I really need help with this it’s on Aleks

Correct Question:-

Find the equations of lines normal to the curve [tex]\rm{y=3x-x^3}[/tex] at points where it cuts the x axis.

[tex]\quad[/tex]

Solution:-

The given curve,

[tex]\longrightarrow\rm{y=3x-x^3}[/tex]

Differentiating wrt x we get,

[tex]\longrightarrow\rm{\dfrac{dy}{dx}=3-3x^2}[/tex]

This term is slope of tangent on the curve at a point (x, y).

Taking reciprocal,

[tex]\longrightarrow\rm{\dfrac{dx}{dy}=\dfrac{1}{3-3x^2}}[/tex]

and multiplying by -1,

[tex]\longrightarrow\rm{-\dfrac{dx}{dy}=\dfrac{1}{3x^2-3}}[/tex]

Now this term is slope of normal on the curve at a point (x, y).

[tex]\longrightarrow\rm{n(x)=\dfrac{1}{3(x^2-1)}}[/tex]

[tex]\quad[/tex]

The points where the curve [tex]\rm{y=3x-x^3}[/tex] cuts x axis is obtained by equating y = 0.

[tex]\longrightarrow\rm{0=y}[/tex]

[tex]\longrightarrow\rm{0=3x-x^3}[/tex]

[tex]\longrightarrow\rm{0=x(3-x^2)}[/tex]

[tex]\longrightarrow\rm{0=x(\sqrt3-x)(\sqrt3+x)}[/tex]

[tex]\Longrightarrow\rm{x\in\left\{-\sqrt3,\ 0,\ \sqrt3\right\}}[/tex]

So the points where the curve cuts x axis are (-√3, 0), (0, 0) and (√3, 0).

[tex]\quad[/tex]

Consider the point (-√3, 0).

The slope of normal at this point is,

[tex]\longrightarrow\rm{n(-\sqrt3)=\dfrac{1}{3((-\sqrt3)^2-1)}}[/tex]

[tex]\longrightarrow\rm{n(-\sqrt3)=\dfrac{1}{6}}[/tex]

Then equation of normal at this point is,

[tex]\longrightarrow\rm{y-0=\dfrac{1}{6}(x+\sqrt3)}[/tex]

[tex]\longrightarrow\bf{x-6y+\sqrt3=0}[/tex]

[tex]\quad[/tex]

Consider the point (0, 0).

The slope of normal at this point is,

[tex]\longrightarrow\rm{n(0)=\dfrac{1}{3((0)^2-1)}}[/tex]

[tex]\longrightarrow\rm{n(0)=-\dfrac{1}{3}}[/tex]

Then equation of normal at this point is,

[tex]\longrightarrow\rm{y-0=-\dfrac{1}{3}(x-0)}[/tex]

[tex]\longrightarrow\bf{x+3y=0}[/tex]

[tex]\quad[/tex]

Consider the point (√3, 0).

The slope of normal at this point is,

[tex]\longrightarrow\rm{n(\sqrt3)=\dfrac{1}{3((\sqrt3)^2-1)}}[/tex]

[tex]\longrightarrow\rm{n(\sqrt3)=\dfrac{1}{6}}[/tex]

Then equation of normal at this point is,

[tex]\longrightarrow\rm{y-0=\dfrac{1}{6}(x-\sqrt3)}[/tex]

[tex]\longrightarrow\bf{x-6y-\sqrt3=0}[/tex]

[tex]\quad[/tex]

Hence the equations of lines normal to the curve [tex]\rm{y=3x-x^3}[/tex] at points where it cuts x axis are,

[tex]\longrightarrow\left\{\begin{array}{ll}\bf{x-6y-\sqrt3}&\bf{=0}\\\bf{x+3y}&\bf{=0}\\\bf{x-6y+\sqrt3}&\bf{=0}\end{array}\right.[/tex]

Since Bob jumps on the cart in example 11.3 (p. 270), a kind of collision which this represents is: d) Perfectly inelastic.

