The first step in solving an inequality is to isolate the variable on one side of the inequality sign. This is also known as "clearing the inequality" of the variable. This can be done by using inverse operations such as addition, subtraction, multiplication, and division.
For example, if the inequality is 3x + 2 > 7, the first step is to isolate the variable x by subtracting 2 from both sides:
3x + 2 > 7
3x > 5
Then, divide both sides by 3 to get x > 5/3
This is the first step in solving an inequality, as now the variable x is isolated on one side of the inequality sign, and it's clear what the inequality is asking for.
It's important to note that when solving inequalities, it's crucial to keep the direction of the inequality sign the same, meaning if you multiply or divide by a negative number, you need to switch the direction of the inequality sign as well.
Also, it's important to check if the inequality is not valid, if the operation you are doing creates a division by zero, it will be an invalid inequality.
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Which trig ratio is 5/11?
Answer:
cos(T) = 5/11
Step-by-step explanation:
cos = adjacent(5)/hypotenuse(11)
So whatever "cosine" of something to choose, the adjacent side to the angle needs to be five. It cannot be the right angle, therefore only the option "T" remains, as eleven would always be the hypotenuse for any angle.
Write a paragraph proof of the corollary interior angles theorem.
A corollary is a theorem that connects to an established theorem in mathematics with a brief proof. As opposed to statement or theorem, the term "corollary" is inherently arbitrary.
Explain about the corollary interior angles theorem?A corollary may be unquestionably true if the idea or theory it is founded on is correct. Any triangle's internal angles, for instance, add up to 180 degrees in all cases. Each interior angle of an equilateral triangle is 60 degrees, which is a corollary of the aforementioned theorem.
A triangle is equiangular if it is equilateral, which is a corollary to the Base Angles Theorem. Converse of Base Angles Theorem Corollary: If a triangle is equiangular, it is also equilateral.
The sum of the measurements of the two distant interior angles determines how large an exterior angle of a triangle must be. the triangle's angle-sum Corollaries: A right triangle's acute angles are complimentary. A theorem whose proof naturally follows from another theorem is called a corollary.
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The corollary interior angles theorem is a mathematical result that relates to the number of sides in a polygon and the sum of the interior angles of that polygon.
What is corollary interior angles theorem?The corollary interior angles theorem states that if a polygon has n sides, then the sum of its interior angles is equal to (n-2) times 180 degrees. This theorem is a direct result of the interior angle theorem, which states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees. To prove the corollary interior angles theorem, we first consider a triangle with three sides. The sum of the interior angles of a triangle is equal to 180 degrees, which confirms that the interior angle theorem holds for a triangle. We can then use this result to extend the theorem to polygons with more sides by induction. If we add one more side to the polygon, the sum of the interior angles increases by 180 degrees. By continuing this process and adding sides to the polygon, we can conclude that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees. This confirms the corollary interior angles theorem.
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Two students can eat 4 doughnuts in 6 minuts. At this rate, how many doughnuts will be eaten by 8 students sin 9 minutes?.
By using the ratio formula, the number of doughnuts that will be consumed of 8 students in the time period of 9 minutes is 24 doughnuts.
The ratio formula compares the connection between two quantities or numbers. In this case, we are given that:
2 students can eat 4 doughnuts in 6 minutes
By using the ratio formula, 1 student can eat = 4/2 = 2 doughnuts in 6 minutes
It takes an average student about 3 minutes to consume a doughnut using the formula= 6/2 = 3 minutes
In one minute, the amount of doughnut can be consumed by a student is 1/3 of a doughnut
This method can be used to predict how many doughnuts 8 students can consume in 9 minutes:
X = 8 x 9 x (1/3) = 24 doughnuts
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What are the mathematical concepts used to calculate insurance premiums?
The mathematical concepts used to calculate insurance premiums include probability, actuarial science, risk assessment, pricing models, financial models, and statistical analysis.
