the attachment is the question

The area of the surface generated when the curve y = 4x^2 is revolved about the x-axis over the interval [0, 2], we can use the surface area formula and approximate the integral using numerical methods like Simpson's rule.

To find the area of the surface generated when the curve y = 4x^2, defined over the interval [0, 2], is revolved about the x-axis, we can use the formula for the surface area of revolution:

A = 2π ∫[a,b] y * √(1 + (dy/dx)^2) dx

In this case, our curve is y = 4x^2, so we need to find dy/dx:

dy/dx = d/dx (4x^2) = 8x

Now, let's calculate the square root term:

√(1 + (dy/dx)^2) = √(1 + (8x)^2) = √(1 + 64x^2) = √(64x^2 + 1)

Substituting these values into the surface area formula, we have:

A = 2π ∫[0,2] (4x^2) * √(64x^2 + 1) dx

Now, we can integrate the expression over the given interval [0, 2] to find the area. However, this integral does not have a simple closed-form solution. Therefore, we will use numerical methods to approximate the integral.

One commonly used numerical method is Simpson's rule, which provides an estimate of the definite integral. We can divide the interval [0, 2] into a number of subintervals and apply Simpson's rule to each subinterval. The more subintervals we use, the more accurate our approximation will be.

Let's say we divide the interval into n subintervals. The width of each subinterval is h = (2-0)/n = 2/n. We can then approximate the integral using Simpson's rule:

A ≈ 2π * [(h/3) * (y0 + 4y1 + 2y2 + 4y3 + ... + 4yn-1 + yn)]

where y0 = f(0), yn = f(2), and yi = f(xi) for i = 1, 2, ..., n-1, with xi = i*h.

By substituting the values of f(xi) into the formula and performing the calculations, we can obtain an approximation of the surface area.

In summary, to find the area of the surface generated when the curve y = 4x^2 is revolved about the x-axis over the interval [0, 2], we can use the surface area formula and approximate the integral using numerical methods like Simpson's rule.

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The closest correlation of rates of return between stocks a and b is approximately -0.487 (negative), indicating opposite movements.

The relationship coefficient between two stocks an and b can be determined utilizing the equation:

relationship coefficient = covariance/(standard deviation of stock a * standard deviation of stock b)

Considering that the covariance between the profits of stocks an and b is - 0.073, and the standard deviation of the paces of return is 0.5 for stock an and 0.3 for stock b, we can substitute these qualities into the recipe to track down the connection coefficient.

relationship coefficient = - 0.073/(0.5 * 0.3) ≈ - 0.487

Consequently, the nearest worth of the connection of the paces of return between stock an and b is - 0.487. This negative relationship coefficient demonstrates that the profits of the two stocks will generally move in inverse bearings. At the point when one stock's return is high, the other stock's return is probably going to be low, as well as the other way around.

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Answer:

There is only one prism

The lowest point should be used for measurement. To acquire a correct reading, students must read the meniscus at eye level. In order to read the meniscus at eye level, students need first set the graduated cylinder on the table and then stoop.

A measuring cylinder, often referred to as a graded cylinder, a cylinder measuring cylinder, or a mixing cylinder, is a piece of lab apparatus used to gauge the quantity of fluids, chemicals, or solutions used during a typical lab session. Compared to common laboratory flasks and beakers, graduated cylinders offer higher precision and accuracy. The graduated cylinder is a scientific tool that employs the metric system rather than the American standard system, so measurements are made in millilitres rather than ounces. The volume of an object or quantity of liquid is measured using a graduated cylinder, a common piece of laboratory glassware. It is a glass cylinder with side markings resembling those on a measuring cup, as its name suggests.

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The volume of raspberries in Mateo's box is 384 cubic centimeters.

To calculate the volume of raspberries in Mateo's box, we need to use the formula for the volume of a rectangular prism, which is length x width x height. In this case, the length and width are both 8 centimeters, as the box has a square bottom. The height is 6 centimeters, as Mateo fills the box to that height with raspberries.

So, the volume of raspberries in Mateo's box is:

Volume = length x width x height
Volume = 8 cm x 8 cm x 6 cm
Volume = 384 cubic centimeters

Therefore, the volume of raspberries in Mateo's box is 384 cubic centimeters. This calculation assumes that the raspberries are tightly packed in the box, without any gaps or air pockets. In reality, the actual volume of raspberries may be slightly less than this, depending on how they are arranged in the box. Nonetheless, this calculation provides a reasonable estimate of the amount of raspberries that Mateo is able to pick and fit in the box.

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Answer:

It will be 5:56

Step-by-step explanation:

Add 32 plus 24 and you get 56 add the 5 and you get 5:56

please give brainliest please and thanks have a good day <3

Answer:

40 m

Step-by-step explanation:

8/12=x/60

x=(8*60)/12

x=40

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. The height of the building when it cast a shadow of 60 meters is 40 m.

