Which sequence is modeled by the graph below?

Which Sequence Is Modeled By The Graph Below?

Answers

Answer 1
(2,9)(3,3)(4,1)

We can observe

9/3=33/3=1

Its a geometric progression having first term 9(3)=27 and common ratio as 1/3

So

The firmula is

a_n=27(1/3)^{n-1}

Option C

Answer 2

Answer:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

Step-by-step explanation:

From inspection of the graph, the given points are:

(2, 9)(3, 3)(4, 1)

If we draw a line through the given points, the line is a curve rather than a straight line. If the line was a straight line, the graph would be modeled as an arithmetic sequence. Therefore, as the line is a curve, the given points are modeling a geometric sequence.

General form of a geometric sequence:

 [tex]a_n=ar^{n-1}[/tex]

where:

a is the first termr is the common ratio[tex]a_n[/tex] is the nth term

Rewrite the given points as terms of the sequence:

(2, 9)  ⇒  a₂ = 9(3, 3)  ⇒  a₃ = 3(4, 1)  ⇒  a₄ = 1

To find the common ratio r, divide consecutive terms:

[tex]\implies r=\dfrac{a_3}{a_2}=\dfrac{3}{9}=\dfrac{1}{3}[/tex]

Calculate the first term (a) by substituting the found value of r and the given values of one of the terms into the formula:

[tex]\implies a_2=9[/tex]

[tex]\implies a\left(\dfrac{1}{3}\right)^{2-1}=9[/tex]

[tex]\implies \dfrac{1}{3}a=9[/tex]

[tex]\implies a=27[/tex]

Substitute the found values of r and a into the general formula to create the sequence modeled by the graph:

[tex]a_n=27\left(\dfrac{1}{3}\right)^{n-1}[/tex]

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Related Questions

C=22°, a = 14 m, b = 8 m find area of ABC to the nearest tenth

Answers

Answer:

  21.0 m²

Step-by-step explanation:

The formula for the area of a triangle from two sides and the included angle is ...

  A = 1/2ab·sin(C)

Area

Using this formula, we find the area to be ...

  A = 1/2(14 m)(8 m)sin(22°) = 21.0 m²

The area of triangle ABC is about 21.0 square meters.

PLSSS HELP ASAP!! ty

On a graph, sketch f(x)=x+3 and g(x)=x. Is there a way of determining the graph of f(x)+g(x) without solving it algebraically? Explain your thinking below.

Answers

From the graph, the equation of f(x) + g(x) is f(x) + g(x) = 2x + 3

How to determine the graph of f(x) + g(x)?

The functions are given as:

f(x) = x + 3

g(x) = x

From the above functions, we can see that the function g(x) is the parent function of a linear function.

When the parent function of a linear function is added to another function to form a composite function, the new function would pass through the following points

(x, y)= (0, b) and (-b, -b)

Where b is the y-intercept of the other function

i.e b = 3 from f(x) = x + 3

So, we have the following points

(0, 3) and (-3, -3)

Next, we draw the points and we connect the points

When the equation of f(x) + g(x) is calculated, we have

f(x) + g(x) = 2x + 3

See attachment for the graph of the functions

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A circle is formed using a ribbon which has a radius of 28 cm. If a square has to be formed using the same ribbon, determine the length of the side of the square formed using the ribbon.​

Answers

The length of the side of the square is [tex]44 cm[/tex].

What is a Circle?A circle is made up of all points in the same plane that are equidistant from one another. Only the bordering points make up the circle.The following are a few examples of circles in daily life: the bicycle's wheel. Dinner dish. Coin.A circle is a particular type of ellipse in mathematics or geometry where the eccentricity is zero and the two foci are congruent. A circle is also the location of points evenly spaced apart from the center. The radius of a circle is measured from the center to the edge.

