Rita is designing a building shaped like a pyramid that's cut off in a plane parallel to its base (this is called a truncated pyramid). The building has a 64×64 m end text square base and is 36 m tall. The cut off section has a16×16m square base and is 12 m tall. What is the volume of the building? Round to the nearest cubic meter.

The area of the surface obtained by rotating the curve of parametric equations x=6t−63t3, y=6t2, 0≤t≤1 about the x-axis is approximately 223.3 square units.

To find the area of the surface obtained by rotating the curve of parametric equations x=6t−63t3, y=6t2, 0≤t≤1 about the x-axis, we can use the formula for the surface area of revolution:
S = 2π ∫ a^b y √(1+(dy/dx)^2) dx

where a and b are the limits of integration for x, and y and dy/dx are expressed in terms of x.

To start, we need to express y and dy/dx in terms of x. From the given parametric equations, we have:
x = 6t − 6/3 t^3
y = 6t^2

Solving for t in terms of x, we get:
t = (x + 2/3 x^3)/6

Substituting this into the expression for y, we get:
y = 6[(x + 2/3 x^3)/6]^2
y = (x^2 + 4/3 x^4 + 4/9 x^6)

Taking the derivative of y with respect to x, we get:
dy/dx = 2x + 16/3 x^3 + 8/3 x^5

Substituting these expressions for y and dy/dx into the formula for the surface area of revolution, we get:
S = 2π ∫ a^b (x^2 + 4/3 x^4 + 4/9 x^6) √(1 + (2x + 16/3 x^3 + 8/3 x^5)^2) dx

Evaluating this integral using numerical methods or software, we get:
S ≈ 223.3

Therefore, the area of the surface obtained by rotating the curve of parametric equations x=6t−63t3, y=6t2, 0≤t≤1 about the x-axis is approximately 223.3 square units.

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\(-14\)

Given:

\(x^2 -7x -4\) divided by \(x -2\).

Please refer to my Answer from this Questions to know more about the Remainder Theorem:

Let \(P(x) = x^2 -7x -4\) so that when we divide \(P(x)\) by \(x -\blue 2\) the remainder will be \(P(\blue 2)\) according to the Remainder Theorem.

Solving for \(P(2)\):

\(P(\blue 2) = (\blue 2)^2 -7(\blue 2) -4 \\ P(\blue 2) = 4 -7(\blue 2) -4 \\ P(\blue 2) = 4 -14 -4 \\ P(\blue 2) = -14\)

The remainder is \(-14\).

Answer: h ≈ 128.64 centimeters

Step-by-step explanation:

volume = π × radius^2 × height

h ≈ volume / (π × (0.1)^2)

h ≈ 403.5874439 / (π × 0.01)

h ≈ 12,864.1022 cubic centimeters

Answer:

$3

Step-by-step explanation:

cut the price in half because the amount of items was reduced by half

Answer:

three dollars

Step-by-step explanation:

$6 for 4

$x for 2

6=4

x=2

cross multiply

2×6=4×x

12=4x

Divide through by 4

x= 3

Answer:

y = 4, x = 0

y = 1, x = -1

Step-by-step explanation:

\(y = 3 {x}^{2} + 6x + 4\)

\(y = - 3 {x}^{2} + 4\)

\( \: \)

Since both of them are equal to y, we can just equate them and solve.

\( \: \)

\(3 {x}^{2} + 6x + 4 = - 3 {x}^{2} + 4\)

\(3 {x}^{2} + 6x + 4 + 3 {x}^{2} - 4 = 0\)

\(6 {x}^{2} + 6x = 0\)

\(6x(x + 1) = 0\)

\(6x = 0\)

\(x = 0\)

\( \: \)

\(x + 1 = 0\)

\(x = - 1\)

\( \: \)

\(for \: x = 0\)

\(y = 3( {0})^{2} + 6(0) + 4\)

\(y = 4\)

\( \: \)

\(for \: x = - 1\)

\(y = 3( { - 1})^{2} + 6( - 1) + 4\)

\(y = 1\)

\( \: \)

\(values \: of \: x \: and \: y \: for \: the \: system \: of \: equations \: are\)

y = 4, x = 0

y = 1, x = -1

The system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

The first equation given as,

y = 3x² + 6x + 4

The second equation given as,

y = -3x² + 4

Equate the value of y from both equation as,

3x² + 6x + 4=-3x²+4

3x²+3x²+6x+4-4=0

6x²+6x=0

6x(x+1)=0

x=0:x=-1

Put these values of x, in first equation,

y = 3(-1)^2 + 6(-1) + 4

y = 3 - 6 + 4

y=1

Put 0 on the place of x,

y = 3(0)^2 + 6(0) + 4

y = 0 +0+ 4

y=4

Thus, the system of equations has been solved and the solution set of the equation are (-1,1) and (0,4).

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The graph of the function f(x)= x+c/x^2-4has a vertical asymptote at x=2.

To determine the presence of a vertical asymptote in the graph of a function, we need to examine the behavior of the function as it approaches a certain value of x. In this case, we are considering the function f(x)= x+c/x^2-4.

To find the vertical asymptote, we look for values of x that make the denominator of the function equal to zero. In this case, the denominator x^2−4 equals zero when x=2 or x=−2.

However, we are specifically interested in the vertical asymptote, which occurs when the denominator approaches zero but the numerator does not. Since the numerator x+c does not approach zero as x approaches 2, we can conclude that there is a vertical asymptote at x=2.

The vertical asymptote indicates a vertical line on the graph where the function approaches infinity or negative infinity as x gets closer to the asymptote.

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Answer:

\( \sqrt{9 } = 3 \)

Answer:

(25 ÷ 5 ) ÷ 4

Step-by-step explanation:

solve the equation for the variable. Then plug that variable value into the expression and simplify to get the answer.

Answer:

C

Step-by-step explanation:

the quotient of 25 and 5 is 25 ÷ 4 , then multiply this by 4 , so

4 × (25 ÷ 5 ) → C

Answer:

First one, true

Second one, 23/45

Third one, 11/29

Step-by-step explanation:

There's thy answer for thy self t-t

Answer:

1.)true

2.) 23/45

3.)11/29

Step-by-step explanation:

Greater levels of inequality emerged with civilizations than had ever before occurred in human societies is the statement that best reflects inequality in the first civilizations.

What is civilization?

  Civilization is a complex society characterized by urban development, social stratification (with a significant central government that concentrates power), a form of symbolic communication (like writing), and the formation of new social and economic patterns. Civilizations can also refer to the cultural response of a society to a set of conditions. Inequality refers to the degree to which resources, privileges, or desirable outcomes are unevenly distributed in a society. While inequality is observed across all human societies, there is a significant difference in the levels of inequality between societies. So, the answer is, greater levels of inequality emerged with civilizations than had ever before occurred in human societies.

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Each friend of Arya will receive 0.625 cupcakes.

To divide 5 cupcakes equally among 8 friends, we can use simple division. We would divide the total number of cupcakes (5) by the total number of friends (8) to find the number of cupcakes each friend would receive. In this case, 5 divided by 8 is equal to 0.625. This means that each friend will receive 0.625 cupcakes. However, since cupcakes are not divisible it is not possible to divide 5 cupcakes equally among 8 friends. In this case, either Arya will have to make more cupcakes or they will have to decide on a different way to divide the cupcakes.

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You can weigh 4 marbles against each other first, then if none are heavier, weigh 3 of the remaining marbles against each other, and if none of those are heavier, weigh the last two marbles against each other to find the heavier one.

An object's power of attraction toward the Earth is measured by its weight. It is the result of multiplying the object's mass by the acceleration caused by gravity.

A scale or balance is a tool used to determine mass or weight. These are also referred to as weight scales, mass scales, weight balances, and mass balances.

To weigh the 12 marbles and find out the heavier one,

This solution will always work because at each step, you are halving the number of marbles you need to check, so you will always be able to find the heavier marble in 3 weighings or less.

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The probability that at least one ball of each color is chosen is 105/8568.

Given that:-

Number of red balls in the urn = 5

Number of white balls in the urn = 6

Number of blue balls in the urn = 7

We have to find the probability that at least one ball of each color is chosen.

Let us consider the that 1 ball of each color has been chosen.

Hence, we are left with 4 red balls, 5 white balls and 6 blue balls.

Now we have to choose 2 balls from them.

Hence,

Number of ways in which we can choose 2 balls from (4+5+6) that is 15 balls = \(^{15}C_2=105\)

Total number of ways in which we can choose 5 balls from 18 balls =

\(^{18}C_5=8568\)

Hence,

Probability that at least one ball of each color is chosen = 105/8568

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Answer:

3 times.

Step-by-step explanation:

She has 1 1/2 hour to spend in the gym.

1 hr = 60 minutes.
1/2 of an hour= 1/2 * 60= 30 minutes.

In total, she spends 90 minutes in the gym.

If 1/3 of an hour is meant in running, it translates into: 1/3 * 60 = 20 minutes.

If 1/6 of an hour is spent in weight-lifting, it translates into: 1/6 * 60 = 10 minutes.

In total, she spends, 20 minutes + 10 minutes = 30 minutes for both activities.

To obtain the number of times she would perform both activities, we divide the total amount of time spent in the gym by the amount of time spent for both activities.

 90 minutes/30 minutes= 3 times for each cycle.

Answer:

A subject and a predicate

Step-by-step explanation:

Have a good day :)

AB = AD [Given]

BC = CD [Given]

AC = AC [Same line segment]

So, ΔABC ≅ ΔADC [By SSS congruence criteria]

So, ∠ABC = ∠ADC [CPCT (Corresponding parts of congruent triangles)]

Hence, proved.

Answer:

I hope it will help U.

Answer:

C/Point B is between points A and C

Step-by-step explanation:

When graphed, the lines are parellel.

Answer:

If you are asking what the solution to this set of equations is, then they are the same line. They map to the same line.

Step-by-step explanation:

Answer:

if $700 is sales then answer would be $513.50

Step-by-step explanation:

5.5% of 700 = 38.5

475+38.5=513.50

Answer:

The correct answer is D. Enough to feel rested.

The probability of hitting the shaded ring, assuming you hit the board is 25%.

We have,

Shaded region area.

= πr²

= π x 5²

= 25π in²

Now,

Area of the dartboard.

= πr²

= π x 10²

= 100π in²

Now,

The probability of hitting the shaded ring, assuming you hit the board.

= Area of the shaded region / Area of the dartboard

= 25π/100π

= 1/4

Now,

As a percentage.

= 1/4 x 100

= 25%

Thus,

The probability of hitting the shaded ring, assuming you hit the board is 25%.

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Answer:

no

Step-by-step explanation:

3:2 is equal to 18:12 not 17

Step-by-step explanation:

The answer is in the pic above

Answer:

2x²+7x-4

Step-by-step explanation:

(2x-1)(x+4)

=2x(x+4)-1(x+4)

=2x²+8x-x-4

=2x²+7x-4

Answer:

x≥3

Step-by-step explanation:

The graph that represents a system of equations with one solution is given as follows:

On a coordinate plane, 2 lines intersect at 1 point.

Considering the graph containing the equations for the system, the solution of the system of equations is given by the point of intersection of all the equations of the system.

On a graph with one solution, we have two curves that intersect at exactly one point.

In the context of this problem, this graph will be given by the two lines that intersect at exactly one point.

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A linear function would be the  best fit for the data.

A function that would be the best for this data is: D. y = -4/25(x) + 10

The amount of snow that would be on the ground when the temperature reaches 55° is 1.2 inches.

In this scenario, the temperature would be plotted on the x-axis (x-coordinate) of the scatter plot while the snow (inches) would be plotted on the y-axis (y-coordinate) of the scatter plot through the use of Microsoft Excel.

On the Microsoft Excel worksheet, you should right click on any data point on the scatter plot, select format trend line, and then tick the box to display an equation for the line of best fit (trend line) on the scatter plot.

From the scatter plot (see attachment) which models the relationship between the temperature and the snow (inches), an equation for the line of best fit is given by:

y = -0.16x + 10

y = -4/25(x) + 10

When x = 55, the amount of snow is given by;

y = -4/25(55) + 10

y = 1.2 inches.

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I WILL USE THE REASONS CORRESPONDING ANGLES AND ANGLES ON THE STRAIGHT LINE. SINCE THE DIAGRAM LACKS FULL LABELLING THAT MAKES ME UNABLE TO EXPLAIN MORE USING DEMONSTRATION

\(3x - 3 + (4x - 6) = 180 \\ 3x + 4x - 3 - 6 =180 \\ 7x - 9 = 180 \\ 7x = 180 + 9 \\ 7x = 189 \\ \frac{7x}{7} = \frac{189}{7} \\ x = 27\)

ATTACHED IS THE SOLUTION x=27°

Answer:

x = 27

Step-by-step explanation:

3x - 3 and 4x - 6 are same- side exterior angles and sum to 180° , that is

3x - 3 + 4x - 6 = 180

7x - 9 = 180 ( add 9 to both sides )

7x = 189 ( divide both sides by 7 )

x = 27

Answer:

3 is first

4 is second

1 is third

2 is fourth

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it helps keep the insulation in so their feet get cold

Answer:

12×3 = 36

6×2 = 12

36/12 = 3

Step-by-step explanation:

cmiiw

The value of the expression (12t) / (6s) when t= 3 and s=2 is 3.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

We have the expression,

(12t) / (6s)

To find the value of expression:

When t = 3 and s =2.

Substitute the value of t and s to the expression,

(12t) / (6s)

= {12(3)} / {6(2)}

By using the PEMDAS,

first, we solve the parenthesis.

(12t) / (6s)

= {12(3)} / {6(2)}

= (36 / 12)

Now, applying division operation.

= (36 / 12)

= 3

Therefore, the value is 3.

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