The tangent or tanθ in a right angle triangle is the ratio of its perpendicular to its base. it is given as,

\(\rm Tangent(\theta) = \dfrac{Perpendicular}{Base}\)

where,

θ is the angle,

Perpendicular is the side of the triangle opposite to the angle θ,

The base is the adjacent smaller side of the angle θ.

As it is given that the height of the pole is 8m, while the shadow cast by the pole is 12 m. If we use the ratio of trigonometry then the height of the building can be written as,

\(\rm Tan(\theta)= \dfrac{\text{Height of the pole}}{\text{Shadow of the pole}}= \dfrac{\text{Height of the building}}{\text{Shadow of the pole}}\)

\(\dfrac{8}{12}= \dfrac{\text{Height of the building}}{\text{60}}\\\\\dfrac{8 \times 60}{12}= {\text{Height of the building}}\\\\\text{Height of the building}=40\ \rm m\)

Hence, the height of the building when it cast a shadow of 60 meters is 40 m.

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The DML Compiler translates Data Manipulation Language (DML) queries into Relational Algebra operations to be used by the Relational Database Management System (RDBMS).

The DML Compiler starts by parsing the query to determine which operations are needed. It then builds an Abstract Syntax Tree (AST) which is a hierarchical representation of the query. Next, the DML Compiler will perform semantic analysis on the AST to ensure that all operations are valid and the query is valid. After the semantic analysis has been done, the DML Compiler will then translate the AST into Relational Algebra operations, which are a collection of mathematical rules used to manipulate data in a relational database. Finally, the DML Compiler will generate an executable code and send it to the RDBMS to be executed. The result of the query is then returned to the user.

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At Station Y, 15 litres of gasoline would cost £18.

Cost is the amount of money spent by a business to produce or create goods or services. It excludes the profit margin markup. Cost is the sum of money spent on making a good or product, as seen from the seller's perspective.

Ellie must have visited Station Y because she paid $24 for 20 litres of gasoline, proving that she did.

b) We can observe from the graph that 20 litres of gasoline at Station Y costs £24. With the help of this data, we can calculate how much a litre of gasoline costs:

Cost of 1 litre of petrol = Cost of 20 litres of petrol / 20

Cost of 1 litre of petrol = £24 / 20

Cost of 1 litre of petrol = £1.20

Therefore, 15 litres of petrol at Station Y would cost:

Cost of 15 litres of petrol = Cost of 1 litre of petrol x 15

Cost of 15 litres of petrol = £1.20 x 15

Cost of 15 litres of petrol = £18

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Answer:

\((f \circ g)(24)=-36\)

Step-by-step explanation:

Given functions:

\(\begin{cases}f(x)=-9x+9\\g(x)=\sqrt{x+1}\end{cases}\)

Function Composition is applying one function to the results of another.

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).  

Therefore (f o g)(24) means to substitute the result of g(24) in place of the x in the function f(x).

Calculate g(24) by substituting x = 24 into function g(x):

\(\begin{aligned}\implies g(24)&=\sqrt{24+1}\\&=\sqrt{25}\\&=5 \end{aligned}\)

Therefore:

\(\begin{aligned}\implies (f \circ g)(24) & = f[g(24)]\\& = f(5)\\& = -9(5)+9\\&=-45+9\\&=-36\end{aligned}\)

Answer:

(f∘g)(24) = -36

Step-by-step explanation:

We are given f(x) = -9x + 9 and  \(g(x)= \sqrt{x+1}\).

We want to find (f∘g)(24).

This means that we first want to find g(24), then substitute the value of that into f(x).  

Start by substituting 24 for x in g(x).

\(g(24)= \sqrt{24+1}\)

Add 24 and 1 together.

\(g(24)= \sqrt{25}\)

Take the square root of 25.

g(24) = 5

Now, substitute 5 as x in f(x) = -9x + 9.

f(5) = -9(5) + 9

Multiply.

f(5) = -45 + 9

Add the numbers together.

f(5) = -36

f(5) in this case has the same value as (f∘g)(24)

This means that (f∘g)(24) = -36

Answer:

pretty sure that's C

Step-by-step explanation:

Answer:

Step-by-step explanation:

Just a simple manipulation question: rearrange for so all but the (y) is on the other side.

\(4x+3y=7\\ 3y=7-4x\\ y=7-4x/3\)

Answer:

70 miles

Step-by-step explanation:

If Nadia has a gas tank that can hold 14 gallons of gas and she uses a quarter of it, she has used 14 * 0.25 = 3.5 gallons of gas.

Since each gallon of gas can go 20 miles, Nadia has gone

3.5 * 20 = 70 miles

The number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

What is integration?

It is defined as the mathematical approach to calculating the smaller parts or components.