Determine the length of the side of the square:

Radius of circle[tex]=28.[/tex]

Circumference[tex]=2\pi r[/tex]

                        [tex]2\pi (28)=176[/tex]

Side of the square[tex]=\frac{176}{4} =44cm.[/tex]

The length of the side of the square is [tex]44 cm[/tex].

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Need help with my math please. Determine the most probable next term in each list of numbers.

Answers

Answer:

23.  216

24.  56

25.  52

26.  -7

27.  5

Step-by-step explanation:

Question 23

Work out the differences between the terms until the differences are the same:

[tex]1 \underset{+7}{\longrightarrow} 8 \underset{+19}{\longrightarrow} 27 \underset{+37}{\longrightarrow} 64 \underset{+61}{\longrightarrow} 125[/tex]

    [tex]7 \underset{+12}{\longrightarrow} 19 \underset{+18}{\longrightarrow} 37 \underset{+24}{\longrightarrow} 61[/tex]

        [tex]12 \underset{+6}{\longrightarrow} 18 \underset{+6}{\longrightarrow} 24[/tex]

As the third differences are the same, the sequence is cubic and will contain an term.  The coefficient of n³ is always a sixth of the third difference.  Therefore, the coefficient of n³ = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n³ and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c |}\cline{1-6} n&1 & 2 & 3&4&5 \\\cline{1-6} n^3 & 1 & 8 & 27 & 64 & 125 \\\cline{1-6} \sf sequence & 1 & 8 & 27 & 64 & 125 \\\cline{1-6}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^3[/tex]

So the next term in the sequence is:

[tex]\implies a_6=6^3=216[/tex]

Question 24

Work out the differences between the terms until the differences are the same:

[tex]2 \underset{+4}{\longrightarrow} 6 \underset{+6}{\longrightarrow} 12 \underset{+8}{\longrightarrow} 20 \underset{+10}{\longrightarrow} 30 \underset{+12}{\longrightarrow} 42[/tex]

     [tex]4 \underset{+2}{\longrightarrow} 6 \underset{+2}{\longrightarrow} 8 \underset{+2}{\longrightarrow} 10 \underset{+2}{\longrightarrow} 12[/tex]

As the second differences are the same, the sequence is quadratic and will contain an term.  The coefficient of n² is always half of the second difference.  Therefore, the coefficient of n² = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +1 & +2 & +3 & +4 & +5 & +6 \\\cline{1-7} \sf sequence & 2 & 6 & 12 & 20 & 30 & 42 \\\cline{1-7}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^2+n[/tex]

So the next term in the sequence is:

[tex]\implies a_7=7^2+7=56[/tex]

Question 25

Work out the differences between the terms until the differences are the same:

[tex]4 \underset{+3}{\longrightarrow} 7 \underset{+5}{\longrightarrow} 12 \underset{+7}{\longrightarrow} 19 \underset{+9}{\longrightarrow} 28 \underset{+11}{\longrightarrow} 39[/tex]

     [tex]3 \underset{+2}{\longrightarrow} 5 \underset{+2}{\longrightarrow} 7 \underset{+2}{\longrightarrow} 9 \underset{+2}{\longrightarrow} 11[/tex]

As the second differences are the same, the sequence is quadratic and will contain an term.  The coefficient of n² is always half of the second difference.  Therefore, the coefficient of n² = 1.

To work out the nth term of the sequence, write out the numbers in the sequence n² and compare this sequence with the sequence in the question.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} n^2 & 1 & 4 & 9 & 16 & 25 &36\\\cline{1-7} \sf operation & +3 & +3 & +3 & +3 & +3 & +3 \\\cline{1-7} \sf sequence & 4&7&12&19&28&39 \\\cline{1-7}\end{array}[/tex]

Therefore, the nth term is:

[tex]a_n=n^2+3[/tex]

So the next term in the sequence is:

[tex]\implies a_7=7^2+3=52[/tex]

Question 26

Given numbers:

-1, 2, -3, 4, -5, 6

As the list of numbers does not increase or decrease, we cannot apply the same method as the previous questions.

