The 1 1/2 cups divided by 2 is 0.75 cups
Division is the opposite of multiplication. If 3 groups of 4 are multiplied by 12, then dividing 12 into 3 equal groups yields 4 in each group when divided.
Dividend: The dividend is the number that is being divided in the division process.
Divisor: The number by which the dividend is being divided by is called the divisor.
Quotient: The quotient is a result obtained in the division process.
Remainder: Sometimes, we cannot divide things exactly. There may be a leftover number. That leftover number is called the remainder.
The relationship between these four parts can be expressed as follows:
Dividend = Divisor x Quotient + Remainder
The main purpose of sharing is to see how many equal groups form, or how many people belong to each group, when sharing equitably.
In the above example, to divide the 12 donuts into 3 similar groups, we need to place 4 donuts in each group. So dividing 12 by 3 gives 4.
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What is the area of this figure?
Answer:
24
Step-by-step explanation:
Rect = 3*4 = 12
Rect 2 = 1*6 = 6
Triangle = (6-3)*1/2*4 = 6
6 + 6 + 12 = 24
Which function is represented by the graph?
A nonlinear function starts at the point (minus 2, minus 1) and also passes through (0, minus 2.4), (2, minus 3), and (7, minus 4)
The option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
As we can see in the picture, we have given a function:
We have a function:
g(x) = 4log(x) + 4
To find x-intercept plug g(x) = 0
0 = 4logx + 4
x = 0.1
(0.1, 0)
The vertical asymptote:
x = 0
The range of a function:
(-∞, ∞)
Thus, the option range of a function is (-∞, ∞), x-intercept of (0.1, 0), and the vertical asymptote is x = 0.
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Find the smallest pair of 4 digit numbers such that the difference between them is 303 and
The smallest pair of 4 digit numbers such that the difference between them is 303 and HCF is 101 are found to be 1010 and 1313.
The HCF is the highest common factor or in other words, the largest number by which two numbers can be divided. List the four-digit numbers that could be the HCF for 101 to begin.
101 x 10 = 1010
101 x 11 = 1111
101 x 12 = 1212
101 x 13 = 1313
These numbers now reveal two further numbers whose difference is 303.
1313 - 1010 = 303
The two smallest 4 digit numbers are 1010 and 1313 as a result.
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Complete question - Find the smallest pair of 4-digit numbers such that the difference between them is 303 and their HCF is 101.
How to convert 9 into cm?
9 inches is equal to 22.86 centimeter
To convert 1 inches to cm, we can use the following formula:
1 inch = 2.54 cm
The conversion factor is 2.54
The conversion is the process of changing the unit of one quantity to another units
The conversion factor is defined as the number that is used to change one unit to another units by multiplying or dividing
Therefore,
The length in cm = conversion factor × The length in inches
Substitute the values in the equation
9 inches = 9 × 2.54 cm
Multiply the numbers
= 22.86 cm ( rounded to two decimal places )
Therefore, 9 inch is 22.86 cm
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cos 0=5/13 and sin 0 0. identify the quadrant of 0 and find sin 0
The solution is, sin∅ = 12/13 & theta is placed on the second quadrant.
that means the answer is C.
What is Pythagorean theorem?Pythagorean theorem, the well-known geometric theorem that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse (the side opposite the right angle)—or, in familiar algebraic notation, a2 + b2 = c2.
here, we have,
Let's solve the equation for theta
cos∅=5/13
so, we get,
∅ ≈ 112.6
This means angle theta is placed on the second quadrant.
We use Pythagorean's Theorem to find the other leg to find the sine function.
13² = 5² + x²
so, we get,
x = 12
It's important to know that the sine function is equivalent to the ratio between the opposite leg and the hypothenuse, and it has to be positive because sine functions are positive when the angle is on the second quadrant.
sin∅ = 12/13
Hence, the answer is C.
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Philippe is 13 years old and his father is 4 times older. In how many years will the father's age be twice the age of his son?
13×4=52
Ok Multiplacation is a simple Math formula everyone can do so you have to do this:
13+13+13+13=52
Now do this:
13×4=52
Answer is 52
The system of equations below represents the amount in dollars that Brianna paid for 5 paint brushes and 3 art canvases and Ahmed paid for 10 paint brushes and 6 art canvases. {5x+3y=4710x+6y=94 Did Brianna and Ahmed pay the same price for the items?
There is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
What is the system of equations?
A system of equations is a set of one or more equations that are to be solved simultaneously. The solution to a system of equations is the set of values for the variables that satisfy all the equations in the system.