It is given that:

A barn is 100 feet long and 40 feet wide.

Find the first derivative of the given function:

After solving the above integration:

= 20(e - 1/e)

The roofing = 100(20(e - 1/e))

= 4701 square feet

Thus, the number of square feet of roofing on the barn is 4701 square feet if the barn is 100 feet long and 40 feet wide.

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Answer:

A answer is A brainly helps you

Answer:

Putting x= 2

\(( - 5) \times 2 = - 10 \\ - 10 = - 10\)

putting x = -2

\(( - 5) \times ( - 2) = - 10 \\ 5 \times 2 = - 10 \\ 10 = - 10 \\ this \: is \: not \: correct \: equation\)

putting x = 50

\(( - 5) \times 50 = - 10 \\ - 250 = - 10 \\ this \: is \: also \: not \: correct \: equation\)

so, x = 2 is applicable.

Answer:

then she only has eight pencils in the bag.

Step-by-step explanation:

Answer:

Eight

Step-by-step explanation:

Answer:

$149,000

Step-by-step explanation:

Subtract acc depreciation for 2020 from acc deprecitation in 2021 and it gives you the depreciation expense solely for 2021.

The Equipment was purchased during 2021 at $1,402,000.

The total amount of depreciation applied to an asset up to a particular point is known as accumulated depreciation. The beginning cumulative depreciation balance is increased with each period's depreciation expense.

Given:

Equipment purchased during 2021

= Cost of equipment on 12/31/2021 - (Cost of equipment on 12/31/2020 - Cost of equipment sold)

=  $2211000 - ( $2062000 - $470000)

= $2211000 - 15,92,000

= $6,19,000

Hence, the Equipment purchased during 2021 at $1,402,000.

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D box plot correctly represents the data

A box plot or boxplot is a technique for illustratively displaying the localization, dispersion, and skewness groups of numerical data through their quartiles.

Using a five-number summary (the minimum, first quartile (Q1), median, third quartile (Q3), and "maximum"), a boxplot is a common method of visualizing data distribution.

The median value for the provided data will be the sixth data point's value, or 3.

The median of the data's lower half is now the first quartile. The third data point's value of 1 will therefore be in the lower quartile.

The median of the data's upper half is now referred to as the upper or third quartile. This means that the value of the ninth data point, which is 6, will represent the upper quartile.

Thus, box-plot D effectively displays the data from above.

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Answer:

The answer is D.

Edg 2023.

square root of 27 is bigger.

What is percentage ?

In math, one percent is equal to a hundredth part; thus, 100 percent represents the entire amount and 200 percent specifies twice that amount

First calculating square root of 27 :

\(\sqrt{27}=5.196\)

and 5.6 % is 0.056

clearly \(\sqrt{27}\) is greater than 5.6%

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Answer:

y=3x+3

Step-by-step explanation:

Answer:

Let's set up an equation;

12/100 * x = 16.5

where 12/100 is 12%

x is the number of the 12%

that would equal 16.5

So solve for x;

12/100 * x = 16.5

12/100x = 16.5

0.12x = 16.5

/0.12    /0.12

x = 137.5

Answer:Holly drank 12 bottles in a week.

Step-by-step explanation:

First change the fraction 1 2/5 litre into a decimal, by doing this, we can know how many litres are there in 2/5.

So= 1 2/5

= 2 ÷5 = 0.4

= 1 + 0.4 = 1.4 liters

1.4 liters is the amount of water in a bottle.

Next, also change the fraction 2 2/5 litres into a decimal.

So=2 2/5

= 2÷5 = 0.4

= 2 + 0.4 = 2.4 liters

She drinks 2.4 liters a day.

To find how many bottles she drank in 1 week, we must multiply the amount of water she drinks in a day to the days in a week.

So= 1 week= 7 days

= 1 day= 2.4 liters

So= 2.4 × 7 = 16.8

She drinks 16.8 in a week.

To find how much bottles she drank in a week, we must divide the amount of liters she drank in one week to the amount of liters are there in a bottle.

So= 16.8 ÷ 1.4= 12 bottles

Holly drinks 12 bottles in a week.

I hope this helps! I'm sorry if it's wrong and complicated.

Answer:

f

Step-by-step explanation:

find the difference using the number line 3-1

Given :-

To Find :-

Solution :-

According to Question ,

When y = 14 and x = 4 ,

When x = 9 ,

Answer:

3 is the answer

Step-by-step explanation:

Answer:

96,470,000

Step-by-step explanation:

10^7=10,000,000

10,000,000 * 9.647= 96,470,000

Hope this helps!

Answer:

7×=5 ×=5/7

Step-by-step explanation:

Answer:

14kilometers

Step-by-step explanation:

diameter=2*radius.

Answer:

1. coefficient

2. variable

3. constant

Step-by-step explanation: