find the center of mass of the portion of the disk in the first quadrant, x 2 y 2 = 36 x2 y2=36 where the mass is given by rho ( x , y ) = 10 y √ x 2 y 2 rho(x,y)=10yx2 y2 . ¯ x x¯ = ¯ y y¯

Answer:

Step-by-step explanation:

3 + 4 x = 6

Plot:

Plot

Alternate forms:

4 x = 3

4 x - 3 = 0

Number line:

Number line

Solution:

x = 3/4

Numbers when multiplied equal -120, added/subtracted gives 7 .

What is quadratic formula?

The quadratic formula in elementary algebra is a formula that yields the answer to a quadratic problem. In addition to the quadratic formula, additional methods of solving quadratic equations include factoring, completing the square, graphing, and others.

Two equations

x y = 7

x + y = 7

solving for one variable

y = 7/x

applying the one variable

x + 7/x = 7

multiplying both sides by x

x^2 + 7 = 7x

rewriting to a quadratic equation

x^2 - 7x + 7 = 0

applying the quadratic formula

x = 1/2 (7 + square root 21) and y = 1/2 (7 - square root 21)

approximate answer

x ~ 5.79129 and y ~ 1.20871

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Answer:

130

Step-by-step explanation:

Angle 1 and 13 are supplementary.

So 13 is 180- angle 1

180-50 = 130

Answer:

130

Step-by-step explanation:

theyre supplementary angles I believe so 180-50=130

3 minutes is the cost of the call that is same for both plans

Two or more expressions with an Equal sign is called as Equation.

Let's assume the call duration in minutes is represented by x.

For David, the cost of the call can be represented by the equation: C(d) = 4 + x

For Alec, the cost of the call can be represented by the equation: C(a) = 1 + 2x

Since the cost of the call is the same for both plans, we can set the two equations equal to each other and solve for x:

4 + x = 1 + 2x

Solve for x.

3 = x

Hence, the call duration that costs the same on both plans is 3 minutes.

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Answer:

4x^2 +9x/4 -7

Step-by-step explanation:

f(x) =x/4 - 3

g(x) = 4x^2 + 2x - 4

(f +g)(x) = x/4 - 3  +  4x^2 + 2x - 4

             = 4x^2 + 8x/4+x/4 -7

             = 4x^2 +9x/4 -7

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

In a two-dimensional space, a point is defined by two coordinates, typically denoted by (x, y), where x represents the horizontal position, and y represents the vertical position. In a three-dimensional space, a point is defined by three coordinates, typically denoted by (x, y, z), where x, y, and z represent the horizontal, vertical, and depth positions, respectively.

We want to minimize the distance between the point (14, 8, 0) and the surface of the cone defined by the equation z² = x² + y², subject to the constraint that we stay on the surface of the cone.

Let f(x,y,z) = (x-14)² + (y-8)² + z² be the function we want to minimize subject to the constraint g(x,y,z) = z² - x² - y² = 0.

The Lagrange multiplier method involves finding the critical points of the function L(x,y,z,λ) = f(x,y,z) - λg(x,y,z), where λ is the Lagrange multiplier.

So we have:

L(x,y,z,λ) = (x-14)² + (y-8)² + z² - λ(z² - x² - y²)

Taking the partial derivatives with respect to x, y, z, and λ, and setting them equal to zero, we get the following system of equations:

2(x-14) + 2λx = 0

2(y-8) + 2λy = 0

2z - 2λz = 0

z² - x² - y² = 0

The third equation simplifies to z(1-λ) = 0, which gives us two possibilities:

Case 1: z = 0

In this case, the fourth equation becomes -x² - y² = 0, which implies that x = y = 0. But this point does not lie on the surface of the cone, so it is not a valid critical point.

Case 2: λ = 1

In this case, the first two equations become x-14 = -xλ and y-8 = -yλ, which imply that x = -7λ and y = -4λ. Substituting into the fourth equation gives:

z² = x² + y² = 65λ²

To minimize the distance between the point (14, 8, 0) and the surface of the cone, we want to find the value of λ that minimizes the function f(x,y,z) subject to the constraint g(x,y,z) = 0. Substituting x = -7λ, y = -4λ, and z = √(65λ²) into f(x,y,z), we get:

f(λ) = (7λ-14)² + (4λ-8)² + 65λ²

To minimize this function, we take its derivative with respect to λ and set it equal to zero:

f'(λ) = 30λ - 80 = 0

Solving for λ, we get λ = 8/3. Substituting this back into x = -7λ, y = -4λ, and z = √(65λ²), we get:

x,y,z=(smaller z-value)=(-56/3, -32/3, 16/3)

x,y,z=(larger z-value)=(56/3, 32/3, -16/3)

These are the points on the cone that are closest to the point (14, 8, 0).

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The slope of the line passing through (-1,1) and (2,-5) is -2.

The formula to find the slope between 2 coordinates of a line is given by;

m = (y₂ - y₁)/(x₂ - x₁)

To find the slope of the line passing through (-1,1) and (2,-5), we can use the formula:

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

where m is the slope of the line, (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given coordinates, we get:

m = (-5 - 1)/(2 - (-1))

m = (-6)/(3)

m = -2

Therefore, the slope of the line passing through (-1,1) and (2,-5) is -2.

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When  we rolled a fair, 6-sided die 1000 times. out of 1,000 rolls, the actual number of even rolls may vary due to the inherent randomness of the process.

If we assume that the die is fair and unbiased, each of the six sides has an equal probability of landing face-up. Since we are interested in the number of times the die comes up even (2, 4, or 6), we need to consider that half of the possible outcomes are even numbers.

Out of the six possible outcomes (1, 2, 3, 4, 5, 6), three are even (2, 4, 6). Therefore, the probability of rolling an even number on a fair six-sided die is 3/6 or 1/2.

If we roll the die 1000 times, we can expect that the die would come up even approximately half of the time, as per the probability. Half of 1000 is 500, so we would expect the die to come up even around 500 times out of 1000 rolls.

It's important to note that this is an expected value based on probability, and in practice, the actual number of even rolls may vary due to the inherent randomness of the process.

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To find all points on the curve x²y² + xy = 2, we can rewrite the equation in the form of a parametric representation.

Let x = t, and then solve for y in terms of t:
x²y² + xy = 2
t²y² + ty = 2
Now, we can solve for y in terms of t:
y(t^2y + t) = 2
y = 2 / (t^2y + t)
Unfortunately, the equation above cannot be simplified further to provide an explicit equation for y in terms of t. However, we can use this parametric representation to find all points on the curve by varying the value of t. To find specific points on the curve, plug in different values of t into the equation above and solve for the corresponding values of y. The points (x, y) will lie on the curve x²y² + xy = 2.

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Answer:

The last graph.

Step-by-step explanation:

The last graph because it shows the continum of time, and it shows him getting closer to the school (decrease in distance), then it shows him picking up Janet (staying constant), then it shows him going back home to grab his books (increase in distance), all as time goes on.

Answer:

4 : 7

Step-by-step explanation:

Given 2 similar figures the if the ratio of perimeters = a : b

The the ratio of areas = a² : b²

Here

ratio of areas = 16 : 49 , then

ratio of perimeters = \(\sqrt{16}\) : \(\sqrt{49}\) = 4 : 7

The implied population in the information provided is (e) the nitrogen concentration (mg nitrogen/1 liter of water) in the entire lake.

The information states that government agencies are monitoring water quality and its effect on wetlands, specifically focusing on the concentration of nitrogen in water draining from fertilized lands. To study this, twenty-eight samples of water were taken at random from a lake, and the nitrogen concentration was determined for each sample.

The purpose of taking these samples and analyzing the nitrogen concentration is to make inferences about the overall nitrogen concentration in the entire lake. The goal is to assess the impact of nitrogen on fish and wildlife in the lake. Therefore, the implied population in this case is the nitrogen concentration in the entire lake, which is the target of the monitoring efforts.

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Answer:

the people will have to walk further

Step-by-step explanation:

Using subtraction, weight put on by kitten is 1,298.43.

When we subtract from the group, the total number of items falls or gets less. The minuend, subtrahend, and difference are the elements of a subtraction problem.