In this case, the system of equations represents the amount that Brianna and Ahmed paid for 5 paintbrushes and 3 art canvases, and 10 paintbrushes and 6 art canvases, respectively. The system of equations is:
5x + 3y = 47 (Brianna's purchase)
10x + 6y = 94 (Ahmed's purchase)
To determine whether Brianna and Ahmed paid the same price for the items, we can compare the value of x and y that satisfy both equations. To do this, we can solve the system of equations using any method we prefer, such as elimination or substitution. Here, we'll use the method of substitution:
From the first equation, we can solve for y in terms of x:
5x + 3y = 47
3y = 47 - 5x
y = (47 - 5x)/3
Substituting this expression for y into the second equation, we get:
10x + 6y = 94
10x + 6((47 - 5x)/3) = 94
Simplifying, we get:
10x + 94 - 10x = 94
94 = 94
This equation is always true, regardless of the value of x.
Therefore, there is a solution to the system of equations, and Brianna and Ahmed paid the same price for the items.
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The elementary school in your town wants to replace its current playground. The space used for the new playground will be similar to that of the current playground. The current space is rectangular and has a length of 24 feet and a width of 26 feet. The length of the new space is 36 feet. Find the perimeter of the space used for the new playground.
Answer:
The perimeter of the new space used for the playground is 108 feet.
The perimeter of the space used for the new playground is 150 feet.
What is Scale factor?A scale factor is a numerical value that can be used to alter the size of any geometric figure or object in relation to its original size. It is used to find the missing length, area, or volume of an enlarged or reduced figure as well as to draw the enlarged or reduced shape of any given figure. It should be remembered that the scale factor only affects how big a figure is, not how it looks.
Given:
The current space is rectangular and has a length of 24 feet and a width of 26 feet.
and, the new space is 36 feet long.
let the width of new space is x.
Since, the two space are similar then the scale factor will be
= 36/24 = 1.5
So, the width of new space = 1.5 x 26 = 39 feet
Thus, the Perimeter of new space
= 2(l +w)
= 2 (36+ 39)
= 150 feet
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The height (h) of an object thrown from the top of a ski lift 2308 feet high after (t) seconds is h= - 16t² +32t+2308.
For what times is the height of the object at least 1300 feet?
The height of the object is at least 1300 feet from _______ seconds to _______ seconds.
The height of the object is at least 1300 feet after 9 seconds. The solution has been obtained by solving the algebraic equation.
What is algebraic equation?
A mathematical expression is said to be "algebraic" if it includes variables, constants, and algebraic operations (addition, subtraction, etc.). The expression has to satisfy the algebraic equation and have the equals sign in it.
We are given an equation as h = - 16t² + 32t + 2308
Since, we need to find the times at which the height of the object at least 1300 feet so, we will substitute h = 1300 in the equation.
From this, we get
⇒1300 = - 16t² + 32t + 2308
⇒0 = - 16t² + 32t + 1008
⇒0 = -t² + 2t + 63 (On dividing both sides by 16)
⇒t² - 2t - 63 = 0
⇒t² - 9t + 7t - 63 = 0
⇒t(t - 9) + 7(t - 9) = 0
⇒(t - 9) (t + 7) = 0
⇒t = 9 , -7
Hence, the height of the object is at least 1300 feet after 9 seconds.
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a cannery claims that its sardine cans have a net weight of 8 oz. you take a simple random sample of 30 cans and encounter a sample mean of 7.85 oz, with a standard deviation of 0.1 oz. what is the probability of seeing a sample mean of less than or equal to 7.85 oz if the true mean is 8 oz? report your answer with no more than two decimal places if needed.
With 95% confidence that the true population mean weight of the sardine cans is between 7.813 oz and 7.887 oz.
What is standard deviation?A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean. Low standard deviation means data are clustered around the mean, and high standard deviation indicates data are more spread out.
here, we have,
In this scenario, we have a cannery that claims their sardine cans have a net weight of 8 oz. We want to test this claim by taking a simple random sample of 30 cans and measuring their weights
From our sample of 30 cans, we calculated a sample mean of 7.85 oz and a standard deviation of 0.1 oz. The sample mean is an estimate of the population mean, and the standard deviation tells us how much the weights in our sample vary from the mean.
To determine the cutoff values for the middle 95% of the mean weights in this distribution based on the sample data, we can use the t-distribution with n-1 degrees of freedom. The degrees of freedom in this case are 29, which is one less than the sample size.