An elastic collision can be defined as a type of collision between two objects wherein the total kinetic energy of the two objects remains the same after the collision. This ultimately implies that, there isn't a net loss of momentum and kinetic energy within the system due to the collision.

An inelastic collision can be defined as a type of collision between two objects wherein the total kinetic energy of the two objects changes the same after the collision. This ultimately implies that, there is a net loss of momentum and kinetic energy within the system due to the collision.

In this context, we can reasonably infer and logically deduce that the coefficient of restitution would be equal to zero (0) when bob jumps on the cart, resulting in a perfectly inelastic inelastic collision.

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Complete Question:

In example 11.3 (p. 270), when Bob jumps on the cart, what kind of collision is this?

a) Inelastic, but not perfectly inelastic

b) Rigid

c) Elastic

d) Perfectly inelastic.

Answer: 3.64

Step-by-step explanation:

3.64

What is the Nearest Hundredth?

Nearest hundredth is the second digit after the decimal point.

How to Calculate Rounding to the Nearest 100th?

If the digit after hundredth is greater than or equal to 5, add 1 to hundredth. Else remove the digit. Example

124.586

The third digit of right of decimal point is 6

The second digit after decimal point is 8 which is greater than 5

So add 1 to 8

Result = 124.59

its 3.6400 I believe since you are rounding to the nearest hundredth which would be in the 2nd place value to the right of the decimal and 32 would round down to 0.

The coordinates' weighted average is 4

The given parameters are:

Coordinate 2 has a weight of 2

Coordinate 3 has a weight of 2

Coordinate 10 has a weight of 1

The weight average is then calculated as:

Weight average = Sum of (Weight * Coordinate)/Sum of Weights

So, we have:

Weight average = (2 × 2 + 3 ×2 + 10 × 1)/(2 + 2 + 1)

Evaluate the quotient

Weight average = 4

Hence, the weight average of the coordinates is 4.

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A maximum of 1,048,576 rows are allowed in Microsoft Excel 2007. 15,384 columns. Columns and rows make up an Excel spreadsheet.

The arrangement of items next to or horizontally across one another is referred to as a row. As a vertical grouping of items according to category, a column can be said to exist. Left to right is the direction of arranging. From top to bottom, the set up is made. At far right is where the total is displayed.

here

Numbers 1, 2, 3, and 4 are used to designate the rows, which are horizontally oriented.

A, B, C, D, etc., are used to denote the letters that run horizontally along the columns.

Cells are what happen when a column and row intersect.

A maximum of 1,048,576 rows are allowed in Microsoft Excel 2007. 15,384 columns.

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Angle can be copied by following 6 steps.

These are the steps to copy an angle:

1.Make point B the center of the working line (l).

2.Create an arc (A, r) that intersects the two sides of angle A at locations S and T by setting your compass to any radius r.

3.Create an arc (B, r) with a point V where it intersects the line l.

4.Build an arc (S, ST).

5.Create an arc at point W where (V, ST) intersects (B, r).

6.You're done after you draw line BW.

Angle can be copied by following 6 steps.

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10 more than 20 will be Addition of 10 and 20 which is supposed to be 10 plus 20 = 30.

Addition is the process of combining items and counting them as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.

The SUM is the result or conclusion that results from adding two or more integers. Addends are the numbers that are added.

We simply changed "more than" to "plus" and found the answer to the straightforward math issue. It is equivalent to 10 + 20 to add 10 to 20. Therefore, the answer is 30 once more.

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Answer:

12 first class and 40 tourist

Step-by-step explanation:

Answer:

40 tourist class passengers, and 12 first class passengers.

Step-by-step explanation:

Here's my explanation:

We let X be the number of passengers booking for the tourist class.

