simplify the expression -3 ^ (-2/5)

Answer:

\(\displaystyle m = \frac{1}{3}\)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Algebra I

Coordinate Planes

Slope Formula: \(\displaystyle m = \frac{y_2 - y_1}{x_2 - x_1}\)

Step-by-step explanation:

Step 1: Define

Identify.

Point (-2, 2)

Point (4, 4)

Step 2: Find slope m

Simply plug in the 2 coordinates into the slope formula to find slope m.

To program a Pascal matrix in Matlab, we need to use nested loops to calculate each element of the matrix based on the sum of the elements in the row above and the column to the left of it.

To program a Pascal matrix in Matlab, we first need to define the size of the matrix, say n. Then we can use nested loops to calculate each element of the matrix based on the rule described above.

The Matlab code for generating a Pascal matrix of size n can be written as follows:

A = zeros(n);

for i = 1:n

   for j = 1:n

       if i == 1 || j == 1

           A(i,j) = 1;

       else

           A(i,j) = A(i-1,j) + A(i,j-1);

       end

   end

end

Let's break down this code step by step.

First, we create a matrix A of size n x n and initialize all its elements to zero using the zeros function.

If the current element is not on the first row or first column, then we use the formula for a Pascal matrix to calculate its value. Specifically, we set the current element to be the sum of the element above it (i.e., A(i-1,j)) and the element to the left of it (i.e., A(i,j-1)).

Finally, after the loops have finished, the matrix A contains the full Pascal matrix of size n x n.

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Option D is the correct.

The given function f: R → R with the rule f(x) = 3x + 2. Let R represent the set of all real numbers.

What is a function?

A function is defined as the set of ordered pairs in which each first element of the ordered pair maps to one unique second element of the ordered pair.

What is an injective function?

A function f(x) is called one-to-one or an injective function, if and only if each and every element of the function domain is paired with exactly one element of the function range.

What is a surjective function?

A function f(x) is called onto or a surjective function, if and only if each and every element of the function range is paired with at least one element of the function domain.

What is a bijective function?

A function f(x) is called a bijection or a bijective function if it is both injective and surjective.

The given function is a function because for every x in R, there is exactly one image (3x+2) in R.

Let x₁, x₂ be two distinct real numbers in R, then3x₁ + 2 ≠ 3x₂ + 2, which implies f is injective or one-to-one.

Therefore, the given function f is both an injective function and a surjective function.

So, the function is a Bijective function

Option D is the correct choice. The given function f: R → R with the rule f(x) = 3x + 2 is Bijective function.

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Answer:

15 in³

Step-by-step explanation:

For cone:

V = (1/3)πr²h

For cylinder:

V = πr²h

The formulas are the same except for the 1/3 fraction in the formula for the volume of a cone. Since the formula for the cylinder does not have the fraction 1/3, if a a cylinder and a cone have the same radius and height, then volume of the cylinder is 3 times greater than the volume of the cone.

5 cu in. * 3 = 15 in.³

Answer: 15 in.³

x can be expressed in terms of y as: x = 2ln(y + e^(x/2)) + 2ln(e^(3x/2) - 1) + x

To solve for x in terms of y in the equation y=ex−e−x2, we can use natural logarithms. First, we can add e^(x/2) to both sides of the equation to get:

y + e^(x/2) = e^(x/2) * e^x - 1

Next, we can divide both sides by e^(x/2) to get:

(y + e^(x/2))/e^(x/2) = e^x - 1/e^(x/2)

Simplifying the right side using the exponent laws, we get:

(y + e^(x/2))/e^(x/2) = e^(3x/2) - 1

Now, we can take the natural logarithm of both sides of the equation to get:

ln[(y + e^(x/2))/e^(x/2)] = ln(e^(3x/2) - 1)

Using the logarithm laws, we can simplify the left side to:

ln(y + e^(x/2)) - ln(e^(x/2)) = ln(e^(3x/2) - 1)

Simplifying the logarithms using the exponent laws, we get:

ln(y + e^(x/2)) - x/2 = ln(e^(3x/2) - 1)

Finally, we can isolate x by adding x/2 to both sides and then multiplying by 2:

2ln(y + e^(x/2)) - x = 2ln(e^(3x/2) - 1) + x

x = 2ln(y + e^(x/2)) + 2ln(e^(3x/2) - 1) + x

To solve for x in terms of y using natural logarithms, given the equation:

y = e^x - e^(-x/2)