Probability:
To calculate premiums, insurance companies use statistical data to determine the likelihood of a claim occurring. Probability is used to estimate the likelihood of certain events happening, such as accidents, illnesses, or natural disasters, and to determine the likelihood of a claim being made.
Actuarial Science:
Actuarial science is the application of mathematical and statistical methods to assess risk and uncertainty in insurance, finance, and other industries. Actuaries use mathematical models to analyze data and make predictions about future events, which is crucial in determining insurance premiums.
Risk Assessment:
Insurance companies use risk assessment to determine the level of risk associated with insuring a particular individual or group. Factors such as age, health, occupation, and location are considered when assessing risk, and premiums are adjusted accordingly.
Pricing models:
Pricing models are used to determine the cost of insurance based on the perceived level of risk. Pricing models like Loss Ratio, Pure Premium, and Captive pricing are used to arrive at the insurance premium.
Financial Models:
Financial models are used to determine the long-term financial stability of an insurance company and to ensure that the company has enough funds to pay out claims. Actuaries use financial models to calculate the amount of money an insurance company needs to set aside in order to pay claims and to determine the long-term financial health of the company.
Statistical Analysis:
Insurance companies use statistical analysis to evaluate data on claims and losses, and to identify patterns that can be used to predict future claims and losses. This analysis is used to identify trends in claims, to identify high-risk groups, and to set premiums.
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Determine whether the point (1, 1) is a solution to the system of equations. Explain your reasoning in complete sentences. graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one. The graphs intersect at the point 0 comma 2
(1, 1) is not solution of system of equations.
What is Graph?Graph is a mathematical representation of a network and it describes the relationship between lines and points.
We need to check the point (1, 1) is a solution to the system of equations.
graph of a line 3 times x plus 2 and the absolute value of x minus 1 plus one.
y = 3x + 2
g = |x-1| +1
We obtain the intersection point
(0,2)
The only point of intersection of the graphs is (0, 2).
The point of intersection is the solution to the system of equations. (1, 1) is not the point of intersection
Hence, (1, 1) is not solution of system of equations.
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When Angel left his house in the morning, his cell phone battery was partially charged. Let
B
B represent the charge remaining in Angel's battery, as a percentage,
t
t hours since Angel left his house. A graph of
B
B is shown below. Write an equation for
B
B then state the
x
x-intercept of the graph and determine its interpretation in the context of the problem.
B =
The x intercept of the function is
Which represents
1.the charge of the battery when Angel woke up
2.the charge of the battery when Angel left his house
3.the number of hours until Angel’s phone dies
4.the percentage charge that Angel’s phone loses each hour
The slope of -6 means that the battery reduces by 6% each hour
What is the linear equation?
Linear equations are the equations of degree 1. It is the equation for the straight line. The standard form of linear equation is ax+by+c =0, where a ≠ 0 and b ≠ 0.
The slope of -6 means that, the battery reduces by 6% each hour and the equation is B = -6t + 48
The points
The points on the graph are represented using the following ordered pair (1, 42) and (5,18)
The slope
Start by calculating the slope (m) using:
m = (B2 - B1)/(t2 - t1)
So, we have:
m = (18 -42)/5-1
m = -24/4
m = -6
The equation
The equation is then calculated as:
B = m(t - t1) + B1
This gives
B = -6(t - 1) + 42
B = -6t + 6 + 42
B = -6t + 48
Hence, The slope of -6 means that the battery reduces by 6% each hour
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NEED HELP ASAP - Algebra 2
Identify the first step that shows an error in the problem below.
Answer: The exponential form should be 10⁵=9x+1 instead of 9x+1=10⁵
Step-by-step explanation:
The exponential form of a logarithm should be the other way around.
What is a 3-dimensional vector?
A 3-dimensional vector is a line segment running from a point called head to the point called tail in 3-Dimensional space.
