Write the first six terms of the sequence, beginning with n=1. a(n)=60n Enter the numbers, separated by commas.

Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.

In the given question, we have to verify the linear approximation at (0, 0).

f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y

Let f(x, y) = √(y+cos^{2}x)

f(x, y) ≈ f(a, b)+fx(a, b)(x-a)+fy(y-b)

f(x) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex]

f(y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]

f(x, y) ≈ 1+0(x-0)(1/2)(y-0)

f(x, y) ≈ 1+1/2y

Hence, left f(x, y) = √(y+cos^{2}x). Then fx(x, y) = [tex]-\frac{1}{\sqrt{y-\cos^{2}x}}\sin x\cos x[/tex] and fy(x, y) = [tex]\frac{1}{2\sqrt{y-\cos^2x}}[/tex]. Both fx and fy are continuous functions for y >0 , so f is Differentiable at (0, 0) by this theorem. So the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)= 1+1/2y.

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The complete question is:

Verify the linear approximation at (0, 0). f(x, y) = √(y+cos^{2}x) ≈ 1 + 1/2y

Left f(x, y) = √(y+cos^{2}x). Then fx(x, y) =.............. and fy(x, y) = ............. Both fx and fy are continuous functions for y >............ , so f is Differentiable at (0, 0) by this theorem. We have fx(0, 0) =........... and fy(0, 0) =............. , so the linear approximation of f at (0, 0) is f(x, y) ≈ f(0, 0)+fx(0, 0)(x-0)+fy(0, 0)(y-0)=........

Perimeter of the NCAA court is 288288 ft

Perimeter of the new court is 259.2ft

Perimeter of NCAA court

=2(length +width)

=2(94ft+50ft)

=2⋅144ft

=288ft

The perimeter of the new court in the school:

=2(length +width)

=2(84.6ft+45ft)

=2⋅129.6ft

=259.2ft

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The change of score of the test score from 8 to 80, would have the greatest effect on A. Mean.

Numbers in a data collection that are significantly greater or smaller than the rest are known as outliers. The metrics of central tendency are mean, median, and mode. The only index of central tendency that is consistently impacted by an outlier is the mean.

The value of 8 was an outlier from the rest of the test scores and so it would have had a great effect on mean. If the score was taken back to 80, then the mean would be adjusted correctly and change the greatest.

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A transformation that leaves a geometric figure's size or shape unaltered is known as a rigid transformation (also known as isometry). is a unique type of metamorphosis in which a figure's size or shape are left unaltered.

During a rigorous alteration of the geometric object, the distance between each pair of its points is maintained. In other words, an object's size and shape are maintained through a hard transformation. For example, the rigid transformation of a triangle preserves the triangle's angles and lengths. Consider a rigid form distortion that resembles a cardboard shape.

There are translations, reflections, and isometric rotations. As a result, none of these changes have an impact on the figure's size. If neither the size nor the shape of the figures are changed, the figures are constant.

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The quadratic equation [tex]2x^{2}+3x-5=0[/tex] has a discriminant of 49.

In mathematics, a discriminant is a parameter that can be determined for an object or system to help with its classification or solution. If the discriminant is positive, the roots of a quadratic or cubic equation with real coefficients are real and distinct, if the discriminant is zero, the roots are real with at least two equal, and if the discriminant is negative, the roots include a conjugate pair of complex roots.

For an equation, [tex]ax^{2}+bx+c=0[/tex]

Discriminant, D = [tex]b^{2}-4ac[/tex]

Given in question,

[tex]2x^{2}+3x-5=0[/tex]

a = 2

b = 3

c = -5

D = [tex]3^{2}[/tex] - 4(2)(-5)

  = 9 + 40

  = 49

Hence, the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] is 49.

Correct Question :

What is the discriminant and nature of roots of [tex]2x^{2}+3x-5=0[/tex] ?

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First make the graph of the functions, then  if the two graphs are symmetric with respect to the line y = x (mirror images over y = x ), then they are inverse functions.

Symmetric

A figure or shape that can be divided into two equal parts by a line is called symmetric figures.

Inverse Functions

The inverse function of a function f  is a function that undoes the operation of f. The inverse of f exists if and only if f is bijective, and if it exists, is denoted by F^-1.

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Answer:

Just use Desmos

Step-by-step explanation:

To be a relation of a function for every value of x there must be a single value of y thus the given relation is not a function.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given table,

At x = 9

y = 9 and y = 3

Since at a single value of x there exist two values of y thus it will not be a function.

Hence "The provided relation is not a function since there must only be one value of y for a relationship to be considered a function.".

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An example of a complex equation is the Navier–Stokes equations, which are used to describe the motion of fluids and are one of the most important equations in fluid mechanics.

A complex equation is a mathematical expression that contains multiple variables, operations, and powers. This can include exponents, logarithms, trigonometric functions, and other variables. Complex equations can be used to solve problems or to make predictions, and can be used in a wide range of fields, including economics, engineering, and physics.

These equations consist of a set of partial differential equations that describe the motion of a fluid, such as air or water, and the forces acting on it. The Navier–Stokes equations are used to predict the behavior of liquids and gases in a wide range of applications, from aeronautics, to weather prediction, to oceanography.
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Answer: x=-1    x=1/3

Step-by-step explanation:

f(x)=3x²+2x-1

[tex]3x^2+2x-1=0\\\\3x^2+(3x-x)-1=0\\\\(3x^2+3x)-x-1=0\\\\3x(x+1)-(x+1)=0\\\\(x+1)(3x-1)=0\\\\x+1=0\\\\x=-1\\\\3x-1=0\\\\3x=1[/tex]

Divide both parts of the equation by 3:

[tex]\displaystyle\\x=\frac{1}{3}[/tex]

By using a² + b² = c² this formula we can find the missing length of a triangle.

A triangle is right-angled if one of the three angles is 90°, i.e., any two sides are perpendicular.

If we know two other sides of the right triangle, all you need to do is apply the Pythagorean theorem:

a² + b² = c²

a = √(c² - b²)

b = √(c² - a²)

c = √(a² + b²)

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Answer:

1d=25m

30d=?

cross mutiply

30×25=750messages

Answer:

The equation is m = 25d

Ashley would send 750 text messages after 30 days.

Step-by-step explanation:

The equation is y = mx + b

We see that each day the number of text increase by 25, so our equation is

m = 25d

Now we ask how many text messages Ashley would send in 30 days. We need to put 30 in for d and solve it.

m = 25(30)

m = 750 text messages

So, Ashley would send 750 text messages in 30 days.

Answer:

5.22 is the answer required

The value of 0 1 is 1.

This is because any number to the power of 0 is equal to 1. This is part of the fundamental rules of exponents in mathematics. For example, if we take 2 to the power of 0, that would be equal to 2^0=1.

Similarly, 5^0=1, and so on. This is because any number to the power of 0 is equal to 1, regardless of the number. This is because any number multiplied by 1 is equal to itself. This holds true for 0 as well, and so 0^1=1. This is why the value of 0 1 is 1.

This is a basic mathematical equation in which the answer is 1. This equation can be used to illustrate the concept of addition, which is the process of combining two numbers to get a total.

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As the correlation coefficient moves from 0 to 1 or -1 to 0, the points would be closer to the line. Option A

The term correlation coefficient is used to show the level of the relationship between the variables. If the correlation coefficient is very close to 1 then it means that there is greater association between the variables. If it is far from one then it means that the variables are not associated at all.

We know that the regression lines show how variables can be associated and they can be used to show us the relationship between variables.

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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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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

According to the properties of geometry the correct option is C.

What is geometry?

The study of measurements, sizes, shapes, locations, angles, and proportions of objects is known as geometry.

Dilation represents the enlargement and compression of a figure. Whether it is an enlargement or compression, It totally depends on the scale factor.

If the absolute value of scale factor is more than 1, then it represents the enlargement and if the absolute value of scale factor is lies between 0 to 1, then it represents the compression.

Image and preimage are similar figures. It means the corresponding angles are congruent or corresponding sides are proportional.

It is given that LMN is dilated by a scale factor of 0.5.

Since scale factor is lies between 0 to 1, therefore it shows the compression.

Therefore sides of L'M'N' is smaller than LMN.

Since corresponding angles of similar figure are congruent.

So, options A, B and D represent the correct statements. Only option C represents a false statement because the sides of similar figure are proportional not congruent.

Therefore option C  is correct.

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The coefficients in a balanced equation compare quantities of two substances by the ratio of the substances' coefficients equals the ratio of their number of moles.

A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

In many chemical situations, mole ratios are employed as conversion factors between products and reactants.

In a balanced chemical equation, the coefficients in front of the formulae can be used to determine the mole ratio.

Complete question:

How do the coefficients in a balanced equation compare quantities of two substances?

A. The ratio of the coefficients equals the ratio of the masses of the

substances

B. The sum of the coefficients of the reactants equals the sum of the

products

C. The ratio of the substances' coefficients equals the ratio of their

number of moles.

D. The coefficient of the reactant tells how many product molecules

will form.

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A mole is defined as 6.02214076 × 10²³ of some chemical unit, be it atoms, molecules, ions, or others. The mole is a convenient unit to use because of the great number of atoms, molecules, or others in any substance.

In many chemical situations, mole ratios are employed as conversion factors between products and reactants.

Complete question:

How do the coefficients in a balanced equation compare quantities of two substances?

A. The ratio of the coefficients equals the ratio of the masses of the

substances

B. The sum of the coefficients of the reactants equals the sum of the

products

C. The ratio of the substances' coefficients equals the ratio of their

number of moles.

D. The coefficient of the reactant tells how many product molecules

will form.

Answer: 0

Step-by-step explanation:

The slope of a line that contains the points (13, -2) and (3, -2) would be 0, since the y-coordinate of both points is the same. The slope of a line is determined by the difference in the y-coordinates of the two points, divided by the difference in their x-coordinates. In this case, the difference in the y-coordinates is 0, so the slope is 0.

Triangles are singular because you can only ever draw one. A triangle can be created using two side lengths and the angle's measurement.

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Answer:

Step-by-step explanation:

3000000000000000000000000000000000000

Using the concept of limit, As the x tends to -infinity value, In the expression f/x, The answer is f/x tends to large(infinity) value with negative magnitude.

A limit in mathematics is the value that a function gets closer to when the input gets closer to a certain value. Calculus and mathematical analysis are not possible without limits, which are also required to determine continuity, derivatives, and integrals. A limit describes the value that a function approaches as its inputs approach a certain value. All calculus is based on the concept of a limit.

According to product law for limits, the limit of a product of functions is equal to the sum of the limits of each individual function. The limit of a quotient of functions is equal to the quotient of the limit of each function, according to the quotient law for limits.

as [tex]\lim_{x \to \infty} \frac{f}{x}[/tex]

=f/ -infinity

=- [infinitely large value]

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The solution to the system of equations is x = 3/2 and y = 7/4.

The given system of equations can be written as:

y = -x^2 + 4

y = 2x + 1

To solve this system of equations, we can use the substitution method. First, we'll substitute the expression for y in the second equation into the first equation. We can then solve the resulting equation for x.

In the first equation, [tex]y = -x^2 + 4[/tex] . Substituting this expression into the second equation, we get:

[tex]-x^2 + 4 = 2x + 1[/tex]

We can rearrange the terms on the left side of the equation to solve for x. To do this, we'll subtract 4 from both sides, then add x^2 to both sides:

-4 = 2x + 1 - 4

-4 + 4 = 2x + 1 - 4 + 4

0 = 2x - 3

Now, we'll divide both sides of the equation by 2 to solve for x:

0/2 = (2x - 3)/2

0 = x - 3/2

We can rearrange the terms on the right side of the equation to solve for x. To do this, we'll add 3/2 to both sides:

0 + 3/2 = x - 3/2 + 3/2

3/2 = x

Now that we have the value of x, we can substitute it into either equation to solve for y:

[tex]y = -x^2 + 4y = -(3/2)^2 + 4y = -(9/4) + 4[/tex]

y = 7/4

Therefore, the solution to the system of equations is x = 3/2 and y = 7/4.

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In lambda expressions and lambda (λ) phrases, the Greek letter lambda () is used to signify binding a variable in a function. You can have typed or untyped lambda calculus.

Functions can only be used in typed lambda calculus if they are able to accept the "type" of data that the input is. The Greek symbol lambda () is commonly used to represent wavelength, which is equal to the speed (v) of a wave train in a medium divided by its frequency (f): wavelength = v/f. The majority of the time, students struggle to understand calculus because they don't practice after class, can't concentrate in class, have gaps in their math knowledge, and believe it's a waste of time.

The actions you can do to make calculus simple are listed below. Calculus is the most difficult math topic, and very few students, whether in high school or elsewhere, succeed in it. In vector space, linear algebra is a subset of abstract algebra. Matrix technology makes things less abstract and easier to understand because it is more concrete. The mean number of events within a particular period of time or space is denoted by the Greek letter lambda () in the Poisson distribution formula. For instance, = 0.748 floods annually.

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Correct Question:

What does λ mean in calculus?

The cost per kilometer for Emanuel's taxi ride is given as follows:

$9/4.

To obtain the cost per kilometer of the tax ride, we apply the proportion, dividing the total cost by the distance of the taxi ride.

From the text given in this problem, the parameters are given as follows:

Then the cost per kilometer for Emanuel's taxi ride is found applying the proportion as follows:

Cost per kilometer = 32/14.22 = 2.25.

We have that the fraction equivalent of .25 is given as follows:

1/4.

Thus the proper fraction that represents the cost is given as follows:

2 + 1/4 = 8/4 + 1/4 = $9/4.

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The number 119.43 when approximated to 1 significant figure is 100

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

Number = 119.43

The number is to be approximated to 1 significant figure

This means that we approximate all number leaving only the first digit

When this is done, we have

Approximation = 100

Hence, the number in 1 significant figure is 100

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The correct statement regarding the comparison of the linear functions is given as follows:

D. The function shown on the graph has a lower slope and a lower starting point.

The slope of a linear function represents the rate of change of the output variable y relative to the input variable x, that is, the change in y when x is increased by one.

Function y in this problem in this problem is given as follows:

y = 6x + 1.

Considering the slope-intercept definition, we have that:

From the graphed function, we have that:

Thus option D is correct.

The graph is given by the image shown at the end of the answer.

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