Problem 4.1
A tank of water breaks and begins draining at a constant rate.
Complete the table.
Time (minutes)
Change in Water
(liters)
Expression
Water in the Tank
(liters)

Applying Pythagoras theorem, and drawing free body diagram we can measure the moments required.

First of all draw the free body diagram.

Now, in triangle AOC, apply Pythagoras theorem,

Now, write the coordinates of the points,

O (0, 0, 0) m

A (0, 15, 20) m

C (0, 0, 20) m

B (2.5, 0, 20) m

Now, write the position vector from A to B,

Now, write the unit vector rAB

Now, write the tensional force on the point A due to the cable AB,

Now, calculate the force ‘T’ about the origin,

Hence the moments about the coordinate axes are,

Mx = 78.9 kN.m

Mx = 13.15 kN.m

Mx = -9.86 kN.m

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The resulting matrix by applying the given row operations −2R2+3R1 →R1 is given by [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .

Matrix A is equal to :

A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]

Now replace the row R1 by applying the row operations -2R2 + 3R1 on the given matrix we get ,

First element of row 1 is replaced by :

-2(8) + 3(-3)

= -16 -9

= -25

Second element of row 1 is replaced by :

-2(5) + 3(5)

= -10 + 15

= 5

Third element of row1 is replaced by :

-2(6) + 3(2)

= -12 + 6

= 6

Therefore, the resulting matrix after applying the row operation is given by : [tex]\left[\begin{array}{ccc}-25&5&-6\\8&5&6\end{array}\right][/tex] .

The above question is incomplete , the complete question is :

Consider matrix A.

What matrix results  apply the given row operation(s) R1 to the matrix in order, and give the resulting matrix represented by −2R2+3R1?

A = [tex]\left[\begin{array}{ccc}-3&5&2\\8&5&6\end{array}\right][/tex]

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The distance across the pond is 52 feet.

Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.

In the given diagram, there are two triangles.

If we prove the two triangles are congruent, we will get the distance across the pond as 52 feet.

Already 2 sides of one triangle is given as equal to 2 sides of the other triangle, which are 41 ft and 29 ft.

Also since the lines are intersecting the included angles of the equal sides of both triangle are equal by vertical angle theorem.

So two sides and an included angle of a triangle is equal to corresponding two sides and an included angle of other triangle.

So the triangles are congruent by SAS theorem.

So all the sides of two triangles are equal.

Distance across the pond is 52 feet.

Hence we get the distance across the pond is 52 feet.

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Answer: C

Step-by-step explanation: TYSM if you give me a brainly... ps love you

Answer:

B.

A trapezoid looks like the following in the image, and B is the same but flipped.

Step-by-step explanation:

Hope it helps! =D

The number of days until I need to go to the store for sausages again is

7.5 days.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

Number of packages = 6

Number of sausages in each package = 2(1/2)

Total sausages.

= 6 x 2(1/2)

= 6 x 5/2

= 3 x 5

= 15

Number of sausages the dog eats each day = 2

The number of days the sausages will be used.

= 15/2

= 7.5

Thus,

The number of days is 7.5 days.

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The least common multiple(LCM) of two coprime numbers is their product, ab.

Let a and b be two positive integers, and let LCM(a,b) be the least common multiple of a and b.

By definition, LCM(a,b) is the smallest positive number which is divisible by both a and b.

Now, suppose that a and b are coprime, meaning that there are no positive integers other than 1 that divide both a and b.

Since 1 divides both a and b, and 1 is the smallest positive integer, we know that 1 is the only positive integer that divides both a and b.

Therefore, LCM(a,b) must be divisible by both a and b, and 1 is the only positive integer that divides both a and b.

Thus, LCM(a,b) = ab.

This proves that the least common multiple of a and b is ab precisely when a and b are coprime.

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The set |x| < 7 using interval notation is given as follows:

0. < x < 7.

The absolute value of a number gives the distance of a number from the origin, hence it basically can be interpreted as the number without the signal.

The expression for this problem is defined as follows:

|x| < 7.

Then the bounds of the open interval are given as follows:

The lowest absolute value is given as follows:

0.

Hence the interval is given as follows:

0 < x < 7.

The problem asks for the interval notation of:

|x| < 7.

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The sum of his scores is -10

A summation, also called a sum, is the result of arithmetically adding numbers or quantities. A summation always contains a whole number of terms. There can be as few as two terms, or as many as a hundred, a thousand, or a million. Some summations contain infinitely many terms.

