what is lhopitals rule calculator online

Bonjour !

Pour obtenir la deuxième ligne de l'équation que vous avez donnée, on peut tout simplement développer le terme Un+1 en utilisant la définition de Un+1 donnée par la relation de récurrence :

Un+1 = 2Un + 1/3(n+1)

En remplaçant Un+1 dans l'expression Un+1 - Un, on obtient :

Un+1 - Un = (2Un + 1/3(n+1)) - Un

On simplifie l'expression en combinant les termes similaires :

Un+1 - Un = 2Un - Un + 1/3(n+1)

Un+1 - Un = Un + 1/3(n+1)

Maintenant, pour obtenir la troisième ligne de l'équation, on peut factoriser Un - Un+1 en utilisant le signe moins :

Un - Un+1 = - (Un+1 - Un)

Un - Un+1 = - (Un+1 - 2Un - 1/3(n+1))

Un - Un+1 = - (-2Un - Un+1 - 1/3(n+1))

Un - Un+1 = 2/3Un + 1/3(n+1) - 1/3Un - 2/3Un - 1/3(n+1)

On simplifie à nouveau en combinant les termes similaires :

Un - Un+1 = -1/3Un + 1/3(n+1)

Enfin, pour obtenir la quatrième ligne de l'équation, on utilise l'associativité de l'addition pour regrouper les termes :

Un - Un+1 = -1/3Un + 1/3(n+1)

Un - Un+1 = 1/3(n+1) - 1/3Un

Un - Un+1 = 1/3(n+3 - Un)

J'espère que cela vous aide à comprendre la démonstration de cette relation de récurrence. N'hésitez pas à me poser d'autres questions si vous en avez besoin !

The perimeter of the room is approximately 49.272 feet.If the area of a rectangular room is 150 square feet, and one side of the room is 11 feet, we can find the length of the other side by dividing the area by the length of the known side:

Length × Width = Area

Width = Area ÷ Length

Width = 150 ÷ 11

Width ≈ 13.636 feet

Now that we know the length and width of the room, we can calculate the perimeter by adding up the length of all four sides:

Perimeter = 2 × Length + 2 × Width

Perimeter = 2 × 11 + 2 × 13.636

Perimeter ≈ 49.272 feet

Therefore, the perimeter of the room is approximately 49.272 feet.

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Answer:

So the probability that Federico scores one point in this situation is 84%.

Step-by-step explanation:

The probability that Federico makes his first shot is 60%, so the probability that he misses it is 40%. If he misses his first shot, he doesn't get a second one, so the probability of scoring one point in this situation is the probability of making the first shot (60%) plus the probability of missing the first shot and making the second one (40% x 60%), which is:

0.60 + 0.24 = 0.84

So the probability that Federico scores one point in this situation is 84%.

s(x) represents the value of s(x) depending on the value of x since s is a function of x.

The first thing you should be aware of in this situation is that the following is contained in the provided expression:

S: stands for a function whose value we are interested in.

In order to understand the function s, we must use the term (numerical value) represented by x.

S is therefore dependent on X.

So, we have:

As s is a function of x, its value depends on the value of x.

As s is a function of x, the value of s (x) depends on the value of x.

Consider the provided notation.

Since s is a function of x. The s(x) value depends on the x value.

For any function f(x); The independent variable is x.

i.e. it depends on the variable x.

Similarly, here s(x) is the dependent variable. which is defined for the corresponding variable x.

Hence, s(x) represents the value of s(x) depending on the value of x, since s is a function of x.

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Answer:

The ladder reaches up to 23.2 feet up the side of the building and the angle of elevation is 78.7 degrees to the nearest tenth. To calculate these values, you can use the Pythagorean Theorem. Let x be the distance the ladder reaches up the wall, and let y be the distance from the base of the building to where the ladder is leaning against the wall. Then, the Pythagorean Theorem states that x2 + y2 = 252, or x2 = 252 - y2. Since y = 2, then x2 = 252 - 22 = 676. Solving for x gives us x = 26, so the ladder reaches up to 26 feet. To calculate the angle of elevation, we can use trigonometry. We know that the opposite side is 26 feet and the adjacent side is 2 feet, so by using the tangent function, we can calculate the angle of elevation as tan-1(26/2) = 78.7 degrees.

the reflection of the given function will be f(-x) = 0.5 4⁻ˣ and the graph of this function is attached below.

