the integral by reversing the order of integration. the result will be F(β) - F(α), which is the integral evaluated after reversing the order of integration.
First, let's rewrite your integral more clearly:
∫∫ R 7x dy dx, where R is the region of integration.
To reverse the order of integration, we first need to determine the limits of integration for R in terms of x and y. Let's assume the current limits are a to b for x and c(y) to d(y) for y.
Now, we need to express these limits in terms of y and x. Let's denote the new limits as α to β for y and γ(x) to δ(x) for x.
After finding the new limits, we can rewrite the integral as:
∫∫ R 7x dx dy
Now, evaluate the integral by integrating first with respect to x and then with respect to y:
1. Integrate 7x with respect to x: (7/2)x^2 + C₁(x)
2. Apply the limits of integration for x: [(7/2)δ(x)^2 + C₁(δ(x))] - [(7/2)γ(x)^2 + C₁(γ(x))]
3. Integrate the result with respect to y: ∫[α, β] [(7/2)(δ(y)^2 - γ(y)^2)] dy
4. Apply the limits of integration for y: F(β) - F(α)
The final result will be F(β) - F(α), which is the integral evaluated after reversing the order of integration.
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n^2 - 5n + 6, n^2 - 4n+ 4 I need help, i know the answer may possibly be (n-3)(n-2)^2 factor it, an di need steps.
The simplified expression is (n - 3) / (n - 2).
What is the simplification of the expression?The expression is simplified as follows;
(n² - 5n + 6) / (n² - 4n + 4)
n² - 5n + 6 can be factored as (n - 2) (n - 3)
n² - 4n + 4 can be factored as (n - 2) (n - 2)
Therefore, the expression becomes:
[(n - 2) (n - 3)] / [(n - 2) (n - 2)]
We can cancel the (n - 2) factor in the numerator and denominator, leaving us with:
(n - 3) / (n - 2)
So the simplified expression is (n - 3) / (n - 2).
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Newton’s Method!!!!!!
The approximate value of x using the newton method is 0.7
Calculating the value of x using the newton methodFrom the question, we have the following expression that can be used in our computation:
[tex]\frac{x}{x^2+1}-\sqrt{1-x}[/tex]
Also, we have the function f(x) to be
[tex]f(x) = x(x^2+1)^{-1} -\sqrt{1-x}[/tex]
And we have the differentiated function to be
[tex]f'(x) = \frac{1}{x^2+1} - \frac{2x^2}{(x^2 + 1)^2} + \frac{1}{2\sqrt{1-x}}[/tex]
The value of x using the newton method is given as
[tex]x_n = x_{n-1} - \frac{f(x_{n-1})}{f'(x_{n-1})}[/tex]
Set [tex]x_{n-1}[/tex] = 0
So, we have
x₁ = 0 - -1/1.5 = 0.67
x₂ = 0.67 - undefined = undefined
So, we have
x₁ = 0.67
When approximated, we have
x = 0.7
This means that the value of x using the newton method is 0.7
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Sentence:
7) Jenny bought a pair of boots priced at $85. If the boots were on gole for 15% off
regular price, how much did Jenny pay for the boots?
Let x =
(Remember to subtract sale
The rectangular model is made up of squares each square is a equal size what percent of the model shaded
The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.
What is the percentage?It is defined as the ratio of two numbers expressed in the fraction of 100 parts. It is the measure to compare two data, the % sign is used to express the percentage.
Total No. of squares = 10×8 = 80
Total No. of squares shaded = 36
Percentage of the model is shaded = (36/80)×100
= 0.45×100
= 45%
Thus, the percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.
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Full Question:
Although part of your question is missing, you might be referring to this full question:
See attached image.
A 60 foot tall building casts a 20 foot. Shadow. Use the principles of similar triangles to determine the length of a shadow cast by a 5 foot 6 inch student
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
To solve this problem, we'll set up a proportion using the principles of similar triangles. The two triangles in this case are the building and its shadow, and the student and their shadow.
Convert the height of the student to feet. 5 feet 6 inches is equal to 5.5 feet.
