What is the range of the function y = 4 - 3x, when the domain is {0, 1, 2, 3,}

The derivative of the function f(x) = 390 by using the rules of differentiation is f'(x) = 0.

To find the derivative of the function f(x) = 390, we can apply the rules of differentiation.

In this case, the function f(x) = 390 is a constant function, which means it does not depend on the variable x. The derivative of a constant function is always zero.

Therefore, the derivative f'(x) of the function f(x) = 390 is:

f'(x) = 0

The derivative of a constant function is zero because a constant value does not change with respect to the variable x. So regardless of the value of x, the rate of change of the function is always zero.

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Answer:

10400MM

1.04 litre

Step-by-step explanation:

volume = length x width x height

13 x 8 x 10 = 1040 cm^3

1cm = 10 mm

1040 x 10 = 10400MM

1cm = 0.001 litres

1040 x 0.001 = 1.04 l

Answer:

7

Step-by-step explanation:

because 1 = 400

2800 divided by 400 = 7

The length and width of the rectangle with perimeter 254 yards are 57 and 70 yards respectively.

Perimeter of rectangle is 2(Length + width)

Given,

Perimeter of rectangle = 254 yards

Width = Length+ 13

Consider the Length of the rectangle as "x". Thus, width of the rectangle is x+13 ( as it is 13 yards more than the Length ).

Put the value in the formula.

=> 254 = 2(x+x+13)

=> 254 = 2(2x+13)

=> 254 -26 = 4x

=> 228= 4x

=>  x = 57 (length)

=>  x+13= 70( width)

Therefore, we get length = 57 yards and width = 70 yards.

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Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Histograms are an effective way to display data graphically. They are used to show how often certain values or ranges of values appear in a data set. Visual interpretation of histograms has many strengths and limitations. Some of the strengths of visually interpreting histograms are that they are easy to read and understand, they provide a clear picture of how the data is distributed, and they can help identify outliers or gaps in the data. However, some of the limitations of visually interpreting histograms are that they can be influenced by the number of bins chosen, the way the data is grouped, and the choice of the scale used. Therefore, it is important to carefully consider these factors when interpreting a histogram. In conclusion, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

Therefore, visually interpreting histograms can be a powerful tool for data analysis, but it is important to be aware of their strengths and limitations.

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\(\tan 60^{\circ}~\text{equals y coordinate divided by x coordinate, where }(x,y) = \left(\dfrac 12, \dfrac{\sqrt 3}2 \right)\)

\(\tan 60^{\circ}\\\\= \dfrac yx \\\\\\=\dfrac{\sin 60^\circ}{\cos 60^\circ}\\\\\\=\dfrac{\tfrac{\sqrt 3}2}{\tfrac 12}\\\\\\=\dfrac{\sqrt 3}2 \times 2\\\\\\=\sqrt 3\)

This rule is enough

Now

Here A=60°

Here, we are supposed to find the value of the stock. Let's begin by determining the expected dividends: Expected dividends1st year dividend (D1)

= $1.55(1 + 26.56%)

= $1.96Second-year dividend (D2) = $1.96(1 + 26.56%) = $2.48Third-year dividend (D3)

= $2.48(1 + 26.56%)

= $3.

= D1/(1+r)^1 + D2/(1+r)^2 + D3/(1+r)^3 + D4/(1+r)^4...∞Where r

= required rate of return Let us substitute the values now PV of the future dividends

= $1.96/(1 + 14.40%)^1 + $2.48/(1 + 14.40%)^2 + $3.14/(1 + 14.40%)^3 + $3.25/(1 + 14.40%)^4...∞PV of the future dividends = $1.96/1.1440^1 + $2.48/1.1440^2 + $3.14/1.1440^3 + $3.25/1.1440^4...∞PV of the future dividends

= $1.72 + $1.92 + $2.04 + $1.86...∞PV of the future dividends

= $7.54We know that the value of the stock is the present value of the expected dividends, so we can calculate it as follows: Value of the stock

= PV of the future dividends Value of the stock

= $7.54

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Answer:

It would be D

Step-by-step explanation:

The angle whose vertex is on the circle and the sides of the angle are the chords is called an Inscribed Angle .

What is an Inscribed Angle ?

An inscribed angle in the circle is formed by the two chords which have a common end point on circle and this common end point is called the vertex of inscribed angle.

The arc formed by the inscribed angle in the circle is called as the intercepted arc .

also the Inscribed Angle Theorem states that inscribed angle on the circle is half the measure of central angle that subtends the same arc .

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the intersect when both graphs are equal to each other, so we can say

\(\begin{cases} y=-3x+7\\\\ y=x^2-4x+1 \end{cases} \\\\[-0.35em] ~\dotfill\\\\ -3x+7~~ = ~~x^2-4x+1\implies 7=x^2-x+1\implies 0=x^2-x-6 \\\\\\ 0=(x-3)(x+2) \implies x= \begin{cases} 3\\ -2 \end{cases}\)

now, when "x" is those values, for the line, let's find out what's "y".

\(y(3)=-3(3)+7\implies y(3)=-2\hspace{7em}(3~~,~-2) \\\\\\ y(-2)=-3(-2)+7\implies y(-2)=13\hspace{5em}(-2~~,~~13)\)

now, let's use those two points at the intersection of the two graphs to get their distance

\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ A(\stackrel{x_1}{3}~,~\stackrel{y_1}{-2})\qquad B(\stackrel{x_2}{-2}~,~\stackrel{y_2}{13})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ AB=\sqrt{(~~-2 - 3~~)^2 + (~~13 - (-2)~~)^2}\implies AB=\sqrt{(-2 -3)^2 + (13 +2)^2} \\\\\\ AB=\sqrt{ (-5)^2 + (15)^2} \implies AB=\sqrt{ 25 + 225} \\\\\\ AB=\sqrt{ 250 }\implies AB\approx 15.81\)

Answer:

7 cm and 49 cm²

Step-by-step explanation:

(a)

A square has 4 equal sides , then

28 cm ÷ 4 = 7 cm

The length of each side of the square is 7 cm

(b)

The area (A) of a square is

A = s² ( s is the side length ) , then

A = 7² = 49 cm²

Answer:

Step-by-step explanation:

Perimeter of square will be equal to the length of the  string

Perimeter of square = 28 cm

4*side = 28

Divide both sides by 4

Side = 28/4

Side = 7 cm

b) Area of square = side * side

                             = 7 * 7

                             =49 cm²

The observed allele frequencies for the T102C locus are as follows: T allele frequency = 0.388 and C allele frequency = 0.612.


To calculate the observed allele frequencies, we divide the number of occurrences of each allele by the total number of alleles observed.

In this case, the T allele is observed in 108 TT genotypes and 194 TC genotypes, giving a total of 108 + 194 = 302 T alleles. Similarly, the C allele is observed in 194 TC genotypes and 48 CC genotypes, giving a total of 194 + 48 = 242 C alleles.

To calculate the T allele frequency, we divide the number of T alleles by the total number of alleles: 302 T alleles / (302 T alleles + 242 C alleles) = 0.388 (or approximately 0.39).

Similarly, the C allele frequency is calculated as: 242 C alleles / (302 T alleles + 242 C alleles) = 0.612 (or approximately 0.61).

Therefore, the observed allele frequencies for the T102C locus are T allele frequency = 0.388 and C allele frequency = 0.612.

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Answer:

C

Step-by-step explanation:

Third expression asks you to basically divide by zero. That is, find a number that multiplied by 0 gives you 3, which is impossible.

Hello!

-----------------------------------------------------------------------------------------------------------------

Option C

Division by 0 is undefined.

6-6=0, and any expression that has 0 it its denominator is undefined.

I hope it helps you! (:

~SparklingFlower

-----------------------------------------------------------------------------------------------------------------

The value of \(\left[\begin{array}{ccc}(2^{x}+2^{-x})^{2} &(2^{x}-2^{-x})^{2}&1\\(3^{x}+3^{-x})^{2}&(3^{x}-3^{-x})^{2}&1\\(4^{x}+4^{-x})^{2}&(4^{x}-4^{-x})^{2}&1\end{array}\right]\) is 0.

A matrix is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns.

\(\left[\begin{array}{ccc}(2^{x}+2^{-x})^{2} &(2^{x}-2^{-x})^{2}&1\\(3^{x}+3^{-x})^{2}&(3^{x}-3^{-x})^{2}&1\\(4^{x}+4^{-x})^{2}&(4^{x}-4^{-x})^{2}&1\end{array}\right]\)=0

As we observe the given determinant the all the row has same elements but the operation is different, in first term there is plus and in second term the operator is minus.

The last column has 1.

When we apply the determinant rule we get 0.

Hence, the value of \(\left[\begin{array}{ccc}(2^{x}+2^{-x})^{2} &(2^{x}-2^{-x})^{2}&1\\(3^{x}+3^{-x})^{2}&(3^{x}-3^{-x})^{2}&1\\(4^{x}+4^{-x})^{2}&(4^{x}-4^{-x})^{2}&1\end{array}\right]\) is 0.

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Answer:

=425832

Step-by-step explanation:

i hope this helps :)

Answer:

425832

Step-by-step explanation:

I was trying as well gg

The equation relating L to D is; L = 9 + D

Please find attached the graph of L = 9 + D, created with MS Excel

An equation is a statement of equivalence between two expressions, and a function maps a value in a set of input values to a value in the set of output values.

The initial length of the road = 9 miles

The length of road the construction crew is adding each day = 1 mile

The length in mile of the road after D days = L

The equation for the length is therefore;

The graph of the length of the road can therefore be obtained from the equation for the length by plotting the ordered pairs obtained from the equation.

Please find attached the graph of the equation created using MS Excel.

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The given differential equation is not linear because it involves the product of x and t. However, it is separable, and we can integrate both sides to find the solution.

The given equation is 9xt(dx/dt) = e^x. To determine whether this equation is separable, linear, or both, we need to rearrange it into a standard form.

Dividing both sides by 9xt, we get:

(dx/dt) = e^x / 9xt

This equation is not linear because it involves the product of x and t in the denominator. However, it is separable because we can separate the variables x and t by writing the equation as:

9xt(dx/dt) = e^x

9x dx = e^x dt/t

Integrating both sides, we get:

4.5x^2 = ln|t| + C

where C is the constant of integration.

Therefore, the given equation is separable but not linear.

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Answer:

Step-by-step explanation:

The graph of y= -3/2x + 1 is given in attachment with slope -3/2.

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

The slope intercept form of a line is y=mx+b, where m is slope and b is the y intercept.

The slope of line passing through two points (x₁, y₁) and (x₂, y₂) is

m=y₂-y₁/x₂-x₁

The given line is  y= -3/2x + 1

slope is -3/2

We have to find few values of x and y.

When x=0

y=1

When x=1

y=-1/2

When x=2

y=-2

Hence, the graph of y= -3/2x + 1 is given in attachment with slope -3/2.

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Answer:

0. Amount of commission = $5,160

1. Linda's gross pay = $7,470

Explanation:

Part 1

Linda's sales for last month = $64,500

She is paid an 8% commission on merchandise she sells.

Therefore:

Amount of commission = 8% of $64,500

=8/100 x 64,500

=0.08 x 64,500

=$5,160

Part 2

Linda's Gross Pay = Monthly salary + Commision

=2,310 + 5,160

=$7,470

Linda's gross pay is $7,470

We know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.

It's possible to multiply, divide, add, or subtract with this mathematical operation.

An expression in mathematics is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division, etc.)

So, the given expressions are:

7x - 4 and 6x - 4 - x

Now,

7x - 4 and 6x - x - 4

7x - 4 and 5x- 4

Then, we can easily say that the given expressions are not equivalent.

Therefore, we know that the given expression 6x - x - 4 is (2) this is not equivalent to 7x − 4.

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Complete questions:
Explain how you can tell if the expressions 7x – 4 and 6x – 4 – x are equivalent. Sample Response: 6x − x = 5x.

1. The new expression is now 5x − 4.

2. This is not equivalent to 7x − 4.

Answer:

5000 worth car after 5 years

The equation of the sine wave function can be written in the form: y = A sin(Bθ + C) + D where A is the amplitude, B is the frequency (inverse of the period), C is the phase shift (horizontal shift), and D is the vertical shift (mean value).

A graph is a visual representation of data or mathematical relationships between variables. It typically consists of a set of points or vertices connected by lines or curves, which can help to illustrate patterns or trends in the data. Graphs are used in a wide range of fields, including mathematics, science, engineering, economics, and social sciences, to analyze and communicate information. Some common types of graphs include line graphs, bar graphs, scatterplots, and pie charts.

Here,

Based on the given information, it can be inferred that the function that describes the relationship between the height y, in feet, of the tip of a windmill blade and the angle of rotation Θ made by the blade is a sine wave function. Sine wave functions are periodic and oscillate between an upper bound and a lower bound as the angle increases. The function has a maximum value (upper bound) at Θ=90° and Θ=270° and a minimum value (lower bound) at Θ=0° and Θ=180°. The amplitude of the function is the distance between the maximum and minimum values divided by 2, and the period of the function is the distance between two consecutive maxima or minima.

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Answer:

$1200

Step-by-step explanation:

5% of $3000 = $150

multiply 8 by $150 = $1200

Answer:

\(a=60\\b=44\\c=76\)

Step-by-step explanation:

You can write these equations to represent the problem:

\(a+b+c=180\\b+c=2a\\b=c-32\)

Now, just solve it as a system of equations. I'll solve by substitution, starting from the bottom as b is already defined there.

\(b=c-32\\b+c=2a\\(c-32)+c=2a\\c+c-32=2a\\2c-32=2a\\a=c-16\)

That's the middle equation done, now I'll do the top one:

\(b=c-32\\a+b+c=180\\a+(c-32)+c=180\\a+2c-32=180\\a+2c=212\\a=-2c+212\)

Now we have just 2 equations with 2 variables. That's another system of equations, but this one is much easier to solve. Using substitution again:

\(a=c-16\\a=-2c+212\\c-16=-2c+212\\3c-16=212\\3c=228\\c=76\)

Finally, we have one variable solved. Using the value of C, now we can solve for A:

\(c=76\\a=c-16\\a=76-16\\a=60\)

Thats 2 done. Now, pick any equation that has all 3 variables and solve for B:

\(a=60\\c=76\\a+b+c=180\\60+b+76=180\\b+136=180\\b=44\)

All 3 variables done.

\(a=60\\b=44\\c=76\)

Now, we can confirm that they're correct by checking with the original equations:

\(a+b+c=180\\60+44+76=180\\180=180\\\\b+c=2a\\44+76=2(60)\\120=120\\\\b=c-32\\44=76-32\\44=44\)

They all work fine.

(a) The fundamental matrix for the given system of equations is Φ(t) = e^(At).

Let's denote the given coefficient matrix as A:

A = [ -1 -4

      1 -1 ]

The fundamental matrix Φ(t) for the system is given by the matrix exponential of the coefficient matrix A multiplied by t:

Φ(t) = e^(At)

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

Finding the fundamental matrix φ(t) satisfying φ(0) = I:

To find the fundamental matrix φ(t) satisfying φ(0) = I, we substitute t = 0 into Φ(t):

φ(0) = Φ(0) = e^(A * 0) = e^(0) = I

So, the fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix.

In summary, for the given system:

(a) The fundamental matrix Φ(t) is e^(At).

(b) The fundamental matrix φ(t) satisfying φ(0) = I is the identity matrix, denoted as φ(t) = I.

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The equation amplitude of motion is 1/3 ft, the period is 1.005 seconds, and the frequency is 0.995 Hz.

The equation of motion, amplitude, period, and frequency of the system, Hooke's Law and the equation of motion for simple harmonic motion.

m₁ = 25 lb (mass of the first weight)

m₂ = 16 lb (mass of the second weight)

k = spring constant

Using Hooke's Law, F = -kx, where F is the force exerted by the spring and x is the displacement from the equilibrium position.

For the 25 lb weight:

Weight = m₁ × g (where g is the acceleration due to gravity)

Weight = 25 lb × 32.2 ft/s² =805 lb·ft/s²

Since the spring is stretched by 6 in (or 0.5 ft),

805 lb·ft/s² = k × 0.5 ft

k = 1610 lb·ft/s²

For the 16 lb weight:

Weight = m₂ × g

Weight = 16 lb × 32.2 ft/s² =515.2 lb·ft/s²

Since the 16 lb weight is pulled down by 4 in (or 1/3 ft) below its equilibrium position, we have:

515.2 lb·ft/s² = k × (0.5 ft + 1/3 ft)

k = 1557.6 lb·ft/s²

Since the system is in equilibrium at the start, the total force acting on the system is zero. Therefore, the spring constants for both weights are equal, and k = 1557.6 lb·ft/s² as the spring constant for the equation of motion.

consider the equation of motion for the system:

m₁ × x₁'' + k ×x₁ = 0 (for the 25 lb weight)

m₂ × x₂'' + k × x₂ = 0 (for the 16 lb weight)

Simplifying the equations,

25 × x₁'' + 1557.6 × x₁ = 0

16 × x₂'' + 1557.6 × x₂ = 0

To solve these second-order linear homogeneous differential equations, solutions of the form x₁(t) = A₁ ×cos(ωt) and x₂(t) = A₂ * cos(ωt), where A₁ and A₂ are the amplitudes of the oscillations, and ω is the angular frequency these solutions into the equations,

-25 × A₁ × ω² ×cos(ωt) + 1557.6 × A₁ × cos(ωt) = 0

-16 × A₂ × ω² × cos(ωt) + 1557.6 × A₂ × cos(ωt) = 0

Simplifying,

(-25 × ω² + 1557.6) × A₁ = 0

(-16 × ω² + 1557.6) ×A₂ = 0

Since the weights are not at rest initially,  ignore the trivial solution A₁ = A₂ = 0.

For nontrivial solutions,

-25 × ω² + 1557.6 = 0

-16 × ω² + 1557.6 = 0

Solving these equations,

ω = √(1557.6 / 25) ≈ 6.26 rad/s

ω = √(1557.6 / 16) ≈ 6.26 rad/s

The angular frequency is the same for both weights, so use ω = 6.26 rad/s.

The period T is given by T = 2π / ω, so

T = 2π / 6.26 ≈ 1.005 s

The frequency f is the reciprocal of the period, so

f = 1 / T ≈ 0.995 Hz

Therefore, the equation of motion for the system is:

x(t) = A × cos(6.26t)

The amplitude A is determined by the initial conditions. Since the 16 lb weight is released with an initial velocity of 2 ft/s upward, it will reach its maximum displacement at t = 0. At this time, x(0) = A = 1/3 ft (since it is 1/3 ft below the equilibrium position).

So, the equation of motion for the system is:

x(t) = (1/3) × cos(6.26t)

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Answer:

Answer: Proved: the difference between squares of consecutive even numbers is always a multiple of 4. ... From the results above, we can see that 12, 20, and 28 are multiples of 4. Therefore, the difference between squares of consecutive even numbers is always a multiple of 4.

Step-by-step explanation:

Answer:

Step-by-step explanation:

Let's call the numbers n and n + 2.

(n + 2)² - n²

= n² + 4n + 4 - n²

= 4n - 4

= 4(n - 1)