A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.

Given, a function as shown in the graph:

To reflect a function over the y-axis we use the rule:

f(-x) reflects the graph of f(x) over the y-axis. In other words,  to reflect f(x) over the y-axis, we just need to replace x with -x.

Let's find f(x) first using the standard exponential growth function:

f(x) = a( 1 + b )ˣ

From our graph, we can infer that f(x) = 1/2 when x =0, so let's replace those values in our function:

f(x) = a( 1 + b )ˣ

1/2 = a(1 +b)⁰

a = 1/2

We can also infer that f(x) = 8 when x =2. Since we already know that a = 1/2, let's replace the values to find and complete our function:

f(x) = a( 1 + b )ˣ

8 = 1/2(1 +b)²

4 = 1+b

b = 3

So putting it all together:

f(x) = 1/2( 1 + 3 )ˣ

Finally, we can apply the reflection rule to find the reflection over the y-axis:

f(-x) = 1/2(4)⁻ˣ

f(-x) = 0.5 4⁻ˣ

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Answer:

The correct answer is B. 200 and 100. When y is inversely proportional to x, it means that the ratio of x to y remains constant. In this case, when x = 20, y = 400, which means that the ratio of x to y is 20/400. Since the ratio is constant, we can use that ratio to find the values of y when x = 40 and x = 80. When x = 40, y = (20/400) x 40 = 200 and when x = 80, y = (20/400) x 80 = 100.

The product of the fraction, 6 and 2/6 is greater.

A fraction is expressed as p/q, where q is equal to 0.

Proper fractions, in which the numerator is less than the denominator, and improper fractions, in which the numerator is higher than the denominator, are the two sorts of fractions.

Given, Are the product of two fractions, First one is 2 and 5/6 which is,

= (5/6)×2.

= 10/6.

= 5/3.

The second product is, 6 and 2/6 which is,

= 5×(2/6).

= 12/6.

= 2.

So, The product of 6 and 2/6 is greater.

Q. Which products are greater than 2 and 5\6 or 5 and 2/6?

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Answer:

Step-by-step explanation:

true

Answer: 3.06

Step-by-step explanation:

The expected value of the game is $16.50.

First we need to multiply the amount you can win by the probability of winning it, then add up all the products.

Let's call the expected value "E":

E = (0.20 x $60) + (0.15 x $30) + (0.25 x $0) + (0.40 x $0)

E = $12 + $4.50 + $0 + $0

E = $16.50

Therefore, the expected value of the game is $16.50.

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D. Post-production is the phase of the development process is where the most thorough testing happens.  

A phase of the development process is a distinct stage or step in the process of developing a software or product, from the initial idea or concept to the final delivery or deployment.

Each phase of the development process has a specific objective, and each phase typically requires the completion of certain activities or tasks before the development can progress to the next phase.  

The phase of testing:

In this phase, the system or product is thoroughly tested to ensure that it meets all requirements and quality standards. This includes various types of testing such as unit testing, integration testing, system testing, acceptance testing, and user acceptance testing.

Post-production is the phase of the development process that occurs after the product or software has been developed and is ready for release. During this phase, thorough testing is performed to ensure that the product or software is functioning as intended and meets all quality standards.  

Therefore,

D. Post-production is the phase of the development process is where the most thorough testing happens.  

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10 and 15

add 2 and 3 together then divide 25 by that and then multiply that number by 2 and 3 to find both of the answers

A parabola equation calculator is an online tool used to find the equation of a parabola based on its vertex and focus points, or other given parameters.

A parabola equation calculator is a type of math calculator used to find the equation of a parabola based on certain given parameters. These parameters could include the vertex and focus points, the directrix, or the x- or y-intercepts. By inputting these parameters into the calculator, users can obtain the equation of the parabola, which is a quadratic function in the standard form y = ax² + bx + c.

Parabolas are widely used in physics and engineering applications, such as the trajectory of a projectile, the shape of a satellite dish, or the design of a parabolic solar collector.

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The equation of each line in slope‐intercept form are y = -4x+2 and y = -x+4

The graph of the linear equation y = mx + c is a line with m as slope, m and c as the y-intercept. This form of the linear equation is called the slope-intercept form, and the values of m and c are real numbers.