Set up the proportion. Let x represent the length of the shadow cast by the student. We have the following proportion:
(height of building) / (length of building's shadow) = (height of student) / (length of student's shadow)
60 / 20 = 5.5 / x
Cross-multiply and solve for x:
60 * x = 20 * 5.5
60x = 110
x = 110 / 60
x = 1.83 (rounded to two decimal places)
The length of the shadow cast by the 5 foot 6 inch student is approximately 1.83 feet.
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Find the cost of one dozen exercise books, if 3 similar exercise books cost $2.70.
Answer:
$10.8
Step-by-step explanation:
We know that 3 books are $2.70, so 1 book is 2.70/3 which is $0.9
1 dozen = 12
To find the price of 12 books, we multiply by the cost of 1 book
12 * 0.9 = $10.8
Find the slope from the data below
Answer:
m = -4
Step-by-step explanation:
Slope = rise/run or (y2 - y1) / (x2 - x1)
Pick 2 points (-3,12) (-2,8)
We see the y decrease by -4, and the x increase by 1, so the slope is
m = -4
So, the slope of the line representing by the data is -4.
The set of values for x that satisfies a quadratic inequality is x < -0.5 or x > 1.5
Write down a possible quadratic inequality. Please help - it’s a gcse maths question
Answer: x-0.5y=1.5
Step-by-step explanation:
Find the perimeter of a square that has a side length of 4.3x + 2 inches.
The calculated perimeter of the square from the side length is 17.2x + 8
Finding the perimeter of a square from the side lengthFrom the question, we have the following parameters that can be used in our computation:
A square that has a side length of 4.3x + 2 inches.
Using the above as a guide, we have the following:
Perimeter = 4 * side length
Substitute the known values in the above equation, so, we have the following representation
Perimeter = 4 * (4.3x + 2)
When teh brackets are opened, we have
Perimeter = 17.2x + 8
Hence, the perimeter is 17.2x + 8
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Which of the data sets below have striking deviations? Select all that apply.
A) 65, 68, 61, 63, 71
B) 99, 95, 93, 97, 98
C) 22, 83, 85, 88, 91
D) 45, 47, 43, 45, 97
E) 72, 78, 71, 67, 35
MarÃa is shopping for party supplies. She finds that paper plates come in packages of 8, napkins come in packages of 10, and paper cups come in packages of 12. What is the least number of packages of plates, napkins, and cups she has to buy so that she has the same number of each item for her party?
The least number of packages of plates, napkins, and cups Maria has to buy is 15 packages .
To find the least number of packages, we need to find the least common multiple (LCM) of the three package sizes: 8 (plates), 10 (napkins), and 12 (cups).
The prime factors of 8 are 2x2x2, of 10 are 2x5, and of 12 are 2x2x3. To find the LCM, we multiply the highest powers of each prime factor: 2³x3x5 = 120.
This means Maria needs 120 of each item. She will buy 120/8 = 15 packages of plates, 120/10 = 12 packages of napkins, and 120/12 = 10 packages of cups.
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Keilantra was given a large box of 24 chocolates for her birthday. If she eats exactly 3 chocolates each day, how many chocolates would Keilantra have remaining 6 days after her birthday?
Answer: 6 chocolates
Step-by-step explanation:
Keilantra had 24 chocolates to begin with, and she ate six lots of three. so the first step is 6 x 3 = 18. Now that we know how many chocolates Keilantra ate, we need to figure out how many chocolates she has left. So we take our product (18) and we subtract it from the total (24). So we end up with 24 - 18 = 6.
If k= ∫ from zero to π/2 of sec²(x/k) dx, find k where k>0.
The value of k = 2
If k= ∫ from zero to π/2 of sec²(x/k) dx, what is value of k?Let u = x/k, then du/dx = 1/k and dx = k du.Substituting into the integral:
k ∫₀^(π/2k) sec²(u) du
= k [tan(u)]₀^(π/2k)
= k [tan(π/2k) - tan(0)]
= k [∞ - 0]
= ∞
This means that the integral diverges unless k = 0.