Vectors are mathematical or geometrical quantity that has two independent properties i.e., direction and magnitude. There are many types of vectors like unit vectors, equal vectors, etc.
The magnitude of the vector is the length of the line segment without it the direction has no power, Similarly unit vectors help us to find the direction of vectors and their magnitude is 1.
A 3-dimensional vector has majorly 3 components i.e., it has projections in the x, y, and z axes. For a three-dimensional vector A(a1,a2,a3), the formula for its magnitude is ∥a∥=√a21+a22+a23.
Along with magnitude and directions, the 3-D vectors also have angles and they are formed from the vector directly to each of the 3 positive axes.\ i.e., x, y, z axes. The formula used to calculate angle is θ = cos-1 [ (a · b) / (|a| |b|) ]
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Can 7 cm 5 cm and 3 cm form a triangle?
Yes, the triangle can be easily formed for the sides 7 cm, 5 cm and 3 cm.
According to the side side side rule of triangle, if the sum of the any two sides of triangle is more than third side, it will form a triangle. Let us check the same by assuming side a to be 7 cm, side b to be 5 cm and side c to be 3 cm.
Side a + side b > side c
7 + 5 > 3
Add the digits in Left Hand Side of the equation
12 > 3
Side b + side c > side a
5 + 3 > 7
Add the digits in Left Hand Side of the equation
8 > 7
side c + side a > side b
3 + 7 > 5
Add the digits in Left Hand Side of the equation
10 > 5
We see that the two sides of the triangle are greater than third side, hence, it is possible to form the triangle.
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Two factories, National Food Inc. and Anderson's Mill, produce canned food. There is a proportional relationship between the amount of time each factory runs and the amount of food it produces.
The number of the cans that is produced is 5832.
What is a direct proportion?
We know that the term direct proportion has to do with a case in which one of the variables is increasing and the other is also increasing along side. This implies that the two variables can be seen to increase at the same time.
We have that the relationship of the process can be given as shown in question in simple format as; y = 243x where;
x = Number of hours
y = Number of cans
After 24 hours, we have;
y = 243(24)
y = 5832
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physical activity is important for good health and can reduce the risk of many diseases. During 31 days last summer a cyclist rode the same number of miles every day for a total of 1,085 miles how many miles did she ride each day
Answer:
Below
Step-by-step explanation:
1085 miles / 31 days = 35 miles/day
tara has 3 boxes of books each box has 48 books tara divides the books amongst 3 friends how many books will each friend get
Each friend will get 48 books. The solution is obtained using arithmetic operations.
What are arithmetic operations?
There are four basic operations which are listed as follows:
Addition(‘+’): This operation deals with finding the sum.Subtraction(‘-’): This operation deals with finding the difference. Multiplication(‘×’): This operation deals with finding the product.Division(‘÷’): This operation deals with finding the quotient.Now, Tara has 3 boxes of books and each box contains 48 books.
So, the total books that Tara has is equal to 3×48= 144.
Thus, Tara has total 144 books.
Tara divides the books among 3 friends.
So, the number of books that each friend will get is equal to 144÷3= 48
Hence, each friend of Tara will get 48 books.
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christine's rectangular bedroom has a perimeter of 44 feet. the llength of her bedroom is 2 more than the width. what are the dimensions of her room
Answer:
Step-by-step explanation:
44/4= 11
44-24/2=12
20/2=10
The room is 10 x 12' long
What are the 3 types of 3D modeling?
Polygonal Modeling: a type of 3D modeling that uses points, lines, and polygons to create a 3D object. NURBS Modeling: a type of 3D modeling that uses mathematical equations to create smooth curves and surfaces. Subdivision Modeling: a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes.
1. Polygonal Modeling: This type of 3D modeling uses points, lines, and polygons to create a 3D object. The polygons are connected together to create the 3D shape, and then textures and colors can be applied to the shape. This type of modeling is often used to create characters and environments for video games and animations.