Using a t-distribution table or calculator, we can find the t-value for a 95% confidence level with 29 degrees of freedom, which is approximately 2.045. We can use this t-value to calculate the margin of error for the sample mean as:
margin of error = t-value * (standard deviation / square root of sample size)
= 2.045 * (0.1 / √(30))
= 0.037
The margin of error tells us how much the sample mean is likely to vary from the true population mean. To find the cutoff values for the middle 95% of the mean weights, we add and subtract the margin of error from the sample mean as follows:
lower cutoff value = sample mean - margin of error
= 7.85 - 0.037
= 7.813
upper cutoff value = sample mean + margin of error
= 7.85 + 0.037
= 7.887
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QUESTION 1 1.1 Draw any AABC with B = 90° in your answer book and find the ratios of the following in terms of the sides. 1.1.1 sinc (1.1.2 sin A 1.1.3 cosc 1.1.4 cosA 1.1.5 tanc 1.1.6 tan (1) ЗЗЗЗЗЕ (1) (1) (1) [6]
Based on the drawing of AABC, the ratios wrt to the sides are given below:
1.1.1 Sin C= c/b1.1.2 Sin A = a/b1.1.3 Cos C= a/b1.1.4 Cos A = c/b1.1.5 Tan C= c/a1.1.6 Tan A = a/cHow to find ratios of sides in geometryThere are several ways to find the ratios of sides in geometry, depending on the specific situation. Here are a few common methods:
Similar triangles: If you have two triangles that are similar, that is, they have the same shape but possibly different sizes, then the corresponding sides are in proportion. That is, if the sides of one triangle are a, b, and c, and the sides of the other triangle are x, y, and z, and the triangles are similar, then:
a/x = b/y = c/z
You can use this property to find the ratio of any two sides of a triangle if you know the ratio of the corresponding sides of a similar triangle.
Proportions: In some cases, you can use proportions to find the ratio of sides. For example, if you have a rectangle with sides of length a and b, and you know that the ratio of a to b is 2:3, then you can set up the proportion:
a/b = 2/3
and solve for either a or b.
Trigonometry: If you know the angles of a right triangle, you can use trigonometric ratios to find the ratio of sides. For example, in a right triangle with angle A, the ratio of the side opposite A (which we'll call a) to the hypotenuse (which we'll call c) is given by the sine of A:
sin(A) = a/c
You can rearrange this formula to solve for a or c, depending on what you know.
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The annual rate of growth in population of a certain city is 8%. If its present population is 1,96,830 then what was the population three years ago?
Answer: The population three years ago was 156250.
Step-by-step explanation:
Let 3 years ago, the population of a city = P
Rate of growth (R) = 8% p.a.
Present population (P) = 1,96,830.
Therefore,
[tex]A=P(1+R100)n[/tex]
P = A÷(1 + 8/100)³
196830 ÷ (1+2/25)³
=156250.
3 years ago, the population of the city = 156250.
−3.6−1.9t+1.2+5.1t does any body know? I’m new at this and don’t know it well.
Answer: 3.2t − 2.4
Step-by-step explanation:
Add −3.6 and 1.2
Then, add −1.9t and 5.1t
3.2t − 2.4
Is it possible to form a triangle with side lengths 8, 9, and 17? If not, explain why not.
This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.
What does a triangle actually mean?Given that they have three quadrants or more, triangles are considered polygons. It has a straightforward geometric shape. The letters ABC form a right-angled triangle when put together. Euclidean geometry creates a new rectangle of square when the borders are incompatible. Given that they have three sides and three corners, triangles are categorised as polygons.
Here,
No, it is not possible to form a triangle with side lengths 8, 9, and 17.
To see why, we can use the triangle inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. Symbolically, for sides a, b, and c, this can be written as:
a + b > c
a + c > b
b + c > a
Let's check if these inequalities are satisfied for the sides of 8, 9, and 17:
8 + 9 > 17 (true)
8 + 17 > 9 (true)
9 + 17 > 8 (true)
All three inequalities are true, which means that the given side lengths satisfy the triangle inequality and a triangle can be formed.
In this case, we see that 8 + 9 = 17, which is exactly the length of the third side.
This means that the given side lengths do not satisfy the converse of the triangle inequality theorem, and thus a triangle cannot be formed with side lengths 8, 9, and 17.
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how many hours until tomorrow
The time right now and the time zone you are in determine how many hours are left before tomorrow. Assuming you mean the following calendar day, tomorrow's hours would be:
The amount of hours until tomorrow if it is currently before midnight is 24 minus the current hour. For instance, if it is 9:00 PM right now, there are 24 – 21 = 3 hours left until tomorrow.