However, if we instead use the identity sec²(x) = 1 + tan²(x), we can rewrite the integral as:∫₀^(π/2k) sec²(x/k) dx
= ∫₀^(π/2k) (1 + tan²(x/k)) dx
= [x + k tan(x/k)]₀^(π/2k)
= π/2
So we have:
π/2 = [π/2k + k tan(π/2k)] - [0 + k tan(0)]
= π/2k + k tan(π/2k)
Multiplying through by k:
π/2 = π/2 + k² tan(π/2k)
Subtracting π/2 from both sides:
0 = k² tan(π/2k)
The only way for this equation to hold for k > 0 is if tan(π/2k) = 0. This occurs when π/2k is an integer multiple of π/2, i.e., when k is an even integer.
Therefore, the value of k that satisfies the original integral is k = 2.
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Write a system of inequalities whose solution is the set of all points in quadrant I not including the axis's.
The set of all points in quadrant I not including the axis's can be represented by the following system of inequalities:
x > 0
y > 0
Inequalities are useful in modeling situations where there are constraints or limitations. For illustration, in real- life scripts, there may be limited coffers or capacity, or certain variables must fall within a specific range. Systems of inequalities are frequently used to represent these constraints or limitations graphically. One common operation of systems of inequalities is in optimization problems, where the thing is to maximize or minimize a particular function subject to certain constraints.
In these situations, the doable region, or the set of all points that satisfy the constraints, is frequently represented as a shadowed region on a graph. The optimal result is also set up by relating the point( s) within this region that maximize or minimize the function.
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For what primary reason have many present-day African nations struggled to unite their people?
F.
Because many African peoples have strong tribal ties
G.
Because much of the African population remains loyal to former colonial powers
'H.
Because the African people refuse to accept centralized authority
J. Because many Africans seek to migrate from the continent
The primary reason many present-day African nations struggled to unite their people is F. Because many African peoples have strong tribal ties.
The strong tribal identities and loyalties that exist among various ethnic groups inside African states today are one of the main causes of the effort to bring people together. Through colonisation, many African nations were developed, and many of them contained numerous groups with various cultural, linguistic, and ethnic origins.
Therefore, as a result, it has been challenging to forge a strong sense of national identity among many individuals who still identify primarily with their own tribe or ethnic group. This has occasionally resulted in disputes and hostilities amongst various diverse groups, impeding efforts to create a community that is more unified.
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Unit 7: Right Triangles & Trigonometry Homework 4: Trigonometry Ratios & Finding Missing Sides #’s 10&11
The value of the sides are;
x = 20.4
x = 13.84
How to determine the valueThere are six different trigonometric identities. They include;
sinetangentcosinecosecantsecantcotangentGiven that the ratios are;
sin θ = opposite/hypotenuse
cos θ = adjacent/hypotenuse
tan θ = opposite/adjacent
Using the tangent identity, we have;
tan 64 = 42/x
cross multiply the values
x = 42/2. 050
x = 20. 4
Using the sine identity;
sin 70 = 13/x
cross multiply the values
x = 13/0. 939
x = 13. 84
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The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions.
which properties were used to simplify the following expression? select all that apply.
4 + 3(9 + 2)
4 + (3 × 9) + (3 × 2)
4 + 27 + 6
4 + 6 + 27
10 + 27
37
The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).
How many properties are used to simplify the expression 4 + 3(9 + 2) into 37?The properties that were used to simplify the expression 4 + 3(9 + 2) into 37 are:
Distributive property: The expression was rewritten as 4 + (3 × 9) + (3 × 2) by distributing the 3 over the parentheses.
Associative property: The order of the terms (3 × 9) and (3 × 2) was rearranged without changing the result because of the associative property of multiplication.
Commutative property: The order of the terms 4, 27, and 6 was rearranged without changing the result because of the commutative property of addition.
Identity property: The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).
The properties used to simplify the expression are Associative property of addition, Commutative property of addition, and Distributive property and Identity property of addition. Therefore, the correct option is A, C, E and F.
The properties used to simplify the expression are as follows.
1. Distributive property (E): 4 + 3(9 + 2) = 4 + (3 × 9) + (3 × 2)
This property is applied when a number is multiplied with the sum of two or more numbers. In this case, the number 3 is distributed over the numbers 9 and 2.
