given f(x)= 1/3(4-x)^2, what is the value of f(16)

The integral ∫∫ r √4 −x2−y2da where r = {(x, y) : x2 y2≤ 4, x ≥ 0} conversion to polar coordinates the value of the integral is (4/3)π.

To convert the integral to polar coordinates, we need to express the limits of integration in terms of the polar coordinates.

Recall that in polar coordinates, x = r cosθ and y = r sinθ, where r is the radial distance from the origin and θ is the angle measured counterclockwise from the positive x-axis to the line connecting the origin to the point (x, y).

In this case, the region r is defined by \(x^2 + y^2\) ≤ 4 and x ≥ 0. In polar coordinates, this corresponds to the region 0 ≤ r ≤ 2 and 0 ≤ θ ≤ π/2. To see why, note that x ≥ 0 implies 0 ≤ θ ≤ π/2, and \(x^2 + y^2 = r^2\), so r ≤ √4 = 2.

So we have:

∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) ∫(r=0 to 2) r√(4-\(r^2\)) dr dθ

To evaluate this integral, we can use the substitution u = 4 - \(r^2\), du = -2r dr, which gives:

∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) ∫(u=4 to 0) -1/2 √u du dθ

Now we can evaluate the inner integral:

∫(u=4 to 0) -1/2 √u du = [-1/3 u^(3/2)](u=4 to 0) = (1/3)(8 - 0) = 8/3

Substituting this back into the original integral, we have:

∫∫ r √4 −x2−y2da = ∫(θ=0 to π/2) (8/3) dθ = (8/3) (π/2 - 0) = (4/3)π

Therefore, the value of the integral is (4/3)π.

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Answer:

-1, 0, 1/2, 1, 4/3

Step-by-step explanation:

Answer:

-the lines should be straight

-there is no 9.5 thousand number of visitors given on the y axis

Step-by-step explanation:

The two faults are the x axis has 2, 3 and 4 and the year is 2017, 2018 etc. However we do not know the relationship between 2 and 2017. and the line is not smooth.

Graph is a mathematical representation of a network and it describes the relationship between lines and points.

Given that Sam has drawn a time series graph to show the numbers, in thousands, of visitors to a theme park.

Jayne, Sam's friend, tells him it is the worst graph she has ever seen

and she can see quite a few things about the graph that are wrong

or misleading.

The x axis has 2, 3 and 4 and the year is 2017, 2018 etc. However we do not know the relationship between 2 and 2017.

The line is not correct when drawing the graph the line used to connect the point should be smooth but the given graph is not smooth.

Hence, the two faults are the x axis has 2, 3 and 4 and the year is 2017, 2018 etc. However we do not know the relationship between 2 and 2017. and the line is not smooth.

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The volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².

Using the formula for the volume of a square pyramid, find the volume and then multiply it by two since there are two square pyramids.

Let V be the volume of the solid formed.

⇒ volume of the solid formed - V = 2 ( \(\frac{1}{3} *B*h\) )

Now substitute the values,

⇒V = 2 ( \(\frac{1}{3}\) * \(28^{2}\) * 10.5 )

⇒V = 2 ( \(\frac{1}{3}\) * 784 * 10.5 )

⇒V = 2 ( 261.3 * 10.5 )

⇒V = 2 ( 2,743.65 )

⇒V = 5,487.3 unit ²

Therefore, the volume of the solid formed using square pyramids are joined at their bases is 5,487.3 unit ².

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The values on the interval [0, 2π) where the two fishes will be at the same height above the water is

To find the values on the interval [0, 2π) where the two fish will be at the same height above the water, we need to find the values of x that satisfy the equation f(x) = g(x).

Given:

f(x) = 2sin(2x - 1)

g(x) = cos(x)

We can solve this by plotting the two equations and the point of intersections denotes the points of equal height

Therefore, the values from the graph, on the interval [0, 2π) where the two fish will be at the same height above the water are:

x = 0.581, 1.194, and π.

The correct answer choice is d. {π}.

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The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

The ratio of the scale of an original thing to a new object that is a representation of it but of a different size is known as a scale factor (bigger or smaller). For instance, we can increase the size of a rectangle with sides of 2 cm and 4 cm by multiplying each side by, let's say, 2.

Given

In line with the posed question.

Triangle ABC's vertices are A(-2, 3), B(0, 0), and C. (1, 2).

As we are aware,

The x-coordinates of each point must be negative while keeping the y-value constant in order to reflect a triangle over the y axis.

As a result, when triangle ABC is mirrored across the y-axis, its vertices are

A'(2,3)

B'(0, 0)

C'(-1, 2)

The vertices of the triangle will also change when it is dialated by a scale factor of 2.

A'(4, 6)

B'(0, 0)

And, C'(-2, 4)

The triangle's vertices will therefore be A'(4, 6), B'(0, 0), and C'(-2,4) if it is mirrored across the y-axis and then dilated by a scale factor of 2.

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Answer: 25y= 60x

190x +25y= 37500

Step-by-step explanation:

Let x = Number of balcony tickets.

then, Number of lower level tickets  = 5x

Let y = Number of mezzanine tickets

Money made from ,

balcony tickets = 15x

lower level tickets = 35 (5x) = 175 x

mezzanine tickets = 25y

Money made from mezzanine tickets=  4 x( money made from balcony tickets.)

⇒ 25y = 4 (15x)

⇒ 25y= 60x              (i)

Also, total cost of the tickets = 15x+175x+25y = 37500

⇒ 190x +25y= 37500          (ii)

From (i) and (ii), the system of linear equations could be used to solve for the number of each type of ticket sold:

25y= 60x

190x +25y= 37500

The system of linear equations which could be used to solve for the number of each ticket type sold are :

Ticket types :

Ticket cost :

The total amount made from tickets sales :

35a + 25b + 15c = 37500

From (1) :

35(5c) + 25b + 15c = 37500

175c + 25b + 15c = 37500

190c + 25b = 37500 - - - - - (2)

Sales from Mezzanine tickets only = 25b

25b = 4(15c)

25b = 60c - - - - (3)

Therefore, the system of linear equation required to solve the problem are equations (2) and (3)

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Answer:

4 and - 2

Step-by-step explanation:

f ( x ) = x^2 - 2x - 3

f ( x ) = 5

x^2 - 2x - 3 = 5

x^2 - 2x - 3 - 5 = 0

x^2 - 2x - 8 = 0

x^2 + 2x - 4x - 8 = 0

x ( x + 2 ) - 4 ( x + 2 ) = 0

( x - 4 ) ( x + 2 ) = 0

x - 4 = 0

x = 4

x + 2 = 0

x = - 2

x has 2 values,

x = 4, - 2

Answer:

1)c = -v 2)(q-5)/4

Step-by-step explanation:

v = c/4-5

v = c/-1

c = -v

q-p=3p+5

q = 4p+5

q-5 = 4p

p = (q-5)/4

Answer:

75%

Step-by-step explanation:

15+15+25+5=60

15/60=25%

100%-25% = 75%

Answer:

C should be the correct answer

Step-by-step explanation:

forgive me if im wrong

Answer:

a, b, c

(all but the last one)

Step-by-step explanation:

a+b+c=180 is true bcuz the sum of interior angles in a triangle is 180

rearrange a+b+c=180 into a+b=180-c

observe that 180-c equals d, so in the equation a+b=180-c replace 180-c with d.

a+b=d   so thats true

we already established that d=180-c  so thats true as well

and the last one is just not true

Answer:

First, we need to solve the equation in the problem for y to put it in slope-intercept form so we can determine its slope:

2y−6x=4

2y−6x+6x=6x+4

2y−0=6x+4

2y=6x+4

2y2=6x+42

2y2=(6x2)+(42)

y=3x+2

The slope-intercept form of a linear equation is: y=mx+b

Where m is the slope and b is the y-intercept value.