For example, If the value of ages of class is given as 5, 6,7,8,5,6. The sum of of their of ages will be 5+6+7+8+5+6 = 37

The score of jake are -12, 3 ,5 , 2 ,0 and -8. The sum of his scores = -12 + 3 + 5 + 2 + 0 + -8

collecting like terms

-12 + -8 + 3 + 5 + 2 + 0

= -10

Therefore the sum of Jake's score is -10

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The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

Any equation using the formula ax² + bx + c = 0 is a quadratic equation.

where a, b and c are constants, and x is an unknown variable.

It is called "quadratic" because the variable is squared (in other words, raised to the power of 2).

The most common way to solve a quadratic equation is to factor it into two linear equations, which can then be solved using the methods of linear algebra.

Another way is to use the quadratic formula, which expresses the roots of the equation in terms of the coefficients a, b and c.

It is called a quadratic equation because it can be written in the form

ax² + bx + c = 0

which is the standard form for a quadratic equation.

Examples:

1) x² + 4x – 5 = 0

2) 4x² – 7x + 3 = 0

3) 2x² + 3x – 4 = 0

Therefore , The values of (a + b)(a - b) is a²-b² = (a-b) (a+b) and (x+7)² is x² + 14x+49 =  (x+7)(x+7)

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The function f(x) = 9 - x² is a one to one function and the value of f⁻¹(x) = √9 - x.

The graph of the function is attached below.

In math the term graph is defined as a pictorial representation or a diagram that represents data or values in an organized manner.

Here we have the function f(x) = 9 - x² and here we also know that on the interval 0≤x≤3 and a=8.

Now, we have to check the given function is one to one or not, for that we have to plot the function on the graph then we get the graph like the following.

While we looking into the graph we have identified that each input value has exactly only one output, therefore it is said to be one to one function.

And the inverse of the function is calculated by rewritten the function as,

=>  f⁻¹(x) = √9 - x.

And the graph of f⁻¹(x) is plotted as follows,

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Answer:

14

Step-by-step explanation:

I don't know it right now

The polynomial X3-8 has a degree of 3 and 2 terms

Algebraic expressions are defined as mathematical expressions comprising of variables, coefficients, terms, constants and factors.

These algebraic expression are also comprised of arithmetic operations, such as;

Polynomials are also described as algebraic expressions composed of arithmetic operations and also non-negative integer exponentiation of variables.

Given the polynomial, the number of terms is 2

Hence, the number of terms is 2 and the degree is 3

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The buoyant force is the upward force on an object submerged in a fluid that is caused by the fluid's pressure.

The magnitude of the buoyant force is equal to the weight of the displaced fluid. Therefore, the correct ranking of the three buoyant forces is fx > fy > fz.

The magnitude of the buoyant force can be calculated using the equation Fb = ρgV, where ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the displaced fluid. For orientation x, the buoyant force fx will be the greatest since the volume of the displaced fluid is the greatest. For orientation y, the buoyant force fy will be the second greatest since the volume of the displaced fluid is second greatest. Finally, for orientation z, the buoyant force fz will be the least since the volume of the displaced fluid is the least.

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The solution to the equations is x = 20/3 and y = -8

From the question, we have the following parameters that can be used in our computation:

3x + 2y=4

3x + 6y=-28

The above equations is a system of linear equations

So, we can subtract them to eliminate x as follows

4y = -32

Divide both sides by 4

y = -8

Substitute y = -8 in the equation 3x + 2y=4

3x - 16 =4

Evaluate the like terms

3x = 20

So we have

x = 20/3

Hence, the soluton is x = 20/3 and y = -8

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The shaded area is 169.56 inch² for the given set of semicircles with radius 6 inch and 12 inch.

The size of a region on a surface is measured in area. Surface area refers to the area of an open surface or the boundary of a three-dimensional object, whereas area of a plane region or plane area refers to the area of a shape or planar lamina. The total space occupied by a flat (2-D) surface or the shape of an object is defined as its area. Draw a square on a piece of paper with a pencil. It is a two-dimensional figure. The area of the shape on the paper is referred to as its Area. Consider your square to be made up of smaller unit squares.

Here,

area1=1/2*3.14*r²

=0.5*3.14*12²

area2=1/2*3.14*r²

=0.5*3.14*6²

area=area1-area2

=0.5*3.14*12²-0.5*3.14*6²

=169.56 inch²

The shaded area for the given set of semicircles with radius 6 inch and 12 inch is 169.56 inch².

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1) product is not defined.
2) product is undefined.
3)  [  -9 ]
    [  5  ]      
    [ -11 ]

Explanation:

1) product is not defined.
because no of column of 1st matrix (2)  is not same as no of row of second matrix.(3)

2) product is undefined.
because no of column of 1st matrix (1)  not same as no of row of second matrix (2).


3)  [    6     5 ]                           [    6  -15    ]                    [  9     ]
    [   -4    -3 ]  X  [ 1  ] =            [     -4   +9  ] =                [   5    ]
    [    7     6 ]       [ -3 ]              [      7  -18   ]                  [   -11   ]   
           

A matrix is a rectangular array of numbers (or other mathematical objects) that defines operations like addition and multiplication. A matrix over a field F is typically a rectangular array of scalars, each of which is a member of F.

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Answer: To determine the order of the temperature of the mixtures from least to greatest, we need to compare the values of the temperatures in their simplified fractional forms.

-33.625℉ = -33 5/8℉

-33 5/6℉ = -33 5/6℉

-33 6/25℉ = -33 24/100℉

We can compare the fractions by comparing the numerators, if they are the same we can compare the denominators.

So, the order from least to greatest temperature of the mixtures is:

-33 6/25℉ < -33 5/6℉ < -33 5/8℉

It's important to notice that these temperatures are negative.

Step-by-step explanation:

Answer:

[tex]\textsf{36)} \quad f(x)=\dfrac{7x}{x-12}[/tex]

[tex]\textsf{37)} \quad g(x)=\dfrac{1}{x+2}[/tex]

[tex]\textsf{38)} \quad h(x)=\dfrac{x-2}{(x-2)(x+3)}[/tex]

Step-by-step explanation:

Given that the function has a horizontal asymptote at y = 7, the degree of the numerator must be equal to the degree of the denominator.

Also, 7 will be the result of dividing the highest degree term of the numerator by the highest degree term of the denominator.

Given that the function has a vertical asymptote at x = 12, the denominator must equal zero when x = 12.

Therefore, a rational function that meets these conditions is:

[tex]f(x)=\dfrac{7x}{x-12}[/tex]

Given limits:

[tex]\displaystyle \lim_{x \to\infty} k(x)=0[/tex]

[tex]\displaystyle \lim_{x \to-2^+} k(x)=\infty[/tex]

The first limit means that as x approaches positive infinity, the function equals zero. Therefore, the rational function has a horizontal asymptote at y = 0. So the degree of the numerator should be less than the degree of the denominator.

The second limit means that as x approaches -2 from the positive side, the function equals positive infinity.  Therefore, the rational function has a vertical asymptote at x = -2.

Therefore, a rational function that meets these conditions is:

[tex]g(x)=\dfrac{1}{x+2}[/tex]

A removable discontinuity (hole) exists on the graph of a rational function at any input value that causes both the numerator and denominator of the function to be equal.

Therefore, a rational function that meets these conditions is:

[tex]h(x)=\dfrac{x-2}{(x-2)(x+3)}[/tex]

For this rational function the hole is at (2, ¹/₅), as when x = 2, the numerator and denominator are both zero.

The functions can be represented as y = 7x/(x - 7), y = 1/(x + 2) and y = (x - 3)/[(x - 3)(x + 1)]

Conditions #1

From the question, we have the following parameters that can be used in our computation:

Vertical asymptote, x = 12

Horizontal asymptote, y = 7

A function with the following features

Vertical asymptote, x = a

Horizontal asymptote, y = b

Can be represented as

y = bx/x - a

So, we have

y = 7x/(x - 12)

Conditions #2

Here, we have the following limits

lim x⇒∝ k(x) = 0 and lim x⇒2⁺ k(x) = ∝

This means that:

Vertical asymptote, x = -2

Using the rule in (1), we have

y = 1/(x + 2)

Condition #3

Here, we have

Function with a hole

This implies that the denominator and the numerator have a common factor

An instance of this is

y = (x - 3)/[(x - 3)(x + 1)]

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code, in communications, a dull rule for replacing a piece of information such as a letter, word, or phrase with a casually selected equivalent.

The term has been frequently exploiting and used as a synonym for cipher, which is a method for transforming a message according to a rule to cover its meaning.

In the past this hazy of the distinction between code and cipher was rather inconsequential; in fact, many historical aught would be more properly classified as codes according to present-day criteria.

In modern communications systems, information is frequently both encoded and encrypted (or enciphered), and so an understanding of the variation between the two is important.

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Answer: hi

Step-by-step explanation: hi

Answer:

10 cm

Step-by-step explanation:

Original measures: 400 m and 200 m

Scale: 1 cm = 40 m

Use proportions.

Length:

1 cm / 40 m = x / 400 m

40 m × x = 400 m × 1 cm

40x = 400 cm

x = 10 cm

length = 10 cm

Answer: 10 cm

The number of sequential coalitions is 13!

From the question, we have the following parameters that can be used in our computation:

System = [13: 14, 6, 4, 2]

This means that

n = 13

The number of sequential coalitiions is calculated as

Coalition = n!

substitute the known values in the above equation, so, we have the following representation

Coalition = 13!

Hence, the coalition is 13!

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Complete question

Consider the weighted voting system [13: 14, 6, 4, 2]

How many sequential coalitions are there?

Answer:

let the price in 2016= Y

Then the price since 2016 ( since the price decreased since 2016)= (1- 27/200)Y= 0.73Y

2016 since 2016

Y 0.73Y

Y now: 4803.40

0.73Y= 4803.40

Y= 4803.40/0.73

= 6580

the cost of the panel in 2016 is 6580

The two reasons why the shape is a square when x = 6 are:

i. It's length of sides are equal.

ii. The measure of it's internal angles are right angle.

A figure that is bounded by four straight sides on a 2 dimensional plane can be categorize as a quadrilateral. Examples are; rectangle, trapezium, rhombus, square etc.

A square is a shape which has an equal length of sides, and other distinguishing properties.

Considering the given question, when x = 6;

a. (3x - 7) = 3(6) - 7

              = 18 - 7

              = 11

b. (x + 5) = 6 + 5

              = 11

Therefore its sides are congruent.

Thus, the two reasons why the shape is a square are:

i. It has equal length of sides.

ii. It can be observed that each angle of the figure is a right angle.

So that the figure is a square.

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Answer:

Okay so Deondra has a total of $32, and if she buys 4 tickets, and if each costs 6.25, then, you will multiply the amount in which each ticket costs by how many tickets total, and then subtract that quotient by the total amount of money Deondra has.

6.25 times 4 = 25

32 - 25 = 7

She has $7 left to spend on popcorn!

Step-by-step explanation:

Hope it helps! =D

median set:130,140,149,150,159.Range set:10,20,149,159.

Step-by-step explanation:

Median:the value of a set that is arranged from lowest to highest and find the number that is right in between.If there are two numbers in the middle,add them and divide➗by two.Range:the difference between the highest and lowest number in a set.For example,the range for the set 10 20,38 and 50 , the highest and lowest numbers are 50 and 10 so we subtract 50-10 (the highest and lowest numbers) and get 40 as our range.

Answer:

0.1 ,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9, 1

As per the given radius, the parameterizations of this curve is 4

The term curve in math is defined as an abstract term used to describe the path of a continuously moving point

Here we have given that consider a circle of radius 2 centered at the origin.

And we have to find the parameterizations of this curve under the following assumption.

Here we have know that we need to find a parameterization for the circle of radius 2 in the xy-plane that one is centered at the origin at the direction of clockwise.

=> x(t) =  2cos(t) ------------------(1)

and

=> y(t) = −2sin⁡(t) -----------------(2)

Here we have to note that the given expression is written as,

=> x²(t) + y²(t)

When we apply the values on it then we get

=4cos²t⁡ + 4sin²t

Then it can be written as,

⁡=> 4(cos²t ⁡+ sin²t⁡)

=> 4

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Probability of getting a marble is 0.3.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Two boxes Probability of selecting either of the box = 0.5

Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,

let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )

Box contains : 3 blue and 5 red marbles,

let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )

So, the final probability of getting a blue ball is 0.3.

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Probability of getting a marble is 0.3.

Probability is a branch of math which deals with finding out the likelihood of the occurrence of an event. measures the chance of an event happening and is equal to the number of favorable events divided by the total number of events. The value of probability ranges between 0 and 1, where 0 denotes uncertainty and 1 denotes certainty.

Two boxes Probability of selecting either of the box = 0.5

Box A contains: 3 blue and 2 red marbles. So, probability of selecting blue marbles,

let p(B1) = [3C1/5C1 ]= 0.6*0.5 = 0.3 (As Probability of selecting box 1 is 50:50 )

Box contains : 3 blue and 5 red marbles,

let p(B2) = [3C2/5C2] = 0.6*0.5 = 0.3 ( As the probability of selecting box 2 is also 50:50 )

So, the final probability of getting a blue ball is 0.3.

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