2. Identity property of addition (F): 4 + 27 + 6 = 4 + 6 + 27
This property states that adding zero to any number does not change its value. Although this property isn't explicitly shown in the given steps, it is implied by the fact that we can rearrange the terms in the addition without changing their value.
3. Commutative property of addition (C): 4 + 6 + 27 = 10 + 27
This property states that changing the order of numbers in an addition does not change the sum. Here, the numbers 4 and 6 were rearranged to make it easier to add them together.
4. Associative property of addition (A): (10 + 27) = 37
This property states that the grouping of numbers in an addition does not affect the sum. In this case, the parentheses are unnecessary since the numbers were already grouped correctly.
In summary, the properties used to simplify the expression are: A) Associative property of addition, C) Commutative property of addition, and E) Distributive property and F) identity property of addition.
Note: The question is incomplete. The complete question probably is: The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions. Which properties were used to simplify the following expression? select all that apply.
4 + 3(9 + 2)
4 + (3 × 9) + (3 × 2)
4 + 27 + 6
4 + 6 + 27
10 + 27
37
A) associative property of addition B) associative property of multiplication C) commutative property of addition D) commutative property of multiplication E) distributive property F) identity property of addition G) identity property of multiplication
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Can you guys help me on this algebra work? thankscompare b(x) = 6x^2 to f(x)compare m(x) = -1/3x^2 - 4
b(x) = 6x² and m(x) = -1/3x²- 4 have similarities and differences as quadratic functions with different coefficients and signs.
How do b(x) and m(x) compare?We can look at the similarities and differences to compare b(x) = 6x² and m(x) = -1/3x² - 4
Similarities:Both b(x) and m(x) are quadratic functions, which means they have an x² term.
They both have a constant term, with b(x) having a constant of 0 and m(x) having a constant of -4.
Differences:The coefficients of the x² term are different: b(x) has a coefficient of 6, while m(x) has a coefficient of -1/3.
The signs of the coefficients are different: b(x) has a positive coefficient, while m(x) has a negative coefficient.
Overall, b(x) and m(x) have some similarities in their form as quadratic functions, but their coefficients and signs are different, which means they will have different shapes and behaviors.
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If p and q are real numbers in the function f(x)=x4+5x3+px2+qx+30 and f(1)=0, which equation is true?
p + q + 36 = 0 is the equation that is true. From this equation, we can say that p + q = -36.
If we substitute x = 1 in the given function, we get:
f(1) = [tex](1)^4 + 5(1)^3 + p(1)^2 + q(1) + 30[/tex]
= 1 + 5 + p + q + 30
= p + q + 36
We are given that f(1) = 0. Therefore, we have:
p + q + 36 = 0
This is the equation that is true. From this equation, we can say that p + q = -36.
Now, let's see why this is the case. When we substitute x = 1 in the given function and get f(1) = 0, it means that (1, 0) is a point on the graph of the function. This point lies on the x-axis, which means that the function intersects the x-axis at x = 1. Since the x-axis is the line y = 0, this means that f(x) = 0 when x = 1.
Using this information, we can write an equation in terms of p and q. If we substitute x = 1 in the given function and get f(1) = 0, it means that:
f(x) = [tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q))[/tex]
Therefore, we have:
[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = 0[/tex]
Since (1,0) is a point on the graph of the function, we know that x = 1 is a root of this equation. Therefore, we have:
[tex](x - 1)(x^3 + 6x^2 + (6+p)x + (30-q)) = (x - 1)(x^2 + (7+p)x + (36-p-q))[/tex]
We know that (x - 1) is a factor of this equation, so we can use polynomial long division to divide the expression [tex](x^2 + (7+p)x + (36-p-q))[/tex] by (x - 1). The quotient will give us the other two roots of the equation. However, we do not need to find these roots to answer the question. All we need to know is that p + q = -36.
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For 50 points can you help me with this I really need help.
The coordinates of the points in the table indicates that the coordinates of the image following the reflections, can be presented on the coordinate plane as shown in the attached graph created with MS Excel.