Therefore the slope of this equation is m=3

A perpendicular line will have a slope (let's call this slope mp) that is the negative inverse of this line. Or, mp=−1m

Substituting gives:

mp=−13

Answer:

-2

Step-by-step explanation:

9514 1404 393

Answer:

  left-to-right

Step-by-step explanation:

[There's a lot to read here. If you read it, maybe you'll have a better understanding.]

This is asking you the first step required to solve each of the equations.

The general process of solving an equation involves performing operations that result in the variable of interest being on one side of the equal sign (by itself), and everything else being on the other side. When variable and constant terms are mixed, we generally want to remove the variable term.

The underlying rule for all of this is "whatever is done to one side of the equation must also be done to the other side." The exceptions are simplification and substitution.

"Inverse" operations are of use in this process. That is why you are taught about the "additive inverse" (negative) of a number, and the "multiplicative inverse" (reciprocal) of a number. Adding the additive inverse results in the additive identity element (0). Similarly, multiplying by the multiplicative inverse results in the multiplicative identity element (1). Adding 0 or multiplying by 1 leaves only the original value.

__

With this in mind, we can look at the given equations to see what is needed to solve them.

2 +2y = y

  We see that the left side of the equation has both a constant term and a variable term. To remove the variable term we add its additive inverse: (-2y). Adding a negative value is the same as subtracting a positive value. That is, we can describe what we want to do as "subtract 2y from both sides".

When we do that, the result is ...

  2 +2y -2y = y -2y . . . . . here, we show the subtraction

  2 = -y . . . . . . . . . . . . . and this is the result of simplifying that.

Notice the y term is now on one side of the equal sign and the constant is on the other side. We are one step closer to the solution, which is the whole point.

__

5(y -4) = 2y

  This equation has parentheses. It often works well as a first step to eliminate the parentheses, generally using the distributive property. That is, we "distribute 5".

When we do that, the result is ...

  5(y) -5(4) = 2y . . . . . . . . here, we show the distribution

  5y -20 = 2y . . . . . . . and this is the result of simplifying that

This puts us one step closer to the solution, which is the whole point.

__

5y = 10 -2y

Here, the unwanted variable term is -2y on the right side of the equation. To remove it, we add 2y to both sides.

When we do that, the result is ...

  5y +2y = 10 -2y +2y . . . . . . . showing the addition of 2y

  7y = 10 . . . . . . . . . . . . . . . simplified

This puts us one step closer to the solution.

__

5 = 25y

This equation has the variable term and the constant term already separated. However, there is a coefficient on the variable term that is not equal to 1. We want to make that coefficient be 1. To do that, we multiply it by its multiplicative inverse: 1/25. That is, we divide both sides by 25.

When we do that, the result is ...

  5/25 = 25y/25 . . . . . . showing division by 25

  1/5 = y . . . . . . . . . simplified (and the fraction reduced)

This gives us the solution. There are no more steps required.

Surface Area of Larger Solid: S2 = k^2 * S1 and Volume of Larger Solid: V2 = k^3 * V1. Substitute in the given values for S1, V1, and k before solving for S2 and V2.

To solve this problem, we need to use the fact that similar solids have corresponding sides that are proportional in length.  

Let's call the scale factor between the two solids "k". This means that if the smaller solid has a side length of "s", then the corresponding side length in the larger solid is "ks".

Now let's use the given information to find the surface area and volume of the larger solid. Let's call the surface area and volume of the smaller solid "S1" and "V1", respectively.

Surface Area:
The surface area of a solid is proportional to the square of its linear dimensions. Since the scale factor between the two solids is "k", the surface area of the larger solid is k^2 times the surface area of the smaller solid. Therefore, the surface area of the larger solid (S2) can be found using the formula:

S2 = k^2 * S1

Volume:
The volume of a solid is proportional to the cube of its linear dimensions. Using the same logic as above, the volume of the larger solid (V2) can be found using the formula:

V2 = k^3 * V1

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Answer:

2. twice a number n subtracted from fifteen and four-tenths

Step-by-step explanation:

The volume of a sphere with a radius of 7 cm (or diameter of 12 cm) is 904.32 cubic centimeters.

To find the volume of a sphere with a radius of 7 cm, we can use the formula:

V = (4/3) * π * r^3

where V represents the volume and r represents the radius. However, you mentioned that the diameter of the sphere is 12 cm, so we need to adjust the radius accordingly.

The diameter of a sphere is twice the radius, so the radius of this sphere is 12 cm / 2 = 6 cm. Now we can calculate the volume using the formula:

V = (4/3) * π * (6 cm)^3

V = (4/3) * 3.14 * (6 cm)^3

V = (4/3) * 3.14 * 216 cm^3

V = 904.32 cm^3

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The price that Maura sell each scarf would be =$33. Maura sells each scarf for $33. That is option A.

To calculate the amount of money that Maura spends on each scarf the following is carried out.

The amount of money that she spends on the scarf material = $5.50

The percentage selling price of each scarf = 600% of $5.50

That is ;

= 600/100 × 5.50/1

= 3300/100

= $33.

Therefore, each price that is sold by Maura would probably cost a total of $33.

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Refer to the photos taken.

let's solve for x :

Response variable defined with:

B. The number or quality of the variable for whom the value the experimenter wants to figure out how the explanatory variable affects.

Option B describes the response variable as the variable of interest that the experimenter is trying to study and understand how it is affected by other variables, known as explanatory variables. The response variable is often the dependent variable in a study and the focus of the analysis.

On the other hand, option A describes a situation in which the effect of two factors on the response variable cannot be distinguished, which is not a definition of the response variable itself. Option C describes a placebo, which is a different concept in experimental design.

Option D is similar to option B but does not describe the response variable as being the focus of the experimenter's study.

The response variable, also known as the dependent variable, is a variable in a statistical model or experiment that is being measured or studied. It is the outcome of interest that the experimenter wants to understand and explain by considering the effects of one or more independent variables, also known as explanatory variables.

The goal of the experiment is to determine how changes in the explanatory variables affect the response variable. In a sense, the response variable is the dependent variable because its value depends on the values of the independent variables.

Understanding the relationship between the response and explanatory variables is important in fields such as science, medicine, and engineering, where researchers are often interested in predicting or controlling outcomes based on various inputs.

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You will need 16 dollars

Step-by-step explanation:

Since there are 3 feet in a yard divide the 6 by three that will be 2 dollars per foot. Then 2×4 equals 8. Take the 8 and multiply it by 2 then you will get the total of 16 dollars

If a company found that raising the price of its muffins resulted in an absolute value of.35 < 1, then the demand for muffins is inelastic.

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None of the given expressions has a value of 16 when n=5.

An algebraic expression consists of unknown variables, numbers and arithmetic operators.

We can evaluate each expression to see which one has a value of 16 when n=5:

25+7 = 32, which is not equal to 16.

30-3n = 30-3(5) = 15, which is not equal to 16.

7+5+5+8 = 25, which is not equal to 16.

5³-114 = 125-114 = 11, which is not equal to 16.

Therefore, none of the given expressions has a value of 16 when n=5.

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If number of dates in a month 0 1 2 3 4 5 probability 0.12 0.27 0.35 0.14 0.09 0.03. The median of the dates that byu students go on per month is 2.5 . So, the correct option is C.

To find the median number of dates that BYU students go on per month from the given data, we need to calculate the cumulative probabilities for each possible number of dates and find the value for which the cumulative probability is greater than or equal to 0.5.

Using the given probabilities, we can calculate the cumulative probabilities as follows:

The median is the value that corresponds to the cumulative probability of 0.5. Looking at the cumulative probabilities, we can see that the median falls between 2 and 3, as the cumulative probability for 2 is 0.74 and the cumulative probability for 3 is 0.88.

To estimate the median more precisely, we can use linear interpolation. The proportion of the median between 2 and 3 can be calculated as:

Proportion of median = (0.50 - 0.74) / (0.88 - 0.74) = 0.40

Therefore, the median number of dates that BYU students go on per month is:

Median = 2 + 0.40 * (3 - 2) = 2.4

So, the median number of dates is approximately 2.4. Therefore, the closest option in the given choices is 2.5. Hence, the answer is 2.5.

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Complete question is:

Number of dates in a month 0 1 2 3 4 5 probability 0.12 0.27 0.35 0.14 0.09 0.03 what is the median number of dates that byu students go on per month?

group of answer choices

a)1

b)2

c)2.5

d)3

e)4

The solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is y=5/2 x.

Substitute x=0, 1, 2, 3, 4,......

When x=0

y=0

When x=1

y=5/2=2.5

When x=2

y=5

When x=3

y=7.5

Therefore, the solutions for the given equation are (0, 0), (1, 2.5), (2, 5) and (3, 7.5).

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"Your question is incomplete, probably the complete question/missing part is:"

Use the equation y=5/2 x to complete the table. Is y proportional to x? Explain why or why not.

The number of stories that the sky scrapper has is; 56 stories

We are given that;

Height of antenna on the building = 52 ft

Total height of building including antenna = 780 ft

Height of each story = 13 ft

Thus;

Height of building without the antenna = Total height of building including antenna - Height of antenna

Height of building without the antenna = 780 - 52

Height of building without the antenna = 728 ft

Since each floor is 13 feet tall, then;

Number of floors = 728/13

Number of floors = 56 stories

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However, it does not appear to be a familiar series, and finding an exact sum may be difficult or impossible.

To determine the convergence of the series, we can use the limit comparison test.

Let's compare the given series with the series 1/n^2, since both of them have positive terms.

lim n→∞ ln[(n^2+8)/(3n^2+1)] / (1/n^2)

= lim n→∞ [ln(n^2+8) - ln(3n^2+1)] / (1/n^2)

= lim n→∞ [(2n/(n^2+8)) - (6n/(3n^2+1))] * n^2

= lim n→∞ [2/(1+(8/n^2)) - 6/(3+(1/n^2))]

The limit of this expression can be evaluated by dividing the numerator and denominator by n^2, which gives:

lim n→∞ [2/(1+(8/n^2)) - 6/(3+(1/n^2))]

= lim n→∞ [2/(n^2/n^2+(8/n^2)) - 6/(n^2/n^2+(3/n^2))]

= lim n→∞ [2/(1+(8/n^2)) - 6/(1+(3/n^2))] * (1/n^2)

Now we can see that the limit is of the form (finite number) * (1/n^2), which goes to zero as n approaches infinity. Therefore, by the limit comparison test, since the series 1/n^2 is convergent (p-series with p=2), the given series is also convergent.

Since the series is convergent, we can find its sum using any appropriate method. However, it does not appear to be a familiar series, and finding an exact sum may be difficult or impossible.

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The function f(x) = 1 - x²/a² equals its average value at x = ±a/√3 on the interval [0, a].

The function f(x) = 1 - x²/a² equals its average value at x = ±a/√3.

To find the point(s) at which the function equals its average value on the interval [0, a], we first need to determine the average value. The average value of a function on a closed interval [a, b] can be calculated by integrating the function over that interval and dividing by the length of the interval (b - a). In this case, the interval is [0, a], so the length of the interval is a - 0 = a.

To find the average value, we integrate the function f(x) = 1 - x²/a² over the interval [0, a]:

∫(0 to a) (1 - x²/a²) dx = x - (x³/3a²) evaluated from 0 to a

= (a - (a³/3a²)) - (0 - 0)

= (a - a/3) - 0

= 2a/3

The average value of the function f(x) over the interval [0, a] is 2a/3.

Now, we set the function equal to its average value:

1 - x²/a² = 2a/3

Multiplying both sides by a², we get:

a² - x² = (2a/3) * a²

a² - x² = 2a²/3

3a² - 3x² = 2a²

3x² = a²

x² = a²/3

x = ±√(a²/3)

x = ±(a/√3)

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