It involves calculating the difference between two numbers. The icon looks like this: (minus). In this operation, we take a number and divide it by a smaller number. In other words, we divide one integer by another.

Weight of kitten when Madison brought her = 787.37 grams

Current weight of Madison = 2085.8 grams

Using subtraction,

Total weight Kitten put on = (2085.8 - 787.37)grams

= 1,298.43

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The activity ratio in the value stream measures the efficiency of the production process by evaluating the ratio of value-added activities to non-value-added activities.

The activity ratio is a performance metric used in value stream mapping, which is a lean management tool for analyzing and improving the flow of materials and information in a production process.

It focuses on distinguishing value-added activities, which directly contribute to meeting customer requirements, from non-value-added activities, which do not add value but consume resources and time.

By calculating the activity ratio, organizations can assess the proportion of time and resources spent on value-added activities versus non-value-added activities.

A higher activity ratio indicates that a greater portion of resources is dedicated to value-added activities, indicating improved efficiency and reduced waste.

Conversely, a lower activity ratio suggests a higher proportion of resources being utilized for non-value-added activities, indicating potential areas for improvement and waste reduction.

The activity ratio serves as a valuable diagnostic tool for organizations to identify process inefficiencies, bottlenecks, and areas for improvement. By analyzing the activity ratio, organizations can streamline their processes, eliminate waste, and optimize resource allocation to enhance overall productivity and customer value.

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Answer:

33 students.

Step-by-step explanation:

There are between 24 and 40 students in a class.

The ratio of boys to girls is 4:7.

4×3:7×3

12:21

12+21=33

33 students in the class, which is between 24 and 40 students in a class.

4×2:7×2

8:14

8+14=22

22 is wrong because it has to be between 24 and 40 students in a class.

4×4:7×4

16:28

16+28=44

44 is wrong because it has to be between 24 and 40 students in a class.

4×1:7×1

4:7

4+7=11

11 is wrong because it has to be between 24 and 40 students in a class.

Answer and Step-by-step explanation:

The word, "Consecutive" means, "Back-to-back" or "One after the other." Therefore, consider these integers:

1, 2, 3, 4, 5, 6, 7, 8, . . .

If we write down these integers in such a way that only even integers follow back-to-back, we have:

2, 4, 6, 8, . . .

If we write down these integers in such a way that only odd integers follow back-to-back, we have:

1, 3, 5, 7, . . .

Since 2, 4, 6, 8, . . . Are all even integers that follow back-to-back, then this is known of consecutive even integers.

Since 1, 3, 5, 7, . . . Are all odd integers that follow back-to-back, then this is known of consecutive odd integers.

In equilateral triangles, 7.0 mm is the length of each edge of the diamond.

The equilateral triangle's definition?

An equilateral triangle is a triangle whose three sides are all the same length, commonly referred to as a "regular" triangle.

                                       A triangle with all three sides equal and interior angles of 60 degrees is said to be equilateral. Triangle with an equal number of sides is known as an isosceles triangle.

V = 0.4783 S³  = 161

   S³   =  161/0.47

       = ∛ 161/0.47

       ≈ 7.0 mm

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Given:

The equation of the graph is, x - y = 19.

The objective is to find the x-intercept and y-intercept of the graph.

Explanation:

At x-intercept the value of y will be zero.

In the given equation, at y = 0,

Thus, the coordinate is (19,0).

Similarly, at y-intercept the value of x will be zero.

In the given equation, at x = 0,

Thus, the coordinate is (0,-19).

Hence, the x-intercept is (19,0) and the y-intercept is (0,-19).

Using the combination formula, it is found that:

There are 364 different orders of top-three finishers that include all seniors.

The probability that the top-three finishers will all be seniors is 15.38%.

The order in which the players are taken is not important, hence the combination formula is used to solve this question.

\(C_{n,x}\) is the number of different combinations of x objects from a set of n elements, given by:

\(C_{n,x} = \frac{n!}{x!(n-x)!}\)

In total, three students are taken from a set of 14, hence:

\(C_{14,3} = \frac{14!}{3!11!} = 364\)

Including only seniors, it would be three students from a set of 8, hence:

\(C_{8,3} = \frac{8!}{3!5!} = 56\)

Hence the probability is given by:

p = 56/364 = 0.1538 = 15.38%.