First, add e^(-x/2) to both sides of the equation:

y + e^(-x/2) = e^x

Now, take the natural logarithm of both sides. Recall that the natural logarithm is a logarithmic function with Euler's constant (approximately 2.71828) as its base:

ln(y + e^(-x/2)) = ln(e^x)

Using the property of logarithms that ln(a^b) = b*ln(a), we can simplify the right side of the equation:

ln(y + e^(-x/2)) = x*ln(e)

Since ln(e) = 1, the equation simplifies to:

ln(y + e^(-x/2)) = x

Finally, we have isolated x in terms of y:

x = ln(y + e^(-x/2))

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Answer:

52

Step-by-step explanation:

Answer:

8/2

Step-by-step explanation:

Answer:

7.65x10^-2

Step-by-step explanation:

Answer:

\(7.65*10^{-2}=0.0765\)

Step-by-step explanation:

All numbers in scientific notation or standard form are written in the form \(m*10^n\), where m is a number between 1 and 10 ( 1 ≤ |m| < 10 ) and the exponent n is a positive or negative integer.

First, move the decimal 2 times to right so that the resulting number, m = 7.65, is greater than or equal to 1 but less than 10

Since we moved the decimal to the right the exponent n is negative

n = -2

so then you would write it as:  \(7.65*10^-^2\)

I hope that wasn't confusing!

Hope this helps! o(〃＾▽＾〃)o

An experiment usually has three kinds of variables: independent, dependent, and controlled. The independent variable is the one that is changed by the scientist.

In mathematical modeling, statistical modeling, and experimental sciences, there are dependent and independent variables. Dependent variables get their name because, during an experiment, their values are investigated under the presumption or requirement that they are dependent on the values of other variables due to some law or rule.

The variable you alter, regulate, or change in an experimental study to examine its effects is known as an independent variable. It is named "independent" because it is unaffected by any other study variables.

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The exact binomial probability that the total number rolled will add up to 3 or less is 1/12.

The exact binomial probability that the total number rolled will add up to 3 or less is calculated as follows;

The total number that can be rolled with 2 dice is 2 to 12, with 7 being the most likely outcome (the sum of two dice has a maximum of 7).

The probability that the total number is 3 or less is the sum of the probabilities of rolling a 2 and a 1;

The probability P = (1/36) + (2/36)

P = 3/36

P = 1/12

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The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a conversion factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn.

(a) The given units can be converted as follows: 6 glints = 1 filn...

(1)12 grees = 1 zool...

(2)2 grees = 10 twibbs...

(3)5 grees = 1 bic...

(4)Note that the grees are in both the numerator and denominator of the second unit conversion factor (3). Hence we can cancel out the grees by using it twice in the numerator and denominator. Now using the given conversion factors in equation (1), we get:

7 glint/twibb=7 glint/ (10 grees/2 grees)=14 glint/10 grees=14 glint/ (5 grees/12 grees)=16.8 filn/strord

(b) We need to convert the result of part (a) from filn/strord to megafiln/strord.

1 mega = 106

Thus 1 megafiln = 106 filn

16.8 filn/strord = (16.8 filn/strord) x (1 megafiln/106 filn) = 1.68 x 10-5 megafiln/strord

The number of megafilns-per-strord should be smaller than the number of filns-per-strord since a mega is a factor of 10³ and is greater than 1, hence 1 megafiln is greater than 1 filn. Similarly, going 1 foot-per-hour would mean going a smaller number of feet-per-hour than going 1 mile-per-hour since there are 5280 feet in a mile.

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First, by solving for y, convert the equation of the given line into slope-intercept form y=mx+c .You obtain the slope of the equation as m. Since the slopes of perpendicular lines are negative reciprocal, the slope of the line we're looking is the negative reciprocal of the perpendicular equation.

By entering the supplied point into the formula y = mx + b and solving for b, we arrive at the value of b. Consequently, the line's equation is formed.

A line's slope in mathematics is defined as the ratio of the change in the y coordinate to the change in the x coordinate.

Both the net change in the y-coordinate and the net change in the x-coordinate are denoted by Δy and Δx, respectively.

m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

A line's slope often indicates the steepness and direction of the line.

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m = y/x = y/x = change in y/change in x

where "m" represents a line's slope.