If there were 52 passengers who paid 1360, then to find the number of passengers who booked first class, we write:

52-x

And if the airline fares are 30 per first class and 25 dollars for tourist class, you would say 30.00(first class)+25.00(tourist class)=1360

Using substitution, plug-in 52-x for the first class:

30(x)+25(52-x)=1360

30x+1560-25x=1360

1360-1560 =25x-30x

-200=-5x

x=40

Plug in 40 for x,

52-40=12

So, 40 tourist class passengers, and 12 first class passengers.

When a point or object is moved but its size and shape don't change, it is said to have undergone rigid motion, sometimes referred to as a rigid transformation.

The separation between each pair of the geometric object's points is preserved during a rigorous change of the object. In other words, a rigid transformation maintains the object's size and shape. For instance, the rigid transformation of a triangle retains the angles and lengths of the triangle. Imagine a stiff shape distortion, similar to a cardboard shape. The form remains the same after being pushed left and right, rotated, and flipped.

When the mold was created using putty, the opposite was true. The thing can then be twisted and stretched. These conversions, nevertheless, are not exact. Stretching a form alters the distances between each pair of its points.

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We can follow Arithmetic series, then the number of cubic feet concrete is required for the first 12 steps = 140.4 cubic feet.

Given that,

The first step requires 1. 8 cubic feet of concrete,

The first 5 steps require a total of 27 cubic feet.

An arithmetic series is the sum of the terms in an arithmetic sequence with a definite number of terms. Following is a simple formula for finding the sum: Formula 1: If [tex]S_{n}[/tex] represents the sum of an arithmetic sequence with terms , then. This formula requires the values of the first and last terms and the number of terms.

For an arithmetic series

[tex]a , a+d , a+2d , a+3d , .......[/tex]  

where a is the first term and d is the common difference, the sum of n terms equals,

[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]         (Equation-1)

Since the first step requires 1.8 cubic feet of concrete, a = 1.8.

Now, the first 5 steps require 27 cubic feet of concrete, that is,

[tex]S_{5}[/tex] = 27

a = 1.8

n = 5

We can substitute values in equation-1,

[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]  

[tex]S_{5}[/tex] = (5) (1.8) + [tex](\frac{5(5-1)}{2} )d[/tex]

[tex]S_{5}[/tex] = (5) (1.8) + [tex](\frac{5*4}{2} )d[/tex]

[tex]S_{5}[/tex] = (5) (1.8) + [tex]\frac{20}{2} d[/tex]

[tex]S_{5}[/tex] = (5) (1.8) + 10 d

[tex]S_{5}[/tex] = 9 + 10 d

Then, [tex]S_{5}[/tex] = 27

27 = 9 + 10d

27 - 9 = 10d

18 = 10d

d = [tex]\frac{18}{10}[/tex]

d = 1.8

Find the concrete required for 12 steps.

Then, we can substitute n = 12

So,

We can write,

[tex]S_{n}[/tex] = [tex]a_{n} +(\frac{n(n-1)}{2} ) d[/tex]  

[tex]S_{12}[/tex] = (12) (1.8) + [tex](\frac{12(12-1)}{2} )d[/tex]

[tex]S_{12}[/tex] = (12) (1.8) + [tex]\frac{12*11}{2} d[/tex]

[tex]S_{12}[/tex] = (12) (1.8) + [tex]\frac{132}{2} d[/tex]

[tex]S_{12}[/tex] = (12) (1.8) + 66 d

[tex]S_{12}[/tex] = 21.6 + 66 d

We can substitute d = 1.8

[tex]S_{12}[/tex] = 21.6 + 66 (1.8)

[tex]S_{12}[/tex] = 21.6 + 118.8

[tex]S_{12}[/tex] = 140.4

Therefore,

We can follow Arithmetic series, then the number of cubic feet concrete is required for the first 12 steps = 140.4 cubic feet.

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Answer: The maximum students that would be able to attend the trip is 40 students. Because 25 multiplied by 40 is = 1,000 and the budget is only 3,000 the answer is 40 students

Step-by-step explanation: Hope this helps =)

An angle is a figure found by two rays with the same initial point. In geometry, various names are given to different angles and their combinations depending upon the type of angles they make.

various geometrical shapes such as a triangle or a quadrilateral contain a set of angles that are governed by a set of rules.