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Answer:

What steps are used to solve this equation?

6f = 48

Complete each statement.

First,

✔ divide by 6

on both sides of the equation.

Next, simplify the equation to determine that the solution of the equation is

✔ f = 8

.

Check the solution by substituting

✔ 8

for f and simplifying.

Step-by-step explanation:

The solution of the given equation would be 8.

An equation is an expression that shows the relationship between two or more numbers and variables.

A mathematical equation is a statement with two equal sides and an equal sign in between.

A system of equations is two or more equations that can be solved to get a unique solution and the power of the equation must be in one degree.

We are given the equation as;

6f = 48

We have to Complete each statement.

First, divide by 6 into both sides of the equation.

f = 48/6

Next, simplify the equation to determine that the solution of the equation is

f = 8

Check the solution by substituting for f and simplifying.

6  x8 = 48

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Answer:

\(y=3750 \cdot 1.0215^t\)

(where \(y\) is the population and \(t\) is time in years after 2021)

5159

Step-by-step explanation:

Part (a)

General form of an exponential function:  \(y=ab^x\)

where:

If \(b > 1\)  then it is an increasing function

If \(0 < b < 1\) then it is a decreasing function

We are told that the initial population is 3750.  Therefore, \(a=3750\)

We are told that the farm grows at a rate of 2.15% annually.  Therefore, if it grows then every year it is 100% + 2.15% = 102.15% of the previous year.

Convert the percentage into a decimal:

102.15% = 102.15/100 = 1.0215

Therefore, \(b=1.0215\)

We are told that the independent variable is \(t\) (in years).

Therefore, the equation is  \(y=3750 \cdot 1.0215^t\)

(where \(y\) is the population and \(t\) is time in years after 2021)

------------------------------------------------------------------------------------------

Part (b)

The year 2036 is 15 years after 2021.  Therefore, substitute \(t = 15\) into the equation and solve for \(y\):

\(\implies y=3750 \cdot 1.0215^{15}\)

\(\implies y=5159.49068...\)

Therefore, an estimate of the population of the town in 2036 is 5159.

Answer:180

Step-by-step explanation:

hope this helps

Answer:

0.8 mm

Step-by-step explanation:

Given that you require the actual size.

The ant has been magnified by 15 X

To find the actual size divide magnified size by 15

actual size = 12 mm ÷ 15 = 0.8 mm

We can see that Savings Account 1 offers a slightly higher interest rate but compounds less frequently compared to Savings Account 2. The choice between the two accounts would depend on an individual's preferences and financial goals.

Based on the information provided in the table, we can complete the statement as follows:

"Savings Account 1 offers an interest rate of 2.25% compounded semiannually, with a minimum deposit requirement of $500. On the other hand, Savings Account 2 offers an interest rate of 2.20% compounded quarterly, also requiring a minimum deposit of $500."

The interest rate represents the annual percentage rate (APR) that the account offers. For Savings Account 1, the interest rate is 2.25%, meaning that for every $100 in the account, it will earn $2.25 in interest over the course of a year. This interest is compounded semiannually, meaning it is added to the account balance twice a year.

In contrast, Savings Account 2 offers an interest rate of 2.20%, slightly lower than the first account. However, the interest is compounded more frequently, on a quarterly basis. This means that the interest is added to the account balance four times a year.

Both accounts have the same minimum deposit requirement of $500, indicating that to open either account, a minimum of $500 must be deposited.

Overall, when comparing the two accounts, we can see that Savings Account 1 offers a slightly higher interest rate but compounds less frequently compared to Savings Account 2. The choice between the two accounts would depend on an individual's preferences and financial goals.

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Answer:

375\(\sqrt[n]{x}\)

Step-by-step explanation:

Answer:

( 3 , 0 )

Step-by-step explanation:

When the reflection is over the y-axis , the y-coordinate is the same

and x-coordinate changes its Sign

So for ( -3 , 0) is reflected over y-axis

Then x-coordinate = 3

Then y-coordinate =0

So the new point = ( 3 , 0 )