of people in the room is 91.

The first step is to determine the total number of chairs in the room. In order to determine this value, divide the fraction of the unoccupied chairs by the number of empty chairs.

8 ÷ 1/8

8 x 8 = 64

Number of people sitting on the chairs = 64 - 8 = 52

Number of people in the room = 52 ÷ 4/7

= 52 x 7/4 = 91

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Answer:

LCM of 3, 5, and 11 is 165.

Step-by-step explanation: