Calculating length of the curve
Can somebody give me a detailed description how we did the last three steps?

Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to locate the vertical asymptotes of a function using limits. Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction).Similary, To find the horizontal asymptotes of a function using limits, consider the behavior of the function as x becomes very large (in either the positive or negative direction). If the y-values of the function approach a fixed value as x becomes very large, then that value is the horizontal asymptote of the function.

An asymtote is a line being approached by a curve but never touching the curve at any finite distance.It is a line that the graph approaches as either x or y in positive or negative infinity.

A vertical line that directs the function's graph but is not actually a part of it is called a vertical asymptote. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.

Consider the behavior of the function when x approaches the value of the vertical asymptote from the left and from the right in order to identify the vertical asymptotes of a function using limits. The vertical asymptote is at that value of x if the function approaches positive infinity as x approaches the asymptote from the left and negative infinity as x approaches the asymptote from the right. Consider the function f(x) = 1/x as an illustration. We may take into account how the function behaves as x approaches 0 from the left and from the right in order to determine the vertical asymptotes of this function using limits.The y-values of the function become closer to negative infinity as x moves toward 0 from the left (negative x-values). The y-values of the function get closer to positive infinity as x gets closer to 0 from the right (positive x-values). As a result, we may infer that the function's vertical asymptote lies at x = 0.

Similary, Consider the behavior of the function when x grows very big in order to determine the horizontal asymptotes of a function using limits (in either the positive or negative direction). The horizontal asymptote of the function is the point at which the y-values of the function begin to approach a fixed value when x increases significantly.

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Yes, triangle inequality theorem apply to all equilateral triangles.

The triangle inequality theorem explains the relation between a triangle's three sides. This theorem states that for any triangle, the sum of the lengths of the first two sides is always greater than the length of the third side. In other terms, this theorem states that a straight line is always the shortest distance between any two places.

So Triangle inequality theorem is not only valid for all equilateral traingles but it is valid for all traingles.

A Triangle is only formed is if follows Triangle inequality theorem so every equilateral triangle needs to follow this theorem.

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The height of the tree is 61.92 feet.

Trigonometric Identities are equality statements that hold true for all values of the variables in the equation and that use trigonometry functions. There are numerous distinctive trigonometric identities that relate a triangle's side length and angle.

Given that,

Distance of Tamara from tree = 30 feet.

Angle of elevation = 62°.

And the height of Tamara from the ground = 5.5 feet.

To find the height of the tree,

Use trigonometric formula,

tan θ = height / distance

tan 62 = x / 30

1.88 = x / 30

x = 56.42 feet

The total height of tree = x + 5.5 = 56.42 + 5.5 = 61.92 feet

The height of the tree is 61.92 feet.

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The first five terms of the expression are -7,-3,1,5, and 9.

The sequence in which every next number is the addition of the constant quantity in the series is termed the arithmetic progression

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that , F(1) = -3 and F(n) = F(n-1) + 4. Calculate the first term of the sequence,

F(1) = F(1-1) + 4

-3 = F(0) + 4

F(0) = -7

The common difference is calculated as,

d = -3 - 7

d = 4

The third term will be, -3 + 4 = 1

The fourth term will be, 1 + 4 = 5

The fifth term will be, 5 + 4 = 9

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Answer:

Step-by-step explanation:

The derivative of a function y = f(x) at the point a is a measure of the rate of change of the function at that point. It is represented by the symbol f'(a) or df/dx.

The derivative can be thought of as the slope of the tangent line to the curve of the function at the point a. It is calculated using the limit definition of the derivative, which states that the derivative of a function at a point is the limit of the difference quotient as the difference between x and a approaches zero.

In other words, the derivative of a function y = f(x) at the point a is the slope of the line that is tangent to the function at that point, and it is calculated using the following formula:

f'(a) = lim(h -> 0) [(f(a+h) - f(a)) / h]

This formula can be used to calculate the derivative of any function at any point. I hope this helps! Let me know if you have any questions.

Answer:

There is no real square root of -4 because it is impossible to square any real number and get a negative answer.

You might think -2 could work. However, a negative times a negative is positive → -2(-2) = +4, so the problem would have to be written as [tex]\sqrt4[/tex] instead of [tex]\sqrt{-4}[/tex]. Hence, there is no real square root of -4.

Note the word real, as it is possible to find a non-real answer to [tex]\sqrt{-4}[/tex] using the imaginary number [tex]i[/tex], which represents [tex]\sqrt{-1}[/tex].

2375 is the amount of his investment and 625 is his total profit

The discount on the shares is 5%, so the price of each share is 100 - (5/100)100 = 95.

The total price Yoezer paid for the shares is 2595 = 2375.

To calculate Yoezer's total profit, we need to find the total dividend he received and the price he sold the shares for.

The dividend rate is 15%, so Yoezer received a dividend of (15/100)100 = 15 on each share.

The total dividend he received is 1525 = 375.

The price Yoezer sold the shares for was increased by a premium of 5%, so the selling price was 100 + (5/100)100 = 105.

The total selling price for the shares is 10525 = 2625.

Yoezer's total profit is the selling price minus the price he paid for the shares plus the dividends he received. This is 2625 - 2375 + 375 = 625.

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Answer:

Step-by-step explanation:

you cant divide fractions so you multiply the reciprocal so your answer would be

1 11/16

The evaluation of the composite figure comprising of a square and an equilateral triangle is as follows;

9 (a) ∠ABD = 90°

(b) ∠BCD = 60°

(c) ∠ADC = 105°

A composite figure is a figure comprising of two or more regular geometric figures.

9. The shape of the quadrilateral ABDE = A square

The kind of triangle specified for the triangle ΔBCD = Equilateral triangle

The sides of the square ABDE are congruent by the definition of a square

Therefore; AB = BD = DE = AE by the definition of congruency

(a) Angle ∠ABD is a corner of the square ABDE, therefore;

The size of angle ∠ABD = 90° (properties of the interior angle of a square)

(b) The size of angle ∠BCD = 60° (Interior angle of an equilateral triangle)

(c) The size of angle ∠ADC is found as follows;

Triangles ΔAED and triangle ΔABD formed by the diagonal AD are congruent by Side-Side-Side, SSS congruency postulate

∠DAB ≅ ∠ADB (base angles of isosceles triangle ΔABD)

∠DAB = ∠ADB (Definition of isosceles triangles)

∠ABD + ∠DAB + ∠ADB = 180° (Angle sum properties of a triangle)

90° + 2 × ∠ADB = 180° (substitution property)

∠ADB = (180° - 90°) ÷ 2 = 45°

∠BDC = 60° (Interior angle of an equilateral triangle)

∠ADC = ∠ADB + ∠BDC (Angle addition postulate)

Therefore, ∠ADC = 45° + 60° = 105°

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Answer:

9r^2+7r-5

Step-by-step explanation:

-15+23r+9r^2-16r+10

=-15 + 9r^2 + 7r +10

= 9r^2 + 7r - 5

Answer:

[tex]9r^2+tr-5[/tex]

The given expression is a polynomial in the variable r. The correct answer among the options provided is D, which has the same terms as the given expression, in the same order, but with an additional term (tr) at the end. The other options do not match the given expression.

Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.

A resultant is referred to as a "Square Number" when a number or integer (not a fraction) is multiplied by itself. For instance, 3 x 3 is 32 when multiplied by itself three times. In essence, the exponential form of multiplying an integer or number by itself is referred to as a square number.

Here,

Try to add up the four stages here.

Multiplication of two-digit numbers using a math shortcut trick

shortcuts: 13 times 13 equals

13X13 = 169 is the answer when a two-digit number is multiplied.

Therefore , the solution of the given problem of squaring comes out to be square of the 13 is 169.

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Answer:

A parallelogram

Step-by-step explanation:

A parallelogram is a shape with four sides and two sets of parallel lines. A common example of a parallelogram is a square.

3xy has two terms, 3 and xy. The term 3 is a constant and the term xy is a product of two variables.

3xy is a multiplication of three individual components. It consists of three distinct parts, namely 3, x, and y. Each of these components is considered a distinct term, so 3xy has three terms in total. The 3 represents a numerical value, while the x and y are variables that can be assigned any numerical value. When multiplied together, the three terms form a single expression, 3xy, which can then be evaluated for a resulting value.

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The length of the side of the square is 12 cm.

Given that, a triangle with an area of 59 cm from a certain square, the area of the remaining shape will be 85 cm².

Area is the amount of space occupied by a two-dimensional figure. In other words, it is the quantity that measures the number of unit squares that cover the surface of a closed figure. The standard unit of area is square units which is generally represented as square inches, square feet, etc.

We know that, the area of a square is a².

Here, total area = Area of a square + The area of the remaining shape

= 59+85

= 144 cm²

So, a²= 144 cm²

⇒ a =12 cm

Therefore, the length of the side of the square is 12 cm.

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The percentage of all patients who took the test and had a false positive result will be 35%. Then the correct option is D.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.

Lyme illness is a disease brought about by microscopic organisms. A test for Lyme infection might be impacted by different prescriptions and ailments. The testing results are summed up in the table.

                                      Tested positive      Tested negative     Row Totals

Has Lyme disease                  53%                         17%                     70%

Doesnt have Lyme disease    12%                         18%                     30%

Column Totals                         65%                        35%                    100%

The level of all patients who stepped through the examination and had a misleading positive outcome will be 35%. Then, at that point, the right choice is D.

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Answer:66.67% to the nearest whole number is 67%

Step-by-step explanation:

The total number of acres available are 30

and only 20 acres of land can be farmed

20 acres out of 30 acres is available for farming

20/30 x 100%

To do with the calculator

20 ÷30 x 100=66.67% then add the percent sign

Answer:

20%

Step-by-step explanation:

let x = percent savings

$3/lb (cost per lb of a 1 lb pack)

$24/10lb = $2.40/lb (cost per lb for a 10 lb pack)

$3 - $3x = $2.40

-3x = -0.60

x = -0.60/3 = 0.20

0.20 x 100 = 20%

Answer:

32 3/11

Step-by-step explanation:

Happy Holidays!

Answer: Roots of given quadratic equation are real and distinct.

If a quadratic equation is given by  ,then nature of its roots can be find by it's discriminate (D).

Roots are real and distinct, if D>0

Roots are real and equal, if D=0

Roots are imaginary (no real root exists), if D<0

Step 1:

Write coefficients of x², x and constant term.

Compare the given equation with standard quadratic equation.

Thus,

Roots of given quadratic equation are real and distinct.

Learn more:

1) Find the nature of roots of quadratic equation 2x sq. + 3x - 7=0

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2) Find the nature of the roots of the following quadratic equations. If real roots exist, find them:

(i) 2x² – 3x + 5 = 0 ...

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Step-by-step explanation:

A function can have an asymptote if it approaches a horizontal or vertical line but never touches it. There are several types of functions that can have asymptotes, including rational functions, exponential functions, and logarithmic functions.

For example, a rational function is a function that can be written in the form of a ratio of two polynomials. These functions can have horizontal asymptotes if the degree of the denominator is greater than the degree of the numerator, and they can have vertical asymptotes if the denominator has a factor that is not present in the numerator.

Exponential functions can have horizontal asymptotes if the base of the exponent is less than 1, and they can have vertical asymptotes if the base of the exponent is greater than 1.

Logarithmic functions can have horizontal asymptotes if the base of the logarithm is less than 1, and they can have vertical asymptotes if the base of the logarithm is greater than 1.

It's also possible for a function to have both horizontal and vertical asymptotes, depending on its form.

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If the exponent's base is less than 1, an exponential function may have a horizontal asymptote; if it is greater, a vertical asymptote may occur.

If the base of the logarithm is less than 1, a logarithmic function may have a horizontal asymptote, and if the base is greater, a vertical asymptote.

Linear equations are one-degree equations. It is a straight-line equation. A linear equation with parameters a and b equal to zero has the conventional form ax + by + c = 0.

A linear equation has the following standard form: ax + by + c = 0.

Here, variables x and y and constants a, b, and c are used.

Also, a ≠ 0, and b ≠ 0.

For linear equations, the slope-intercept formula is: y=mx+b

Where m stands for the line's slope and b represents the y-intercept.

The three types of linear equations are point-slope, slope-intercept, and standard form.

When an algebraic equation is graphed, it always produces a straight line since each term has an exponent of 1 or 0. This is known as linear equations.

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The circumference of the circle is C = 144.44 yd .

From the given figure :

we observe that the radius r = 23 yd

we know that ,

What is circumference of circle ?

Circumference is the distance around the perimeter of a circle. It is calculated by multiplying the distance across the center .

A circle's perimeter is known as its circumference.

Formula :

C = 2πr

= 2 * 3.14 * 23

= 46 * 3.14

= 46 * 314 / 100

= 14444 / 100

= 144.44 yd

Hence the circumference of the circle is 144.44 yd .

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Full question :

is in the image uploaded

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

A figure or ratio that reflects a fraction of 100 is known as a percentage in mathematics. In addition to ratios, fractions, and decimals, it is one of the ways to depict a dimensionless connection between two numbers. Frequently, the symbol "%" is used after the number to indicate percentages.

given,

The number of phone calls handled by the communications switch in a 10-second period is represented by the Poisson random variable n.

a)the chance that no call will be handled in 10 seconds is

for 10 sec= λ= 10*0.5 = 5 calls per sec

P(X=0) [tex]e^{-5}[/tex](5)° / 0!

P(X=0)= 0.0067

b) percent of classes will be processed in two seconds at least is

for 2 sec =λ = 0.5 *2 = 1

P(X≥2) = 1- P(X<2)

= 1-[P(X=2) + P(X=1)]

=0.2642

a)The chance that no call will be handled in 10 seconds  is 0.0067

b) 0.2642 percent of classes will be processed in two seconds at least.

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The numeric value of the expression 4000×20÷408-44 is given as follows:

4000×20÷408-44 = 152.08.

The expression for this problem is defined as follows:

4000×20÷408-44

We have a multiplication, a division and a subtraction operation, hence the precedence of the operations is given as follows:

Then the multiplication is given as follows:

4000×20 = 80,000.

The division is given as follows:

80000/408 = 196.08.

Finally, the subtraction is calculated as follows:

196.08 - 44 = 152.08.

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Answer:

Given that a circle has a center (0,4) and the radius 5. 5. So the standard equation of the given circle is x2+(y−4)2=25.

Step-by-step explanation:

The median of the distribution 34 22 13 is 22.

To find the median of a set of scores, you first need to arrange the scores in numerical order. The median is the middle score in the set. If there is an odd number of scores, then the median is the middle score. If there is an even number of scores, then the median is the average of the two middle scores.

In this case, the scores are 13, 22, and 34.

After arranging the scores in numerical order, we have 13, 22, and 34.

There are three scores in this set, so the median is the middle score, which is 22.

The median of the set is 22.

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5.5 is  is the median of the set of numbers .

What are the mean, median, and example?

The most frequent number, or the one that happens the most frequently, is known as the mode.

             Example: Since the number 2 appears three times, more than any other number, it is the mode of the numbers 4, 2, 4, 3, and 2.

Since the number of observations is even, the median is the average of  

                               = (n/2) th and (n/2 +1)th observation.

The average of 5th and 6th observations = (5+6)/2 = 11/2 = 5.5.

Hence, the median of the given set of numbers is 5.5.

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The graph of the equation will be a parabola that opens upwards, starting at the y-axis and increasing in value as x increases. The vertex of the parabola will be the lowest point on the graph, and the parabola will be symmetrical about the line of symmetry.

When the degree of an equation is even and the leading coefficient is positive, the graph of the equation will be a parabola. This parabola will open upwards, meaning that it will start at the y-axis and increase in value as x increases. The vertex of the parabola will be the lowest point on the graph, and this vertex will always be located to the right of the y-axis. Additionally, the parabola will be symmetrical about the line of symmetry, which is the vertical line that passes through the vertex. To further illustrate, consider the equation y = 4x^2 + 5x + 1. In this equation, the degree is even (2) and the leading coefficient is positive (4). Therefore, the graph of this equation will be a parabola that opens upwards and has its vertex to the right of the y-axis. Additionally, the parabola will be symmetrical about the line of symmetry, which is the vertical line that passes through the vertex. The vertex of the parabola will have coordinates (2.5, -2.625), and the parabola will increase in value as x increases from this point.

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The larger number is 8 and the smaller number is -4.

Let us assume that the larger number is x and the smaller number is y.

Now according to the question:

The sum of two numbers is 4, so

x+y= 4....(1)

A two-variable linear equation has two variables and can be represented as: ax+by=c

Here x and y are the variables, a and b are the respective cofficients of the variables and c is a constant term.

And the larger number is 12 more than three times the smaller number.

So

x=y+12 ...(2)

By equation (1) and (2)

y+12+y=4

2y= 4-12=-8

y = -4

Now put the value of y in equation (2)

x= y+12=-4+12=8

So the larger number is 8 and the smaller number is -4.

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