GIven are two graphs of lines, we need to find the slope‐intercept form of the lines,

We know that, the slope‐intercept form of the line is given by:

y = mx+c, where m is slope and c is the y-intercept,

m = y₂-y₁ / x₂-x₁

1) The line is passing through two points (0.5, 0) and (0, 2) :-

y-0 = 2-0 / 0-0.5 (x-0.5)

y = -4(x-0.5)

y = -4x+2

2) The line is passing through two points (4, 0) and (0, 4) :-

y-0 = 4-0 / 0-4 (x-4)

y = -1(x-4)

y = -x+4

Hence, the equation of each line in slope‐intercept form are y = -4x+2 and y = -x+4

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Answer:

Multiply the denominator of the fractional part by the whole number, and add the result to the numerator.

For example, suppose you want to convert the mixed number to an improper fraction. First, multiply 3 by 5 and add 2:

(3 · 5) + 2 = 17

Use this result as your numerator, and place it over the denominator you already have.

Place this result over the denominator:

This method works for all mixed numbers. Furthermore, if you start with the fractional part reduced, the answer will also be reduced.

Step-by-step explanation:

A log base 2 calculator calculates the logarithm of a number with respect to base 2.

A tool that helps in calculating a number's logarithm in relation to base 2 is a log base 2 calculators. A base must be increased to the logarithm, or exponent, in order to yield a given number.

The base in this situation is 2, and the exponent to which 2 must be increased in order to equal the supplied number is the logarithm. The base-2 logarithm offers a measure of the number of bits necessary to express a particular amount, making it important in computer science, information theory, and other fields that need computations involving binary integers.

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The choice that represents the quotient of the radicals is given as follows:

D. [tex]x\sqrt{2}[/tex]

The quotient of the radicals for this problem is defined as follows:

[tex]\frac{\sqrt{18x^3}}{\sqrt{9x}}[/tex]

As both the numerator and the denominator have the same root(square root), we can apply the quotient and then take the square root, thus:

[tex]\sqrt{\frac{18x^3}{9x}}[/tex]

Then we can simplify the expression inside the square root as follows:

Hence the square root is taken as follows:

[tex]\sqrt{2x^2} = x\sqrt{2}[/tex]

Meaning that option D is the correct option.

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The sides of the given right triangle are:

g = 33.80

h = 31.20

j = 13

What is a triangle?

A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total. Any three points in Euclidean geometry, when they are not collinear, produce a distinct triangle. A right triangle is a triangle with two perpendicular sides and one angle that is a right angle.

The given figure has a large right triangle with sides g,h and j and a small right triangle with sides 12, j and 5.

Using the small triangle, we can find the value of j.

By Pythagoras theorem,

j² = 12² + 5² = 144 + 25 = 169

j = 13

Now using trigonometric relation we can find the angle ∅  between j and 5.

sin ∅ = 12/13 = 0.923

∅ =  sin ⁻¹ (0.923) = 67.37°

This angle is common for both triangles.

So for large triangle,

tan 67.37 = h/j = h/13

2.4 = h/13

h = 31.2

By Pythagoras theorem,

g² = h² + j²  = 31.2²  + 13² = 1142.44

g = 33.8

Therefore the sides of the given right triangle are:

g = 33.80

h = 31.20

j = 13.

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Answer: y = 0.1x^2 - 0.8x + 1.2

hope this helped

The three rules of logs are the product rule, quotient rule, and power rule.

The three rules of logs are fundamental rules that are used in manipulating logarithmic expressions.

Product rule:

The product rule states that the logarithm of the product of two numbers is equal to the sum of the logarithms of the individual numbers.

Quotient rule:

The quotient rule states that the logarithm of the quotient of two numbers is equal to the difference of the logarithms of the individual numbers.

Power rule:

The power rule states that the logarithm of a number raised to a power is equal to the product of the power and the logarithm of the base.

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The magnitude of the vector is calculated by using the formula √((c-a)²+(d-b)²) where A(a,b) and B(c,d) are point on the plane.

A vector is any quantity that has a magnitude as well as directiom and that also follows the vector law of addition.

Let us say that there are any two points on the co-ordinate plane A(a,b) and B(c,d).

