Solve the seperable differential equation 1 9yy' = 2. Use the following initial condition: y(9) = 7. = Express x? in terms of y. x2 = (function of y).

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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Answer: x-0.5y=1.5

Step-by-step explanation:

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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The approximate value of x using the newton method is 0.7

From 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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The value of k = 2

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.

∫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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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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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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The area of the sector is approximately 73.14 square centimeters.

The formula to calculate the area of a sector is given by A = (θ/2) × r^2, where θ is the central angle measure in radians, and r is the radius of the circle.

Substituting the given values in the formula, we get A = (4/7π/2) × 16^2

Simplifying this expression, we get A = (8/7) × 16^2 × π/2

A = 128π square centimeters/7

Using the approximation π ≈ 3.14, we can calculate the value of A as follows:

A ≈ (128 × 3.14) square centimeters/7 ≈ 573.44 square centimeters/7 ≈ 73.14 square centimeters (rounded to two decimal places)

Therefore, the area of the sector is approximately 73.14 square centimeters.

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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]

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:

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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The area of the playground include the following: 900 square yards.

In Mathematics and Geometry, the area of a regular polygon can be calculated by using this formula:

Area = (n × s × a)/2

Where:

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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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

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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Therefore , the solution of the given problem of unitary method comes out to be  it is consistently a constant proportion or percentage of the preceding value.

The task can be completed using the well-known minimalist technique, actual variables, and any essential components from the very first Diocesan specialised question. In response, customers can be given another opportunity to use the item. If not, significant effects on our comprehension of algorithms will disappear.

Here,

According to the students' responses, all instances of exponential decay share the following characteristics:

They begin with a baseline value. (y-intercept).

They get smaller with time. (or successive periods).

They get closer to a horizontal asymptote, which stands for the function's minimum or limit value.

The graphs also demonstrate that, although the rate of decay—or the rate at which values decrease—can vary from circumstance to circumstance,

it is consistently a constant proportion or percentage of the preceding value.

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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!

Answer:

24

Step-by-step explanation:

add all of them up

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.

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 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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Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.

The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.

Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:

AC < AB + BC

AC < 12 + 20

AC < 32

This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.

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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.

The pool is draining at a rate of 1.36% per hour according to Inayah's claim.

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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The value of the sides are;

x = 20.4

x = 13.84

There are six different trigonometric identities. They include;

Given 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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If A car accelerates away from the starting line at 3. 6 m/s2 and has a mass of 2400 kg, Therefore, the net force acting on the vehicle is 8640 N.

The net force acting on the vehicle can be calculated using Newton's second law of motion, which states that the force applied to an object is equal to its mass multiplied by its acceleration:

Net force = mass x acceleration

In this case, the mass of the car is 2400 kg and the acceleration is 3.6 m/s^2. Thus, we can calculate the net force as:

Net force = 2400 kg x 3.6 m/s^2

Net force = 8640 N

Therefore, the net force acting on the vehicle is 8640 N.

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A square pyramid with the maximum volume that can fit inside a cube has a same base as a cube ( 30 cm x 30 cm ) . The height of the pyramid is also same as a side length of a cube ( h = 30 cm ).

    The volume of the pyramid:

    V = 1/3 · 30² · 30 = 1/3 · 900 · 30 = 9,000 cm³

    The maximum volume of the pyramid is 9,000 cm³.

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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The percentage of the model is shaded is 45% if the total number of square is 80 option (H) is correct.

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.

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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