2. NURBS Modeling: NURBS stands for Non-Uniform Rational B-Splines. This type of 3D modeling uses mathematical equations to create smooth curves and surfaces. NURBS modeling is often used for creating organic shapes such as cars and furniture.
3. Subdivision Modeling: Subdivision modeling is a type of 3D modeling that uses subdivision surfaces to create smooth, organic shapes. This type of modeling is often used for creating characters and creatures for video games and animations.
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How do the functions from part a differ from functions you have used in algebra in the past?
The functions differ from functions that we have used in algebra in the past as the functions can be combined and are more about rotation rather than where they move.
An output variable and one or more input variables are the minimum number of variables in a function.
An equation can have any number of variables and declares that two expressions are equal (none, one, or more). Although not all equations are functions, a function is frequently expressed as an equation.
It should be recalled that a function is merely an equation in which the x inserted produces precisely one from the equation.
In this instance, the functions are different from the ones we have used in algebra in the past since they may be coupled and focus more on rotation than on where they travel.
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One bag holds 11 cherries how many cherries are in 143 bags
143x11
=1573 cherries
One bag holds 11 cherries and there are 143 bags. To find out how many cherries there are, we would need to multiply the amount of cherries by the number of bags.
[tex]11\times143[/tex]
[tex]=\fbox{1573 total cherries}[/tex]
d/4-9=-3
show work
show check
Answer:
d = 24
Step-by-step explanation:
d/4 - 9 = -3
d/4 - 9 + 9 = -3 + 9
d/4 = 6
d/4 * 4 = 6*4
d = 24
Check:
(24)/4 - 9 = -3
6 - 9 = -3
-3 = -3 (Correct)
Hope this helps!
A map has a scale of 1 cm to 10 km. What would the distance be in kilometres if the distance displayed on the map is 7.211102550928 cm?
The real distance by means of scales used in the map that is described in the statement is approximately equal to 72.11102550928 kilometers.
How to predict the real distance from a map by using scales
Scales are a useful resource to represent any system in a size different than real. Maps are usually created from application of scales. Mathematically speaking, scales are described by following mathematical ratio:
r = s / R
Where:
r - Map scale, in centimeters per kilometer.s - Scale distance, in centimeters.R - Real distance, in kilometers.If we know that r = 0.1 centimeters per kilometers and s = 7.211102550928 centimeters, then the real distance derived from the distance shown in the map that is described in the statement is:
R = s / r
R = (7.211102550928 cm) / (0.1 cm / km)
R = 72.11102550928 km
By using scales on the map, the real distance is approximately equal to 72.11102550928 kilometers.
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If the scale factor of figure A
too figure B is 7:2 find the perimeter of figure A
The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.
What is perimeter?
A boundary is a closed path that encompasses, encircles, or delimits a two-dimensional shape or a one-dimensional length. A circle's or an ellipse's perimeter is its outermost portion. Numerous applications in real life involve the perimeter calculation. The radius of a shape's edge is known as the perimeter. By summing the lengths of the sides of various forms, discover how to calculate the perimeter. By multiplying the lengths of the sides, one can always get a shape's perimeter. The area surrounding an object is called its perimeter. An enclosed garden is one example at your home. The distance around anything is called its perimeter. A 200-foot fence will be needed for a yard that is 50 feet by 50 feet.
Ratio factor of A to B = 7:2
Proportion between the perimeters = 7/2
We now understand that a shape's perimeter equals the sum of all its sides. Consequently, using the values from the provided figure, enter the following expression:
A1 / 9+5+9+12 = 7/2
A1 = (7*35)/2
A1 = 122.50 units.
The perimeter of a particular form is equal to the sum of its sides, hence the scale factor indicates that the perimeter of Figure A is 122.50 units.
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can someone show mw how to do liner programming on desmos :)?
Find the range for the measure of the third side of a triangle when the measures of the other two sides are 18 ft and 23 ft.
Answer:
The measure of the third side of a triangle, when the measures of the other two sides are 18 ft and 23 ft, must be greater than the difference between the measures of the other two sides (which is 18 ft - 23 ft = -5 ft) and less than the sum of the measures of the other two sides (which is 18 ft + 23 ft = 41 ft).
This is because according to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. So the measure of the third side must be between the difference of the two given sides and the sum of the two given sides.
Therefore the range of the measure of the third side of a triangle with side lengths 18 ft and 23 ft is:
(-5 ft < x < 41 ft)
or
[x > -5 ft and x < 41 ft].
It is also important to note that any value of x within this range will produce a valid triangle, however, any value less than -5 or greater than 41 will not.
Step-by-step explanation:
can someone post the back of the paper on Quiz 3-1 Parallel Lines, Transversals, and Special Angle Pairs
The following statements are true:
Segment DEF is parallel to ABC
The line segment AB is parallel to DE
Line FC is parallel to AD
the line that is skewed to DE is BC
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)
Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;
DEF is parallel to ABC
CADF is parallel to CBEF
For the lines, the lines that are parallel to each other are:
AD is parallel to BE
AB is parallel to DE
FC is parallel to AD
Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC
The missing image is attached with the answer below.
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need answer asap <3 ! thank you so much to anyone that answers !
Answer:
A. -1
Step-by-step explanation:
imma human calculator and no one can stop me
Write an equation of the perpendicular bisected of the segment with endpoints (3,7) and (-1,-5)
The equation of perpendicular line that bisects the line segment is y = - (1 / 3) · x + 4 / 3.
How to find the equation of the perpendicular line that bisects a line segment
In this problem we must determine the equation of the line that is perpendicular to a line segment and partitions the line segment in two parts of equal length, it happens when the perpendicular line passes through the midpoint of the line segment.
The equation of the line in explicit form is shown below:
y = m · x + b
Where:
m - Slopeb - Interceptx - Independent variabley - Dependent variableIn addition, two lines are perpendicular to each other when the following relationship is observed:
m · m' = - 1
Where:
m - Slope of the original line.m' - Slope of the perpendicular line.Besides, the slope of a line can be determined by secant line formula:
m = Δy / Δx
Where:
Δx - Change in independent variable.Δy - Change in dependent variable.And lastly, the midpoint of a line segment is determined by this formula:
M(x, y) = 0.5 · A(x, y) + 0.5 · B(x, y)
First, find the midpoint of the line segment:
M(x, y) = 0.5 · (3, 7) + 0.5 · (- 1, - 5)
M(x, y) = (1.5, 3.5) + (- 0.5, - 2.5)
M(x, y) = (1, 1)
Second, determine the slope of the line related to line segment:
m = (- 5 - 7) / (- 1 - 3)
m = (- 12) / (- 4)
m = 3
Third, calculate the slope of the perpendicular line:
3 · m' = - 1
m' = - 1 / 3
Fourth, find the intercept of the equation of perpendicular line:
b = y - m · x
b = 1 - (- 1 / 3) · 1
b = 1 + 1 / 3
b = 4 / 3
Fifth, write the equation of perpendicular line:
y = - (1 / 3) · x + 4 / 3
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Kenny is using division to write a fraction equivalent to 30/100 she tried to divide the numerator and denominator by three she got stuck what advice would you give her
The advice I will give Kenny that was using division to write a fraction equivalent to 30/100 after she tried to divide the numerator and denominator by three, is to also divide them by factor of 10.
How can fraction equivalent be obtained?The concept that will be used is division,
The given values is 30/100, if we divide the numerator and denominator by three, we have 10/100.
Then we can also divide the numerator and denominator of 10/100 by factor of 10, then we will have 1/10.
It should be noted that Division in mathematics is the process of dividing an amount into equal parts.
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6 x. _. = 3 what is the missing number
Answer:
1/2
Step-by-step explanation:
6 x __ = 3
We divided by 6 into both sides
x = 3/6 = 1/2
So, the missing number is 1/2
compare the end behavior of the functions g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20 and h(x) = "-3x^4" - 16x - 1. Explain your reasoning.
The end behavior of the functions g(x) and h(x) are the same and both functions approach negative infinity as x becomes large in either direction.
What is end behavior?Generally, The end behavior of a function refers to the behavior of the function as x approaches positive or negative infinity. To compare the end behavior of g(x) and h(x), we can look at the leading term of each function, which is the term with the highest degree.
In the function g(x) = -3x^4 + 15x^3 - 12x^2 + 3x + 20, the leading term is -3x^4, so as x approaches positive or negative infinity, the function will approach negative infinity.
In the function h(x) = -3x^4 - 16x - 1, the leading term is also -3x^4, so as x approaches positive or negative infinity, the function will also approach negative infinity.
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where
h (t) = 5+40t - 16t²
. tis in seconds after being thrown in the air
• height is measured in feet above the ground.
We can use this model to answer some questions like how high the ball will reach.
As a reminder, the velocity of the ball at time t is v(t) = h' (t) and the acceleration is at a (t) = h" (t).
(Side note on projectile motion: there are variations on this model, for example, if the ball is not thrown st
will not focus on those in this example.)
Question 1
1 point possible (graded)
When is the ball the highest?
To obtain how fast the ball traveling 2 seconds after it is thrown, we differentiate the position equation with respect to time once;
dh(t) = d (-16[tex]t^{2}[/tex] + 40t +5 )
dt dt
dh(t) = -32t + 40
dt
with t= 2:
h'(2) =-32 (2) +40
h'(2) =-24 ft/s.
What is velocity?Velocity is a vector expression of the displacement that an object or particle undergoes with respect to time . The standard unit of velocity magnitude (also known as speed ) is the meter per second (m/s). Alternatively, the centimeter per second (cm/s) can be used to express velocity magnitude. The direction of a velocity vector can be expressed in various ways, depending on the number of dimensions involved.Velocity is relative. Consider a car moving at 20 m/s with respect to the surface of a highway, traveling northward. If you are driving the car, the velocity of the car relative to your body is zero. If you stand by the side of the road, the velocity of the car relative to you is 20 m/s northward. If you are driving a car at 15 m/s with respect to the road and are traveling northward, and another car moving 20 m/s with respect to the road passes you in the same direction, that other car's velocity relative to you is 5 m/s northward. But if that other car passes you going the opposite way on the road, its velocity relative to you is 35 m/s southward.To learn more about Velocity refer to:
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if In = 5 x" (1+x)0.5 dx ,n= 0,1,2....
where the integral is for x e [0,1].
By first finding a bound on the integrand, which of these is an upper bound on In?
Pick ONE option
O 1/(n+1)
O 1/2(n+1)
O 1/(n+1) + 1/(n+2)
O N^N
The correct option is 1/(n+1).The upper bound for the integral is 1/(n+1).
To determine the upper bound, we can use the fact that the integrand is bounded by its maximum value on the interval. The maximum value of the integrand on the interval [0, 1] is:
f(x) = 5x(1 + x)^(0.5)
At x = 1, f(x) = 5(1 + 1)^(0.5) = 5√2.
Therefore, an upper bound for the integral is:
In ≤ 5√2∫x^n dx
0
Using integration by parts, we obtain:
In ≤ 5√2[x^(n + 1)/(n + 1)]_0^1
= 5√2/ (n + 1)
Therefore, the upper bound for the integral is 1/(n+1).
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use the distributive property to simplify the expression
1/2( 2n +4+6m)
Answer:
n + 2 + 3m
Step-by-step explanation:
[tex]\frac{1}{2} (2n+4+6m) = (\frac{1}{2}*2n)+(\frac{1}{2}*4)+(\frac{1}{2}*6m)\\ =n+2+3m[/tex]