[tex]\begin{array}{| c | c | c | c | c | c | c |}\cline{1-7} n&1 & 2 & 3&4&5&6 \\\cline{1-7} \sf list & -1 & 2 & -3 & 4 & -5 & 6 \\\cline{1-7}\end{array}[/tex]

From comparing the position of the term to its number in the list, we can see that the nth term is the same as n, but the odd numbers are negative and the even numbers are positive.

Therefore, the rule is:

[tex]\implies a_n=n \quad \textsf{where }n \textsf{ is an even natural number}[/tex]

[tex]\implies a_n=-n \quad \textsf{where }n \textsf{ is an odd natural number}[/tex]

So the next term in the sequence is:

[tex]\implies a_7=-7[/tex]

(since 7 is an odd natural number)

Question 27

Given numbers:

5, 3, 5, 5, 3, 5, 5, 5, 3, 5, 5, 5, 5, 3, 5, 5, 5, 5

The pattern of these numbers appears to be an ascending number of 5s with a 3 in between:

One 5, followed by a 3Two 5s, followed by a 3Three 5s, followed by a 3Four 5s, followed by a 3

Therefore, the next number of 5s will be five.  This means the next number in the list will be 5, since there are only four 5s after the last 3.

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The side length of each square is 6 units.

Answers

The area of the square A2 is 20 squared units

How to determine the area of A2?

The complete question requires that we calculate the area of square A2

The side length of each square is 6 units.

So, the side length (L) of A2 is

L^2 = (2)^2 + (6 - 2)^2

This gives

L^2 = 20

The above represents the area of the square A2

Hence, the area of the square A2 is 20 squared units

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Answer:

Triangle Area = 4 units^2

Step-by-step explanation:

assuming you are looking for the area of ​​the triangles, there is no specific question, they are right-angled triangles congruent with the catheti of 2 and 4 units.

Triangle area = 1/2 base x height.

so 1/2 2 * 4 = 4 units^2

A trapezoid is shown. The lengths of the bases K L and J M are 10 feet and 5 feet. The length of side L M is 6 feet. An altitude is drawn from point K to a point on side J M.

A plot of land has an area of 33.75 square feet. Jackson wants to put a 4-foot by 4-foot shed on the land. He can only do this if the height of the trapezoid is at least 4.5 feet. What is the height of the trapezoid?

feet

Answers

The given height of this trapezoid is given to be 4.5m

How to solve for the height of the trapezoid

We have to solve for this by making use of the height of a trapezoid. The height is given as

A = (1/2) h (b1 + b2)

The variables here are

h = height

b1 = lenght at base 1

b2 = length at base 2

If the trapezoid that we have is a isosceles triangle, then base 1 is going to be the same length as that of the first base

b1 = 4 ft is the area. Given that the height has to be at least 4.5feet, then this would ensure that the trapezoid would be able to hold the shed.

Hence the height would begiven as 4.5 ft

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Answer: 4.5

Step-by-step explanation:

A line has a slope of -2/5 and passes through the point (10,7) . Write the equation of this line in point-slope form, slope-intercept form, and standard form.

i will give brainliest if you help

Answers

[tex](\stackrel{x_1}{10}~,~\stackrel{y_1}{7})\hspace{10em} \stackrel{slope}{m} ~=~ -\cfrac{2}{5} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{7}=\stackrel{m}{-\cfrac{2}{5}}(x-\stackrel{x_1}{10})[/tex]

ms bloom had 4 /7/12 boxes of pencils but 2/1/12 boxes of pencils were broken after she threw out the broken pencils how many boxes of pencils were left

Answers

Concluding, there are (2 + 12) boxes of pencils left.

How many boxes of pencils were left?

We know that Ms. Bloom had (4 + 7/12) boxes of pencils, and we also know that (2 + 1/12) of the boxes were broken.