In this case, the number of hours until tomorrow would be equal to the time difference between now and midnight + 24. If it is 1:00 AM, for instance, there are (24 - 1) + 1 = 24 hours until tomorrow.
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by what number should we divide 135 to get a perfect cube?
Answer:
5
Step-by-step explanation:
Can someone help me?
Answer:
yeah sure, what you need?
A farmer sells 6.6 kilograms of apples and pears at the farmer's market. 3 5 of this weight is apples, and the rest is pears. How many kilograms of pears did she sell at the farmer's market?
Answer: 3.1 kg
Step-by-step explanation:
Total amount sold of apples and pears = 6.6 kg
Of that 6.6 kg, 3.5 kg is the weight of the apples.
Subtract the weight of the apples from the total weight of the apples and pears.
6.6 kg (total weight) - 3.5 kg (weight of apples) = 3.1 kg (weight of pears)
help me please i will mark you as brainiest if you get this answer right
Answer:
a = √c²-b²
Step-by-step explanation:
Sup bro,
The correct answer is a = √c²-b²
pls help me solve this
The perimeter of the figure is 28 units
What is perimeter of a figureThe perimeter of a figure is the total length of its boundary or outer edge. It is the sum of the lengths of all the sides of the figure. The perimeter is usually measured in units such as centimeters, meters, inches, or feet, depending on the measurement system being used.
The perimeter of this figure is the sum total length of the boundaries.
This can be calculated as;
P = 2 + 4 + 5 + 3 + 7 + 7
P = 28 units
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Jay's unpaid credit card balance is $3390.88. His APR is 18.6%. What is his new balance if he made one new transaction of $128?
Jay's new balance if he made one transaction of $ 128, given the credit card balance is
How to find the new balance ?To find the new balance, you first need to find the interest on the old balance by the formula :
= 3, 390.88 x 18. 6 % / 12 months per year
= $ 52. 56
Jay's new balance is :
= Old balance + Interest + New transaction
= 3, 390. 88 + 52. 56 + 128
= $ 3, 571. 44
The new credit card balance is $ 3, 571. 44.
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A stainless-steel patio heater is shaped like a square pyramid. The length of one side of the base is 12 feet. The slant height is 13 feet. What is the height of the heater? Round to the nearest tenth of a foot.
The height of the heater is 5 feet.
What is Pythagorean Theorem?The well-known Pythagorean Theorem states that the square on the hypotenuse of a right triangle equals the sum of the squares on its legs.
Given:
The length of one side of the base is 12 feet.
The slant height is 13 feet.
Using Pythagorean theorem we get
H² = slant height² - 1/2 base diagonal²
H² = 13² - 12²
H² = 169- 144
H² = 25
H= 5 feet
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which of the following is the factored expression of 20+16
The factored expression of 20 + 16 is 4 (5 + 4).
What is factored form?Factoring is the process of representing a given number or algebraic statement as the sum of its components.
A relevant strategy is used, depending on the situation, to identify the components.
Locating GCD (Greatest Common Divisor)
It is possible to factor an equation where every term has GCD 0 by eliminating GCD as a common component.
Employing Identity
The given expression is:
20 + 16
20 can be written as 4(5).
16 can be written as 4(4).
20 + 16 = 4(5) + 4(4)
Taking the common term out we have:
20 + 16 = 4 (5 + 4)
Hence, the factored expression of 20 + 16 is 4 (5 + 4).
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Find the length of X
Write the radical expression [tex]\frac{8}{\sqrt[7]{x^1^5} }[/tex] in exponential form.
The value of the exponential equation is A = ( 8 ) x ^ -105/2
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
A = 8 / ( 7√x¹⁵ ) be equation (1)
On simplifying the equation , we get
The value of √x¹⁵ = x ^ 15/2
Now , the 7th root of √x¹⁵ is = x ^ 105/2
Now , the equation will be
A = ( 8 ) x ^ -105/2
Hence , the exponential equation is A = ( 8 ) x ^ -105/2
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What size is a 1/4-20 drill hole?
The size is a 1/4-20 drill hole is 5.1mm
Many factors contribute to tap failure or breakage, but one fundamental and obvious factor is often overlooked. The problem is that this factor cannot be calculated accurately using traditional tap/drill charts.
There have been many changes since the tapping/drilling chart was first developed - programmable machines, rigid tapping, synchronous tapping, better tool holders, special tapping fluids, higher quality taps, etc.