What is a reflection transformation?A reflection transformation is one in which the mirror image of the preimage is created across a line of reflection.
The coordinate points of the image after the specified reflections can be presented as follows;
Original [tex]{}[/tex]Reflection across the x-axis Reflection across the y-axis y = -x
(0, 15) [tex]{}[/tex] (0, -15) (0, 15) (-15, 0)
(1, 15) [tex]{}[/tex] (1, -15) (-1, 15) (-15, -1)
(1, 13) [tex]{}[/tex] (1, -13) (-1, 13) (-13, -1)
(3, 15) [tex]{}[/tex] (3, -15) (-3, 15) (-15, -3)
(3, 12) [tex]{}[/tex] (3, -12) (-3, 12) (-12, -3)
(1, 10) [tex]{}[/tex] (1, -10) (-1, 10) (-10, -1)
(1, 8) [tex]{}[/tex] (1, -8) (-1, 8) (-8, -1)
(3, 10) [tex]{}[/tex](3, -10) (-3, 10) (-10, -3)
(3, 7) [tex]{}[/tex] (3, -7) (-3, 7) (-7, -3)
(1, 5) [tex]{}[/tex] (1, -5) (-1, 5) (-5, -1)
(1, 2) [tex]{}[/tex] (1, -2) (-1, 2) (-2, -1)
(4, 4) [tex]{}[/tex] (4, -4) (-4, 4) (-4, -4)
(5, 7) [tex]{}[/tex] (-5, 7) (5, -7) (-7, -5)
(7, 8) [tex]{}[/tex] (7, -8) (-7, 8) (-8, -7)
(6, 5) [tex]{}[/tex] (6, -5) (-6, 5) (-5, -6)
(8, 6) [tex]{}[/tex] (8, -6) (-8, 6) (-6, -8)
(9, 9) [tex]{}[/tex] (9, -9) (-9, 9) (-9, -9)
(11, 10) [tex]{}[/tex] (11, -10) (-11, 10) (-10, -11)
(10, 7) [tex]{}[/tex] (10, -7) (-10, 7) (-7, -10)
(12, 8) [tex]{}[/tex] (12, -8) (-12, 8) (-8, -12)
(13, 6) [tex]{}[/tex] (13, -6) (-13, 6) (-6, -13)
(11, 5) [tex]{}[/tex] (11, -5) (-11, 5) (-5, -11)
(14, 4) [tex]{}[/tex] (14, -4) [tex]{}[/tex] (-14, 4) (-4, -14)
(12, 3) [tex]{}[/tex] (12, -3) (-12, 3) (-3, -12)
(9, 4) [tex]{}[/tex] (9, -4) (-9, 4) (-4, -9)
(7, 3) [tex]{}[/tex] (7, -3) (-7, 3) (-3, -7)
(10, 2) [tex]{}[/tex] (10, -2) (-10, 2) (-2, -10)
(8, 1) [tex]{}[/tex] (8, -1) (-8, 1) (-1, -8)
(5, 2) [tex]{}[/tex] (5, -2) (-5, 2) (-2, -5)
(2, 0) [tex]{}[/tex] (2, 0) (-2, 0) (0, -2)
The above coordinate points can be used to plot the graphs showing the image of the points following the specified reflections across the x-, y-, and y = -x, axis.
Please find attached the required graph of the coordinate points following the reflection transformations, created with MS Excel.
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the measure of an angle is 156°. what is the measure of its supplementary angle
Answer:
24°
Step-by-step explanation:
Supplementary angles: 2 angles that add up to 180°.
We are given that one angle is 156°, so we can write an equation:
180=156+x
subtract both sides by 156
24=x
So, the measure of the supplementary angle is 24°.
Hope this helps!
A proportional relationship is shown in the table below:
x - 0, 3, 6, 9, 12
y - 0, 0.5, 1.0, 1.5, 2.0
What is the slope of the line that represents this relationship?
Graph the line that represents this relationship.
The slope of the line that represents the proportional relationship between x and y in the given table is 1/6. To graph the line, we can plot the points from the table and connect them with a straight line passing through the origin (0,0).