The number of boxes of pencils left is given by the difference between the two above numbers, then we get:

N = (4 + 7/12) - (2 + 1/12) = (4 - 2) + (7/12 - 1/12) = 2 + 6/12

Now we can simplify the fraction:

N = 2 + 1/2

Concluding, there are (2 + 12) boxes of pencils left.

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If h(x) = 5 x and k (x) = startfraction 1 over x endfraction, which expression is equivalent to (k circle h) (x)?

Answers

The equivalent expression to [tex](k o h)(x)[/tex]is [tex]\frac{1}{5 + x}[/tex]

Therefore  [tex](k o h)(x) = \frac{1}{5 + x}[/tex]

Given that the functions h is defined by h(x)=5+x

and k is defined by k (x) = [tex]\frac{1}{x}[/tex]

To find the composition of k and h that is: (k o h) (x)

Therefore

k (h(x)) = k (5+x)

k (h(x)) = [tex]\frac{1}{5+ x}[/tex]

The equivalent expression to is [tex]\frac{1}{5+ x}[/tex]

What is expression?An expression, often known as a mathematical expression, is a finite collection of symbols that are well-formed in accordance with context-dependent principles.Numbers (constants), variables, operations, functions, brackets, punctuation, and grouping can all be represented by mathematical symbols, which can also be used to indicate the logical syntax's order of operations and other features.Expressions are syntactic devices. It must be properly constituted, which means that the permissible operators must have the right amount of inputs in the right places, legal characters for these inputs, a clearly defined order of operations, etc.The syntax requirements must be followed for a string of symbols to be considered a valid mathematical expression.

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Allison is saving money to buy a new phone that costs $600 by selling her graphic designs. She is using an app to manage her sales, but it keeps a fraction of each sale. Her net pay is modeled by the function P(x) = x2 + 18x – 160, where x represents the number of sales. How many sales does Allison to make to earn $600?

Answers

Answer:

20

Step-by-step explanation:

x^2+18x-160

If you put this into your calculator or desmos, you will get a parabola. You want to know the value of x when y=600. You can look at the table for the graph or scan to where y = 600. The value of x is 20 at that point.

To check you can plug 20 in for x. When you do that, y = 600.

Y=2x^2+2x-4 what is the x intercepts for the parabola

Answers

Answer:

Step-by-step explanation:

To find the x intercepts, substitute in 0 for y and solve for x

So,

2x^2+2x-4 = 0

2(x^2+x-4) = 0

2/2(x^2+x-4) = 0/2

x^2+x-4 = 0

(x-1) (x+2) = 0

now,

x-1 = 0

x = 1

or

x+2 = 0

x = -2

The x intercepts for the parabola (1,0), (-2,0)

Use the laplace transform to solve the given initial-value problem. y'' − 4y' + 4y = t3e2t, y(0) = 0, y'(0) = 0

Answers

The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex].

According to the statement

we have given that the equation and we have to solve this problem with the help of the Laplace transform.

So, According to the statement

the given equation is

y'' − 4y' + 4y = t^3e^2t, y(0) = 0, y'(0) = 0

And the Laplace transform is an integral transform method which is particularly useful in solving linear ordinary differential equations.

Firstly fill the value of the Laplace of the second order derivative and put x = 0 in the equation

And same it with the first order of the derivative.

And then the Laplace of the equation become

[tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]

So, The Laplace of the given equation is [tex]y=-\frac{15e^2}{8}e^{2t}+\left(-3e^2+\frac{15e^2}{4}\right)e^{2t}t+\frac{e^2t^4}{4}+e^2t^3+\frac{9e^2t^2}{4}+3e^2t+\frac{15e^2}{8}[/tex]

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A circle's diameter has endpoints at
(-4,-7) and (5,-2).
a) What is the length of the diameter?
b) What is the length of the radius?

Answers

Part (a)

We'll use the distance formula.

[tex](x_1,y_1) = (-4,-7) \text{ and } (x_2, y_2) = (5,-2)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(-4-5)^2 + (-7-(-2))^2}\\\\d = \sqrt{(-4-5)^2 + (-7+2)^2}\\\\d = \sqrt{(-9)^2 + (-5)^2}\\\\d = \sqrt{81 + 25}\\\\d = \sqrt{106}\\\\d \approx 10.2956\\\\[/tex]

The diameter is exactly [tex]\sqrt{106}[/tex] units long which approximates to roughly 10.2956 units. Round that decimal value however your teacher instructs.

========================================================

Part (b)

We divide the diameter in half to get the radius.

Therefore, the radius is exactly [tex]\frac{\sqrt{106}}{2}[/tex] units long which is approximately 5.1478 units.

urgent please help!!

Answers

Answer:

14cm.

Step-by-step explanation:

X is the hypotenus, 7√3 is the opposite and the other side is the adjacent. Choose sin from (soh, cah, toa) because you have to find 'H' (hyp) and opposite is given. Hence, sin 60= 7√3 over x. Cross multiply and you'll get x * sin 60= 7√3. Make x the subject of formula and 14 will be the answer.

A candlemaker uses 240 cubic centimeters of wax to create a scented candle using a cylindrical mold. he decides to offer a larger-sized candle, which uses twice as much wax as the smaller-sized candle. which mold can he use to make the larger-sized candle?

Answers

The mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

Cylinder

A cylinder is a surface created by projecting a closed two-dimensional curve along an axis intersecting the plane of the curve.

smaller-sized candle = 240 cubic centimeters

larger-sized candle = 2(smaller-sized candle)

= 2(240 cubic centimeters)

= 480 cubic centimeters

Therefore, the mold the candlemaker can use to make the larger-sized candle is 480 cubic centimeters.

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Answer:

A cylinder with a height that is double the height of the original mold, and a radius that is the same as the radius of the original mold.

Hope this helps!

Step-by-step explanation:

The rock does 1,000 bicep curl-ups on monday.on tuesday he does 30% more bicep curl-ups. on wednesday he does 45% more. how many more bicep curl-ups does he do on wednesday compared to monday

Answers

Answer:

either 885 more or 450 more

Step-by-step explanation:

Monday: 1000

Tuesday: 1000*1.3 = 1300

Wednesday:

I'm assuming 45% more from tuesday?

          1300*1.45 = 1885

or if not:

          1000*1.45 = 1450

either 885 more or 450 more

you can also just do 1000*1.3*1.45 = 1000*1.885 = 1885 if thats what the question means

What is the slope of (2,-1) and (8,4)

Answers

Answer:

5/6

Step-by-step explanation:

slope = 4-(-1)/8-2 = 5/6

Determine what type of model best fits the given situation: principal p is invested at an annual interest of rate r, compounded k times a year for t years.

Answers

The most appropriate model for a given situation is exponential.

What is compound interest?The interest you earn on interest is known as compound interest.Compound interest is a use of exponential functions. A specific sum is added to the account balance each time money is invested (or lent out). Interest is the amount of money that is added to the balance. The sum will continue to accrue interest after that interest has been added during the subsequent compounding period.In the settings of investments and savings, compound interest is used. A = P(1 + RT) is the formula for simple interest. The next section contains a definition of the variables. This indicates that the account value is the sum of the initial investment amount multiplied by one and the rate multiplied by the time.

The most appropriate model for a given situation is exponential.

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PLEASE HELP IM STUCK PLS

Answers

Step-by-step explanation:

the general slope-intercept form is

y = ax + b

a is the slope, b is the y-intercept.

we need to transform x + 2y = 6, so that we end up with y being all alone on one side, and the rest on the other side.

x + 2y = 6

2y = -x + 6

y = -x/2 + 6

if csc(θ)=2 and tan (θ)<0, determine the exact value of cos(θ)

Answers

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

What is the exact value of a trigonometric function?

In this question we have hints from two trigonometric functions necessary to find the exact value of the cosine function. In accordance with trigonometry, cosecant function is positive and tangent function is negative in the third quadrant of Cartesian plane and therefore the cosine function must be a negative number. Therefore, we can derive the value of the latter function by trigonometric formulas:

cos θ = - √[1 - (1 / csc θ)²]

If we know that csc θ = 2, then the exact of the cosine function is:

cos θ = -√[1 - (1 / 2)²]

cos θ = -√(3 / 4)

cos θ = -√3 / 2

By trigonometric functions and formulae, we find that the exact value of the cosine function is -√3 / 2.

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what is a real world example of a rational function, and how could you graph it and put it in a table?

Answers

An example of the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

What is a rational function?

This is the term that is used to refer to the fraction that is represented by the use of a rational fraction. That is there is denominator and a numerator.

The denominator must have a variable and this variable has to be of degree 1. Hence the real world example of a rational function would be when a person would decide to share a cookie with their friend. Each of them would get half of the cookie each.

How to graph a real world situation

First you have to know if it is an inequality or not. Then you have to assign x and y variables to numbers. From here you form an equation. This equation is plotted on a graph.

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A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?

Answers

The area of the trapezoidal tarp in the hotel is 47.3 square inches.

What is a trapezoid?A trapezoid is a quadrilateral having one pair of parallel opposite sides. It can have right angles (a right trapezoid) and congruent sides (isosceles), but neither is needed.

How do determine the area of the trapezoid?

The area of a trapezoid is calculated using:Area = 0.5 × (Sum of parallel sides) × Height

From the complete question, the parallel sides are 10ft and 12ft.

So, Area = 0.5 × (10 +  12) × h

Evaluate,

Area = 11 × h

The height (h) is computed using the cosine function shown below:

cos(120 - 90) = h/5

This gives

cos(30) = h/5

Make h the subject:

h = 5cos(30)

Evaluate:

h = 4.3

So, we get:

Area = 11 × 4.3

Evaluate:

Area = 47.3

Therefore, the area of the trapezoidal tarp in the hotel is 47.3 square inches.

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The complete question is given below:
A hotel builds an isosceles trapezoidal pool for children. it orders a tarp to cover the pool when not in use. what is the area of the tarp?

to find the height. first find that d is 60,45, or 120. this means the height of the trapezoid is approximately 2.5,4.3, or 3.5 feet. so the area of the tarp is approximately 47.3,30.0 or 38.5 square feet.

I'm not sure how to do both of them

Answers

The total surface area of the shape is 10053 cm²

Calculating Surface area

From the question, we are to determine the surface area of the shape

The surface area of the shape = Surface area of hemispherical part + Surface are of the cylindrical part

∴ Surface area of the shape = 2πr² + 2πrh + πr²

Where r is the radius

and h is the height of the cylindrical part

From the given information.

r = 20

h = 50

Putting the parameters into the equation, we get

Surface area of the shape = 2π(20)² + 2π(20)(50) + π(20)²

Surface area of the shape = 2π×400+ 2π×1000 + π×400

Surface area of the shape = 800π+ 2000π + 400π

Surface area of the shape = 3200π cm²

Surface area of the shape = 10053.096 cm²

Surface area of the shape ≈ 10053 cm²

Hence, the total surface area of the shape is 10053 cm²

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How to name a angle in 4 different ways?
First answer and correct answer gets to be brainliest!

Answers

Hey there!

4 ways to name angles

⇒ Use the vertex as the middle letter, and the point from each side (<ABC or <CBA)

⇒ Use the vertex only (<B)

⇒ Use a number (<1)

Classify angles according to their measure.