For example, there are three interior angles in a triangle, the sum of which is always equal to 180 degrees. This means that if we are cultured of two of the angles in a triangle, we can find the third.

alike using different rules and the available information we can find the missing angle in a geometrical figure.

But, before understanding different state where we can find the missing angles, we should first recall some of the properties of different geometric shapes that will be useful in finding missing angles.

1. The sum of the measure of the three interior angles of a triangle is always 180 degrees.

2. If one of the angles of a triangle is 90 degrees, the sides that make the right angle is called the base and the perpendicular while the third side is called the hypotenuse.

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In Euclidean geometry, parallel lines (lines that never intersect) are equidistant in the sense that the distance of any point on one line from the nearest point on the other line is the same for all points.

A point is said to be equally far from a group of objects if there is an equal distance between it and each member of the group. 

The perpendicular bisector of two specified (different) points is their location in two-dimensional Euclidean geometry. The locus of points equidistant from two provided points in three dimensions is a plane, and generalizing further, the locus of points equidistant from two given locations in n-dimensional space is a (n1)-space.

The circumcenter of a triangle is a location that is equally spaced from each of the three vertices.

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Answer:

we can conclude that there are 3 solid combined in this

a + b + c = d as the total volume

[(6)(6)(2)] + [(6)(3)2)] + [(6)(2)(2)]

= 72 + 36 + 24

= 132 ft³

Step-by-step explanation:

In fact, if we knew that 64 = 8 sqrt 64 = pm 8 64 = 8, then x would no longer be a function and would instead be a relationship, causing the graph to be repeated twice with the value 64. (en 8 y -8).

For instance, the 64-bit number, which is written as 4, is 4, since 64. Additionally, it is the length of a 64-volume cube's arista.

What our community finds fascinating. La raiz sexta es 2 because cuando dividimos 64/2 obtenemos un resultado especfico and cuando multiplicamos seis veces dos obtenemos 64.

conversation of 64 into binary

Binary value for 64 is 1000000. In a binary number system, we only utilize the digits 0 and 1, as opposed to the decimal number system, which uses the numbers 0 to 9 to express a number (bits).

= [tex]64_{10}[/tex] = [tex]1000000_{2}[/tex]

here, the binary of [tex]64_{2} = 1000000_{2}[/tex]

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Go to the Home tab and choose Number from the drop-down menu. In addition, you have the following choices: When choosing Number, press CTRL + 1. Right-click the cell or cell range, choose Format Cells..., then choose Number.

To calculate and represent a quantity, a number, an arithmetic value, is needed. Numbers are represented by mathematical inscriptions, such the letter "3." Using logical symbols or digits to represent numbers is known as a number system.

here ,

The cells you want to format should be selected.

Place your cursor over the Dialog Box Launcher next to Number on the Home tab.

Click Fraction in the Category list.

Select the desired fraction format type from the Type list by clicking it.

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Answer:

Line 1 to Line 2 = Distributive property

Line 2 to Line 3 = ASSOCIATIVE PROPERTY OF MULTIPLATION

Line 3 to line 4 = COMMUNITIVE PROPERTY OF MULTIPLICATION

Pls can you give me brainliest

pls :(

Answer: -1

Step-by-step explanation:

slope form is [tex]m = \frac{y^{2} - y^{1} }{x^{2} - x^{1} }.[/tex] M is the slope. x1 and y1 are coordinates of a point along the line. x2 and y2 are the coordinates of another point along the line.

So we need to substitute in the points you have. let's put in (1, -2) for x1 and y1, and (2, -3) in x2 and y2. it makes [tex]m = \frac{-3-(-2)}{2-1}[/tex]

Now all you have to do is solve the equation.