The relationship between x and y is proportional, which means that there is a constant ratio between the two variables. We can find the slope of the line that represents this relationship by calculating the ratio of the change in y over the change in x between any two points on the line. Let's use the first and last points
slope = (y2 - y1) / (x2 - x1) = (2.0 - 0) / (12 - 0) = 2/12 = 1/6
So, the slope of the line that represents this proportional relationship is 1/6.
To graph the line, we can plot the points from the table and connect them with a straight line. The line will pass through the origin (0,0) and have a slope of 1/6. The graph will look like.
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Inayah claims that the pool is draining at a rate of 1. 36% per hour
The pool is draining at a rate of 1.36% per hour according to Inayah's claim.
What is the claimed rate at which the pool is draining?According to Inayah's claim, the pool is experiencing a draining at a rate of 1.36% per hour. This means that for every hour that passes, the pool's water level decreases by 1.36% of its total volume.
Understanding the rate at which a pool is draining is essential for monitoring and managing water levels. If the rate of drainage is accurate, it can help estimate how long it would take for the pool to reach a certain level or completely drain. Additionally, it aids in determining the necessary actions to maintain the pool's water balance and prevent potential issues such as overflow or inadequate water supply.
It is crucial to verify the accuracy of the claim by monitoring the pool's water level over a specific period. This can be done by measuring the change in water volume or using other reliable methods to ensure the drainage rate aligns with the claimed percentage.
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Finding Positive Numbers In Exercise, find three positive integers x, y, and z that satisfy the given conditions. The sum is 32, and P= xy^2z is a maximum. =
To find three positive integers x, y, and z that satisfy the given conditions, we need to use the concept of maximizing a function subject to certain conditions. Solving for y and z, we have y = 15 and z = 16.
In this case, we want to maximize the function P= xy^2z, subject to the condition that the sum of x, y, and z is 32.
To maximize P, we need to find the values of x, y, and z that make P as large as possible. One way to do this is to use the method of Lagrange multipliers, which involves finding the critical points of a function subject to a constraint.
In this case, we have the function P= xy^2z and the constraint x+y+z=32. Using Lagrange multipliers, we can set up the following equations:
∂P/∂x = λ∂(x+ y+ z)/∂x
y^2z = λ
∂P/∂y = λ∂(x+ y+ z)/∂y
2xyz = λ
∂P/∂z = λ∂(x+ y+ z)/∂z
xy^2 = λ
x+y+z=32
Solving these equations simultaneously, we get:
y^2z/x = 2xyz/y = xy^2/z = λ
Simplifying, we get:
y^2z/x = 2yz = xy^2/z
Rearranging, we get:
x = 2y^3/z
y = (x/2z)^(1/3)
z = (x/4y^2)^(1/3)
Substituting these expressions for x, y, and z into the constraint x+y+z=32, we get:
2y^3/z + (x/2z)^(1/3) + (x/4y^2)^(1/3) = 32
Solving this equation for x, y, and z, we get:
x = 16
y = 4
z = 2
Therefore, the three positive integers x, y, and z that satisfy the given conditions are x=16, y=4, and z=2. These values make P= xy^2z a maximum, since any other values of x, y, and z that satisfy the constraint x+y+z=32 would yield a smaller value of P.
To find three positive integers x, y, and z that satisfy the given conditions, we need to consider the following:
1. The sum of x, y, and z is 32: x + y + z = 32
2. The product P = xy^2z is a maximum.
First, let's express z in terms of x and y using the sum condition:
z = 32 - x - y
Now, substitute this expression for z into the product P:
P = xy^2(32 - x - y)
To maximize P, we should make y as large as possible, since it has the largest exponent in the product formula. Let's allocate the majority of the remaining sum to y. For example, if x = 1, we get:
1 + y + z = 32
Solving for y and z, we have y = 15 and z = 16. Now let's check the product:
P = (1)(15^2)(16) = 3600
This is one possible solution for x, y, and z that gives a maximum product P with the given conditions. The three positive integers are x = 1, y = 15, and z = 16, and the maximum product P = 3600.
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list the elements of U
39 A sample of a substance with an initial mass of 963 grams is decaying
at a rate of 27% per hour.