Now the magnitude of the vector AB can be found by using the formula,

AB = √((c-a)²+(d-b)²)

and the direction of this vector will be from A to B on the coordinate plane. If we want to find direction, then it is given by, tab A = (d-b)/(c-a)

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The value of centimeter to inches can be calculated by simply by dividing the length  value by 2.54 so 13 cm to 5.118 inches.

Unit conversion is the process of converting the measurement of a given amount between various units, often by multiplicative conversion factors that alter the value of the measured quantity without altering its effects.

You've also come to the right place if you've been wondering how many inches are in 13 centimetres or how many inches are in 13 centimetres.

On our website, inches are denoted by "in" or "′′, while centimetres are always written as cm.

You must divide 13 centimetres by 2.54 to get the answer in inches.

Hence, in inches, the comparable height, width, or length is:

13 cm equals 5.11811 inches.

13 cm is equal to 5.11811 inches.

5.11811 inches in 13 cm.

13 cm in inches: 13/2.54 = 5.11811 inches is the conversion factor for 13 cm.

You can convert 13 inches to centimetres here.

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Answer:

boys-75,

Step-by-step explanation:

the ratio is 3:2 and the total ratio is 5, which stands for total learners in grade 8

boys;

3/5×125= 75

girls;

2/5×125= 50

A rectangle of 24 1/2 sqaure feet if the length of the rectangle is 4 3/8 feet, and the width of the rectangle is 4 feet.

What is the area of the rectangle?

To find the area of a rectangle, we multiply the length of the rectangle by the width of the rectangle.

To find the width of the rectangle, we can use the formula for the area of a rectangle:

Area = Length x Width

We are given that the area of the rectangle is 24 1/2 square feet and the length is 4 3/8 feet. Substituting these values into the formula, we get:

24 1/2 = 4 3/8 x Width

To solve for the width, we can first convert both mixed numbers to improper fractions:

24 1/2 = 49/2

4 3/8 = 35/8

Substituting these values, we get:

49/2 = 35/8 x Width

To solve for Width, we can cross-multiply:

49/2 * 8/35 = Width

Simplifying, we get:

4 = Width

Therefore, the width of the rectangle is 4 feet.

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For testing the hypotheses H0: μdiff = 0; Ha: μdiff > 0, the P-value is 0.6294.

We have,

The hypotheses are as follows:

Null Hypothesis (H0): The mean difference in exam scores is equal to 0. μdiff = 0

Alternative Hypothesis (Ha): The mean difference in exam scores is greater than 0. μdiff > 0

To calculate the t-statistic, we use the formula:

t = (x - μ) / (s / √n)

Where:

x is the sample mean difference (given as -1.75)

μ is the hypothesized population mean difference under the null hypothesis (0 in this case)

s is the sample standard deviation (given as 7.12)

n is the sample size (given as 35)

Substitute the given values:

t = (-1.75 - 0) / (7.12 / √35)

t ≈ -0.33071

The degrees of freedom (df) for the t-distribution.

The degrees of freedom for this test is equal to the sample size minus 1:

df = 35 - 1 = 34

The P-value is associated with the calculated t-statistic.

Since we are testing for a one-sided alternative (μdiff > 0), we need to find the area under the t-distribution curve to the right of the t-statistic.

Using the t-table, with df = 34 and t ≈ -0.33071, we find the P-value to be approximately 0.6294.

Thus,

For testing the hypotheses H0: μdiff = 0; Ha: μdiff > 0, the P-value is 0.6294.

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The indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

The integral of cos(x) is sin(x) + C, where C is the constant of integration.

The notation for the integral of cos(x) is ∫cos(x) dx, where the symbol ∫ represents the integral sign, cos(x) is the function being integrated, and dx represents the variable of integration, which in this case is x.

The antiderivative of cos(x) is sin(x), meaning that if we take the derivative of sin(x), we get cos(x). The constant of integration, C, is added because the derivative of a constant is always zero.

Therefore, the indefinite integral of cos(x) is sin(x) + C, and we can find the definite integral of cos(x) between two limits by evaluating sin(x) + C at the upper and lower limits and subtracting the results.

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The true statement about the function y = 40x is that it is a linear function

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

y = 40x

The given function is y = 40x, which represents the total number of dollars Mark earns depending on the number of lawns he mows.

Here are some properties of the function:

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