[tex]m = \frac{-3-(-2)}{2-1}[/tex]

[tex]m = \frac{-1}{1}[/tex]

m = -1

(btw the line's equation would be y = -x - 1)

Answer:

-1

Step-by-step explanation:

To find the slope between two points we can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -2 - -3)/(1 -2)

   = ( -2 +3)/( 1-2)

  = 1/-1

  = -1

It will take 2 year the population to reach 300 students.

What is rounding to the nearest tenth?

Look at the hundredth number to round the decimal number to the nearest tenth. If it's more than 5, add one to the tenth value. Remove all the numbers that are present after the tenth place and leave the tenth place value alone if it is less than 5. To the nearest tenth, 4.6, for instance, is 4.624.

Given that, the initial number of students is 242.

The student population is growing at 12% a year.

The number of students that increases is 300 - 242 = 58.

Applying formula

I = PRT

I = The number of students that increased = 58

P = initial number of students = 242

T = Time

R = rate of increasing =12% = 0.12

Therefore,

58 = 242 × T × 0.12

T = 58/(242 × 0.12)

T = 1.997

T = 2.0 years

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Three types of numbers fall under the heading of "real numbers," which we will discuss in a moment. Real numbers include all types of numbers, including whole, rational, and irrational numbers.

A real number is a quantity that may be represented mathematically by an endless decimal expansion. In contrast to the counting-derived natural numbers 1, 2, 3,..., real numbers are used to quantify constantly altering quantities such as size and time. Rational and irrational numbers are both included in real numbers. Real numbers include both irrational and rational numbers such as 3, 22/7, and integers such as (-2, 0, 1), fractions such as (1/2), and decimal numbers such as (1/2).

whole = 0,1,2,3,4,5,6,7,8,9...….

rational = 1,2,3,3/4,5/6,...…

irrational =  [tex]\sqrt{8}[/tex], etc

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The amount of earned income the Salazars can report for EITC purposes in 2021 is $21,000.

The maximum amount of earned income the Salazars can report for EITC purposes in 2021 is $21,000. This is calculated by adding Braden's nontaxable combat pay ($14,000) and his wife's earned income ($7,000).

Formula:

Maximum Earned Income for EITC = Braden's Nontaxable Combat Pay + Wife's Earned Income

Maximum Earned Income for EITC = $14,000 + $7,000

Maximum Earned Income for EITC = $21,000

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The probability with which bob plays l in the mixed strategy equilibrium = 0.9090

What is Probability?

The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true. An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.

Here suppose Alice plays U with probability P and D * with probability ( 2 - P)

Therefore, when Bob plays L, Bob gets payoff 8 with probability P and (2) with probability ( 2 - P). Hence

= 8 * P + 2 * ( 2 - P)

= 8P +4 - 4P

= 4 + 8P

Also, when Bob plays R, Bob gets pay off 4 with probability P and 7 probability (2-P). Hence expected payoff is

= 4*P+7(2-P)

= 4P+14-7P

=14-3P

At mixed strategy nash equilibrium the expected payoffs are equal. hence,

4 +8P = 14-3P

3P+8P = 14-4

11P = 10

P = 10/11

P = 0.9090

In the mixed strategy equilibrium, Bob's chances of playing l are equal to 0.9090.

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Here suppose Alice plays U with probability P and D * with probability ( 2 - P)

Therefore, when Bob plays L, Bob gets payoff 8 with probability P and (2) with probability ( 2 - P). Hence

= 8 * P + 2 * ( 2 - P)

= 8P +4 - 4P

= 4 + 8P

Also, when Bob plays R, Bob gets pay off 4 with probability P and 7 probability (2-P). Hence expected payoff is

= 4*P+7(2-P)

= 4P+14-7P

=14-3P

At mixed strategy nash equilibrium the expected payoffs are equal. hence,

4 +8P = 14-3P

3P+8P = 14-4

11P = 10

P = 10/11

P = 0.9090

In the mixed strategy equilibrium, Bob's chances of playing l are equal to 0.9090.

The given statement w.r.t clinical trials is true.

Clinical trials are prospective biomedical or behavioral research studies on human participants designed to answer specific questions about biomedical or behavioral interventions, including new treatments and known interventions that warrant further study and comparison.

Given is a statement about the clinical trials.

The given statement that Clinical trials enroll individual subjects and enable randomization of subjects to receive or not receive the intervention is true.

Therefore, the given statement w.r.t clinical trials is true.

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The factors of the expression 2[tex]x^{2}[/tex] -5x -12 are (x - 4) and (2x+3)

given that

2[tex]x^{2}[/tex] -5x -12 =0

in the above equation

a = 2[tex]x^{2}[/tex]

b =-5x

c = -12

now we need to multiply a and c

a * c = 2[tex]x^{2}[/tex] * -12 = -24[tex]x^{2}[/tex]

now split b into two terms such that sum is equal to -5x  and their product is -24

-5x = -8x +3x

2[tex]x^{2}[/tex] -5x -12 =0

2[tex]x^{2}[/tex] -8x + 3x -12 =0

2x(x - 4)+3(x-4) =0

(2x+3)(x-4) =0

The factors of the expression 2[tex]x^{2}[/tex] -5x -12 are (x - 4) and (2x+3)

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Observing the graph and the lines drawn, The graph is inequality is known if it is showing the region for which the inequality exists. Usually it is shown with arrows at the end of the line.

An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made. Less than, larger than, less than or equal to, and more than or equal to are the four fundamental inequalities.

The graph of a function f in mathematics is the collection of ordered pairs where f(x)=y. These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.

Using a given graph,

We know that the graph is inequality if it is showing the region where the inequality exists,

It is usually shown using arrows at the end of the line towards the direction where the inequality is satisfied.

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The graph of the equation given is mentioned below.

What is plot point in graph ?

Whenever we draw a point on our grid, we'll call it "plotting a point." The grid is really called a "graph" and the points we plot are called "coordinates." These are really locations on a plane -- we're just finding and labeling them.

Equation given,

y = 3/5x - 1    ----eq(i)

y = 2/5x        -----eq(ii)      

Now, for this two equation we infinite points for real numbers.

Now, take some points to plot the graph.

First for the eq(i)

Put x = 0, so y = -1

Put x = 5, so y = 2

Points for eq(i) is (0, -1) and (5, 2)

Now, for eq(ii)

Put x = 0, so y = 0

Put x = 5, so y = 2

Points for eq(ii) is (0, 0) and (5, 2)

Common point is (5, 2)

Now, plot this point on graph.

Hence, for more clarity graph of the equation given is mentioned below.

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Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

graph: (attached picture)

Step-by-step explanation:

Answer:

Vertex = (0,0)

Focus = (0, -1/8)

Axis of symmetry; x = 0

directrix, y = 1/8

Step-by-step explanation:

Answer:

All the options except for option B.

Answer:

A,C and D are not.

where as B is solution

Answer:

[tex]36.77150[/tex], or 37 (rounded)

Step-by-step explanation:

1. [tex]\sqrt{97} = 9.84885[/tex]

2. [tex]9.84885[/tex] + [tex]8.169178744[/tex] = [tex]18.01803[/tex]

3. [tex]\frac{18.01803}{0.49}[/tex]

4. = [tex]36.77150[/tex]

You can simplify 36.77150 to 37

... Hope this helped! Have a wonderful New Year!

The value of the equation is A = 36.77

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

A = ( √97 + 2.014³ ) / 0.49   be equation (1)

On simplifying the equation , we get

√97 = 9.8488578

2.014³ = 8.169178744

Substituting the values in the equation , we get

A = ( 9.8488578 + 8.169178744 ) / 0.49

A = 18.018036544 / 0.49

A = 36.77150

Therefore , the value of A is 36.77

Hence , the equation is A = 36.77

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