Create a function that can be used to find y, the mass of the
substance in grams remaining after x hours.
Record your answer in the space provided.
A function that can be used to find y, the mass of the substance in grams remaining after x hours is [tex]P(x) = 963(0.63)^x[/tex]
How to create a function that can be used to find the mass of the substance?In Mathematics and Statistics, a population or substance that decreases at a specific period of time represent an exponential decay. This ultimately implies that, a mathematical model for any population or substance that decreases by r percent per unit of time is an exponential equation of this form:
[tex]P(x) = I(1 - r)^x[/tex]
Where:
P(x) represents the total mass or population.x represents the time or number of years.I represents the initial value of the substance.r represents the decay rate.By substituting given parameters into the , we have the following:
[tex]P(x) = I(1 - r)^x\\\\P(x) = 963(1 - 0.27)^x\\\\P(x) = 963(0.63)^x[/tex]
In conclusion, we can reasonably infer and logically deduce that the decay rate is equal to 63%.
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Select the correct answer from each drop-down menu.
The three vertices of a triangle drawn on a complex plane are represented by 0 + 0i, 4 + 0i, and 0+ 3i.
The length of the hypotenuse is
units, and the area of the triangle is
square units. (Hint: Use the Pythagorean theorem.)
The area of the triangle is (a-6, b-12) square units 6 sq unit.
What is the triangle?A triangle is described as a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.
This means that the sum of the interior angles of a triangle is equal to 180°
Now that we have the points they make a 3-4-5 triangle.
The two legs are 3 and 4, so the hypotenuse has to be 5.
We could also use the Pythagorean theorem a² + b² = c² 3² + 4² = c² 25 = c² c = 5
We then calculate the area
Area =1/2 b*h
Area = 1/2(3*4)
Area = 6 sq unit
The area of the triangle is (a-6, b-12) square units 6 sq unit.
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What is the first quartile (Q1) of the data set? 51, 42, 46, 53, 66, 70, 90, 79
Answer:47.25
Step-by-step explanation:
Answer:
48.5
Step-by-step explanation:
To find the first quartile (Q1) of the data set, we need to arrange the numbers in ascending order:
42, 46, 51, 53, 66, 70, 79, 90
Q1 is the median of the lower half of the data set. Since we have 8 data points, the lower half will be the first four numbers.
42, 46, 51, 53
To find the median of these numbers, we take the average of the two middle numbers:
(Q1) = (46 + 51) / 2 = 48.5
Therefore, the first quartile (Q1) of the data set is 48.5.
CAN SOMEONE SHOW ME STEP BY STEP ON HOW TO DO THIS SOMEONE GAVE ME THE WRONG STEPS
A city just opened a new playground for children in the community. An image of the land that the playground is on is shown.
A polygon with a horizontal top side labeled 45 yards. The left vertical side is 20 yards. There is a dashed vertical line segment drawn from the right vertex of the top to the bottom right vertex. There is a dashed horizontal line from the bottom left vertex to the dashed vertical, leaving the length from that intersection to the bottom right vertex as 10 yards. There is another dashed horizontal line that comes from the vertex on the right that intersects the vertical dashed line, and it is labeled 12 yards.
What is the area of the playground?
900 square yards
855 square yards
1,710 square yards
1,305 square yards
The area of the playground include the following: 900 square yards.
How to calculate the area of a regular polygon?In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:
Area = (n × s × a)/2
Where:
n is the number of sides.s is the side length.a is the apothem.In Mathematics and Geometry, the area of a parallelogram can be calculated by using the following formula:
Area of a parallelogram, A = base area × height
Area of playground, A = 45 × 20
Area of a playground, A = 900 square yards.
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Which correctly compares the numbers? 158,364 > 158,379 > 158,397 158,364 > 158,379 > 158,397 518,317 > 518,246 > 518,197 518,317 > 518,246 > 518,197 290,061 > 289,937 > 290,324 290,061 > 289,937 > 290,324 678,200 > 678,194 > 678,227
The correct comparison of the numbers is:
678,200 > 678,194 > 678,227
Therefore, the answer is the last option, "678,200 > 678,194 > 678,227".
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