Acute angle: less than 90°

Right angle: exactly 90°

Obtuse angle: between 90° and 180°

Straight angle: exactly 180°

Thank you,

Eddie

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Find the limit. use l'hospital's rule if appropriate. if there is a more elementary method, consider using it. lim x→[infinity] ln(x) x

Answers

The limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex]  using L'Hospital rule is 0.

According to the given question.

We have to find the limit of ln(x)/x when x approaches to infinity.

If we let x = ∞, we get an indeterminate form [tex]\frac{\infty}{\infty}[/tex] ie. [tex]\frac{ln(x)}{x} = \frac{\infty}{\infty}[/tex].

And, we know that whenever we get indeterminate form ∞/∞ we apply L'Hospital rule.

Therefore, defferentiating numerator ln(x) and x with respect to x.

[tex]\implies \frac{d(ln(x))}{dx} = \frac{1}{x}[/tex] and [tex]\frac{d(x)}{dx} =1[/tex]

So,

[tex]\lim_{x\to \infty}\frac{\frac{1}{x} }{1}[/tex]

[tex]= \lim_{x \to \infty} \frac{1}{x}[/tex]

As, x tends to ∞, 1/x tends to 0. Because ∞ is very large number and 1 divided by a very large number always approaches to 0 and it is very close to zero.

Therefore,

[tex]\lim_{x \to \infty} \frac{1}{x} = 0[/tex]

Hence, the limit of [tex]\lim_{x \to \infty} \frac{lnx}{x}[/tex] is 0.

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Nereo and Azeneth start recording video at the same time. Nereo's phone starts with 1,0001{,}0001,0001, comma, 000 megabytes (MB\text{MB}MBstart text, M, B, end text) of free space and uses 7 MB7\,\text{MB}7MB7, start text, M, B, end text of space per second of video. Azeneth's phone has 1,255 MB1{,}255\,\text{MB}1,255MB1, comma, 255, start text, M, B, end text of free space and uses 10 MB10\,\text{MB}10MB10, start text, M, B, end text of space per second of video. How much free space will they have when they first have the same amount of space left?

Answers

Using a linear function, it is found that they will have 405 MB of free space when they first have the same amount of space left.

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The free space for each of Nereo and Azeneth can be modeled by a linear function, in which the slope is negative with the amount that each second of video takes and the y-intercept is the initial free space. Her the functions for the amount of free space after x seconds are given by:

N(x) = 1000 - 7x.A(x) = 1255 - 10x.

They will have the same amount of free space when:

N(x) = A(x)

1000 - 7x = 1255 - 10x

3x = 255

x = 255/3

x = 85.

The space will be of:

N(85) = 1000 - 7 x 85 = 405 MB.

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1/4a-3=1/4a(a-?) I need to finish this quick can someone repy fast!

Answers

Answer:

12

Step-by-step explanation:

Factoring out a 1/4 from 1/4a - 3, you get 1/4 (a - 12) as 12 * 1/4 = 3. Thus, ? = 12.

A company reduced the prices of its goals by 13% during a promotional sale. A product was sold for 435.00 during the promotional sales. What was the price before the promotional sales?




Answers

The price of the product before promotional sales was 500,000.

How to find out what the previous price was?

To find what the previous price of the product was, we must take into account that we know that 87% of the value is equal to 435,000. So to find out how much the 13% (discount) that the product had is equivalent to, we do the following operation:

435,000 × 100 ÷ 87 = 500,000

So we know that the 13% discount was 65,000

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PLEASE HELP

debra has $5. She bought 3 cakes of the same price and has 0.80$ left. what is the pride of 1 cake.​

Answers

Answer:

$1.40

Step-by-step explanation:

5.00-0.80=4.20

4.20 ÷ 3= 1.40

I need help with this one

Answers

A) Sqrt(4^(2/3x)) * 2^x = 1
4^(1/3x) * 2^x = 1
2^(2/3x) * 2^x = 1
2^(5/3x) = 1
Log(2)1 = 5/3x
0 = 5/3x
x = 0
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