Most importantly, the drill bits used to make the holes to cut have improved. Enhanced drill bit geometries, new chip flute geometries, coolant holes, improved HSS and carbide grades, and coatings such as TiN and TiCN greatly improve hole quality and size.
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what is big number calculator?
A big number calculator is a software application or program designed to perform arithmetic operations on large numbers that cannot be easily handled by standard computer hardware and software.
Big numbers are typically defined as numbers that are too large to be stored in the registers or memory of a typical computer processor.
In a big number calculator, arithmetic operations such as addition, subtraction, multiplication, and division are performed using algorithms that are specifically designed to handle large numbers. These algorithms may use techniques such as long division, long multiplication, and other mathematical strategies to perform the required computations.
Big number calculators are often used in scientific and engineering applications where very large numbers are encountered. They can also be useful in cryptography, where large prime numbers are used for encryption and decryption operations.
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During football practice,Ivan run 300 m east. Then he runs 200 m west. Finally he runs 50 m east again. What is the distance?
Ivan ran a total distance of 550 meters during football practice.
How to determine the distanceTo calculate the total distance Ivan ran, we need to add up the distances he covered in each direction:
Ivan ran 300 m east.Then he ran 200 m westFinally, he ran 50 m east.To find the total distance, we can add up the absolute values of each distance, since distance is a scalar quantity and is always positive:
Total distance = |300 m| + |(200 m)| + |50 m|
= 300 m + 200 m + 50 m
= 550 m
So Ivan ran a total distance of 550 meters during football practice.
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Use substitution to solve the following system of equations. Show all of your work. Write the solution as an ordered pair.
4x+2y=36
y=2x-2
Using the substitution to solve the following system of equations, 4x+2y=36
y=2x-2 we get value of x as 5 and y is equal to 8.
There are two methods for solving simultaneous linear equations: graphical methods and algebraic methods. The algebraic technique includes the substitution method as one of its categories.
We have two equations as,
4x+2y=36
y=2x-2
Substituting the value of y = 2x - 2 in the equation 1 we get,
4x + 2(2x - 2) = 36
4x + 4x - 4 = 36
8x = 36 + 4
8x = 40
x = 5
And y = 2 x 5 - 2 = 8
Therefore, the value of x is 5 and y is 8.
The algebraic approach for solving simultaneous linear equations is the substitution method. The value of one variable from one equation is substituted in the second equation, as the name implies. In this manner, a pair of linear equations is reduced into a single linear equation with only one variable, which can then be solved quickly. Before beginning to solve linear equations using the substitution approach, learn about the algebraic and graphical methods.
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the function f is continuous and ∫80f(u)du=6. what is the value of ∫31xf(x2−1)dx?
Using integration by substitution, the value of ∫31xf(x^2-1)dx is 6.
What is the value using integration by substitutionTo solve this problem, we can use integral by substitution.
Let's set u = x^2 - 1, then du/dx = 2x, or dx = du / (2x).
Using this substitution, we can rewrite the integral as:
∫(3^2-1)^(8^2-1) f(u) * (du / 2)
Next, we can use the fact that f is continuous and the integral of f from 8 to 0 is 6. We can split the integral into two parts:
∫(3^2-1)^(8^2-1) f(u) * (du / 2) = ∫0^(8^2-1) f(u) * (du / 2) - ∫0^(3^2-1) f(u) * (du / 2)
The first integral on the right-hand side is the integral we're given:
∫0^(8^2-1) f(u) * (du / 2) = 6
The second integral can be rewritten using our substitution:
∫0^(3^2-1) f(u) * (du / 2) = ∫(3^2-1)^(0) f(u) * (du / 2)
Notice that we've switched the limits of integration, which means we need to negate the integral:
∫(3^2-1)^(0) f(u) * (du / 2) = -∫0^(3^2-1) f(u) * (du / 2)
Substituting back into our original integral and using these results, we get:
∫(3^2-1)^(8^2-1) f(u) * (du / 2) = 6 - (-∫0^(3^2-1) f(u) * (du / 2)) = 6 + ∫0^(3^2-1) f(u) * (du / 2)
Finally, we can substitute back in for x and simplify to get our answer:
∫31xf(x^2-1)dx = (1/2) * ∫(3^2-1)^(8^2-1) f(u) * du = (1/2) * (6 + ∫0^(3^2-1) f(u) * du) = (1/2) * (6 + ∫0^8 f(u) * du) = (1/2) * (6 + 6) = 6
∫31xf(x^2-1)dx = 6.
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