Additionally, the slope of the line may be shown as

tan θ = Δy/Δx

The resultant velocity and acceleration for the given parametric equations x = 3.50T^2 , y = 20.0+ 0.120* - 3.00T^4+1    (0 < t < 4.00s) is equal to  768.5 m/s and  576.04 m/s².

Parametric equations is,

x = 3.50T^2

y = 20.0+ 0.120* - 3.00T^4+1    (0 < t < 4.00s)

The resultant velocity and acceleration of a skier at t = 4.00 seconds,

First find the velocity and acceleration vectors at that time.

The velocity vector is the first derivative of the position vector with respect to time,

r(t) = (x(t), y(t))

v(t) = dr/dt = (dx/dt, dy/dt)

Taking the derivatives of the given parametric equations, we get,

dx/dt = 7T

dy/dt = -12.0T^3

Substituting t = 4.00 seconds, we get,

dx/dt = 7(4.00)

        = 28.00 m/s

dy/dt = -12.0(4.00)^3+1

        = -12.0(64)

        = -768 m/s

So the velocity vector at t = 4.00 seconds is,

v(4.00) = (28.00,  -768 )

The acceleration vector is the second derivative of the position vector with respect to time,

a(t)

= dv/dt

= (d²x/dt², d²y/dt²)

Taking the derivatives of the velocity components we found earlier, we get,

d²x/dt² = 7

d²y/dt² = -36.0t²

Substituting t = 4.00 seconds, we get,

d²x/dt² = 7

d²y/dt² = -36.0(4.00)²

           = -576

So the acceleration vector at t = 4.00 seconds is,

a(4.00) = (7, -576)

To find the resultant velocity and acceleration,

The magnitude of each vector,

|v(4.00)|

= √(28.00)² + (-768)²)

= 768.5

|a(4.00)|

= √((7)² + (-576)²)

= 576.04 m/s²

Therefore, the resultant velocity at t = 4.00 seconds is 768.5 m/s, and the magnitude of the acceleration vector at t = 4.00 seconds is 576.04m/s².

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The given question is incomplete, I answer the question in general according to my knowledge:

A ski jump is designed to follow the path given by the parametric equations: x = 3.50T^2,  y = 20.0+ 0.120* - 3.00T^4+1 ,  (0 < t < 4.00s) where distances are in meters Find the resultant velocity and the acceleration of a skier when t = 4.00 sec.

Answer:

of(x) = (x-7)(x-5)(x - 5)(x + 2)

Step-by-step explanation:

The weight of the last fish wouid be 3.8kg

The weight of the last fish can be determined as follows :

sum of weight of the first 7 fishes :

Mean weight = 4.5125

Let the weight of last fish = x

(32.3 + x )/8 = 4.5125

32.3 + x = 36.1

x = 3.8

Therefore, the weight of the last fish wouid be 3.8 kg

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Answer:

Contents of this laser is 0.744 um and is a concise description of many of the in struments used in

Step-by-step explanation:

1.Introduction for the Royal College of Ophthalmologists and Ophthalmologists and I will #ثوره_طلابية غاضبة على قرار وزاره التعليم العالي باصدارها القرار المجحف وعليه يبداء من الان الاعتصام الطلاب #والاضراب_عن_الدوام لحين تحقيق المطالب.

تعليم الكتروني = امــتـحـان الكتروني

تعليم حضوري = امــتـحـان حضوري07725134341

Since, LHS = RHS = 0, They are the roots of equation.

Answer:

Proof below.

Step-by-step explanation:

Quadratic Formula

\(x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when }\:ax^2+bx+c=0\)

Given quadratic equation:

\(5x^2-6x-2=0\)

Define the variables:

Substitute the defined variables into the quadratic formula and solve for x:

\(\implies x=\dfrac{-(-6) \pm \sqrt{(-6)^2-4(5)(-2)}}{2(5)}\)

\(\implies x=\dfrac{6 \pm \sqrt{36+40}}{10}\)

\(\implies x=\dfrac{6 \pm \sqrt{76}}{10}\)

\(\implies x=\dfrac{6 \pm \sqrt{4 \cdot 19}}{10}\)

\(\implies x=\dfrac{6 \pm \sqrt{4}\sqrt{19}}{10}\)

\(\implies x=\dfrac{6 \pm2\sqrt{19}}{10}\)

\(\implies x=\dfrac{3 \pm \sqrt{19}}{5}\)

Therefore, the exact solutions to the given quadratic equation are:

\(x=\dfrac{3 + \sqrt{19}}{5} \:\textsf{ and }\:x=\dfrac{3 - \sqrt{19}}{5}\)

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Answer:

the formula of volume is:

V=πr2h/3

Answer: V=πr2h/3

The volume of a cone = (1/3) πr2h cubic units Where, ‘r’ is the base radius of the cone

step by step explanation:

Since a cone is a pyramid whose base is circular, therefore, the volume of a cone is: Volume = 1/3 πr²h The volume of irregular solids Since not all solids are regular in shape, their volumes cannot be determined using a volume formula.

Hope this helps!

Kayla-

Answer:Yes

Step-by-step explanation: Without parentheses, this equation equals 44. Put the parentheses around 8-4 to make the equation true

Answer:

you forgot the number before times

Step-by-step explanation:

For the 6th point, the answer is PR because this is the formula from the Pitagoras theorem, PT and RT are the hicks, so PR is the hypotenuse.

For the 7th point, the answer is QR because this is the formula from the Pitagoras theorem, QT and RT are the hicks, so QR is the hypotenuse.

The value of upper quartile of the box plot is, 350.

We have to given that;

the Creekview History Museum kept track of how many people visited the museum each day last month.

Now, We know that;

The value of upper quartile of the box plot shown in right side of box.

Hence, By given box plot;

The value of upper quartile of the box plot is,

⇒ 350.

Thus, The value of upper quartile of the box plot is, 350.

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Answer:

A

Step-by-step explanation:

12≤x+14                subtract 14 by both sides

-2 ≤ x

this means x is greater than or equal to -2

hope this helped have a great day :)

Answer:

(-2,3)

Step-by-step explanation:

When a point is reflected over the Y axis, the coordinate changes. the Y coordinate stays the same.

Answer:

Population in 15 year= 475

Step-by-step explanation:

.035x459=16

16+459=475 estimate

Answer:

B.  p - 200

Step-by-step explanation:

Start with the original price, p.

When the price is reduced by $200, you are taking away $200 from the price, so you need to subtract $200 from the original price, p.

Answer:  B.  p - 200

Varying 'a' in the equation og graph \(y = a(x-2)^2 + 5\) changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).

A graph is a visual representation of data or information that displays a relationship or pattern between two or more variables.

The graph of \(y = a(x-2)^2 + 5\) is a quadratic function that has been shifted 2 units to the right and 5 units up from the standard form of \(y = x^2.\) The variable 'a' represents the vertical stretch or compression factor of the parabola.

In summary, varying 'a' in the equation \(y = a(x-2)^2 + 5\) changes the steepness and orientation of the parabolic curve, while keeping the vertex fixed at (2, 5).

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Answer:

i dont know

Step-by-step explanation:

False. The columns of matrix P are not necessarily eigenvectors of matrix A. While the diagonal matrix D contains the eigenvalues of A, the eigenvectors are not explicitly determined by the columns of P.

False. The columns of matrix P are not guaranteed to be eigenvectors of the transpose of matrix A (A.T).

In the given equation, \(a = PDP^(-1),\)

where D is a diagonal matrix and P is an invertible matrix.

The diagonal elements of D represent the eigenvalues of matrix A, while the columns of P correspond to the eigenvectors of A.

When considering the transpose of matrix A (A.T), we have \((A.T) = (PDP^(-1)).T = (P^{(-1)})^T D^T P^T.\)

Taking the transpose of a product involves reversing the order of the matrices and transposing each matrix individually.

Therefore, we have \((A.T) = P^T D^T (P^{(-1)})^T.\)

Since P is an invertible matrix, its transpose \(P^T\) is also invertible. Similarly, the transpose of the inverse of \(P, (P^{(-1)} )^T,\) is also invertible.

However, the key point is that the diagonal matrix\(D^T\) is not guaranteed to have the same eigenvalues as matrix A.

The eigenvalues of A are present in D, but they may not remain on the main diagonal after transposing.

Thus, the columns of matrix P, which correspond to the eigenvectors of A, may not necessarily be the eigenvectors of A.T.

In conclusion, the statement is false.

The columns of matrix P do not have to be eigenvectors of the transpose of matrix A (A.T).

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Answer:

452.39cm^2

Step-by-step explanation:

Answer:

-XxanimexX