Find the volume of this sphere.
Use 3 for TT.
V ≈ [?]ft³ 3
14 ft
V = πr³
Tr3

Answer:

Step-by-step explanation:

This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts.

Using the given table of transforms,

\(L\left\{ y'' - y' - 2y \right\} = L\left\{ 1-x \right\}\)

\((s^2 Y(s) - sy(0) - y'(0)) - (s Y(s) - y(0)) - 2 Y(s) = \dfrac1s - \dfrac1{s^2}\)

(where Y(s) is the Laplace transform of y(x))

Solve for Y(s) :

\((s^2 - s - 2) Y(s) - s = \dfrac1s - \dfrac1{s^2}\)

\((s^2 - s - 2) Y(s) - s = \dfrac{s-1}{s^2}\)

\((s^2 - s - 2) Y(s) = \dfrac{s-1}{s^2} + s\)

\((s^2 - s - 2) Y(s) = \dfrac{s^3 + s - 1}{s^2}\)

\(Y(s) = \dfrac{s^3 + s - 1}{s^2 (s^2 - s - 2)}\)

\(Y(s) = \dfrac{s^3 + s - 1}{s^2 (s + 1) (s - 2)}\)

Decompose the right side into partial fractions:

\(Y(s) = \dfrac as + \dfrac b{s^2} + \dfrac c{s+1} + \dfrac d{s-2}\)

Solve for the coefficients.

\(\implies s^3 + s - 1 = as(s+1)(s-2) + b(s+1)(s-2) + cs^2(s-2) + ds^2(s+1)\)

\(\implies s^3 + s - 1 = -2 b + (-2 a - b) s + (-a + b - 2 c + d) s^2 + (a + c + d) s^3\)

\(\implies \begin{cases}-2b = -1 \\ -2a-b = 1 \\ -a+b-2c+d = 0 \\ a+c+d = 1 \end{cases} \implies a=-\dfrac34, b=\dfrac12, c=1, d=\dfrac34\)

Then

\(Y(s) = -\dfrac34 \times \dfrac1s + \dfrac12 \times \dfrac1{s^2} + \dfrac1{s+1} + \dfrac34 \times\dfrac1{s-2}\)

Take the inverse transform and solve for y(x) :

\(F(s) = \dfrac1s \implies f(x) = 1\)

\(F(s) = \dfrac1{s^2} \implies f(x) = x\)

Using the frequency-shifting property,

\(F(s) = \dfrac1{s+1} \implies f(x) = e^{-x}\)

\(F(s) = \dfrac1{s-2} \implies f(x) = e^{2x}\)

So, the particular solution to the ODE is

\(\boxed{y(x) = -\dfrac34 + \dfrac x2 + e^{-x} + \dfrac{3e^{2x}}4}\)

Answer:

D 0.89275

Step-by-step explanation:

Answer:

When the absolute value of the scale factor is less than one, a compression occurs. When the absolute value of the scale factor is equal to one, neither an expansion nor a compression occurs.

Answer:

A is the answer

Step-by-step explanation:

if its wrong than its C

Answer:

im pretty sure its 0.36

Step-by-step explanation:

The unit rate or cost of one ounce of the drink is $0.36.

Given that:

A 6-ounce drink costs $2.16.

It is required to find the unit rate.

Now, the unit rate can be defined as the quantity of something with respect to another quantity.

Here, the unit rate is the cost of the drink per ounce of the drink.

Cost of 6-ounce drink = $2.16

Let the cost of one ounce drink = x

Here, the proportional concept can be used.

6 / 2.16 = 1 / x

Cross multiply.

6x = 2.16

Divide both sides by 6.

x = 0.36

Hence the unit cost is $0.36.

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We substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

The given system of equations are 2x-1/3y = -2...(1)

3x+y=1...(2)

We solve this system of equations by using substitution method.

Let us solve for x in equation to substitute it in equation (2).

2x=-2+1/3y

Divide both sides of equation by 2.

x=-1+1/6y

Now plug in the value of x in equation 2.

Hence, we substitute -1+1/6y for x in the second equation (bottom equation) in order to solve the system by the substitution method.

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Answer:

g(1) = 1

Step-by-step explanation:

the absolute value function always gives a positive result, that is

| - a | = | a | = a

to evaluate g(1) substitute x = 1 into g(x)

g(1) = - 3| 1 - 2| + 4

    = - 3| - 1| + 4

   = - 3(1) + 4

  = - 3 + 4

  = 1

Teacher: In all your subjects I am giving you D's.

Student: Well I am also going to be giving you D's.

Teacher: What do you mean?

Student: Deeez nuts!

Answer:

2/3

Step-by-step explanation:

2-2/3=4/3

1/3+1/3=2/3, 1/3+1/3+1/3+1/3=4/3

4/3 is double 2/3

4/3 is spent on math, and 2/3 is spent on english

Answer:

vp=1186380cm^3

Step-by-step explanation:

Answer:

Step-by-step explanation: hi it’

Perimeter of a triangle = Length of the first side + Length of the second side + Length of the third side

( 14x – 4 ) = (3x-2) + ( 5x +3) + Length of the third side

14x – 4 = ( 8x +1 ) +Length of the third side

(14x-4) + (-8x-1) =Length of the third side

6x - 5 = Length of the third side

So; The length of the third side = 6x – 5

I hope I helped you^_^

Answer:

6x-5

Step-by-step explanation:

A triangle has 3 sides; the perimeter= a+b+c

P= 14x-4

a= 3x-2

b= 5x+3

c=?

14x-4 = (3x-2) + (5x+3) + c

14x-4= 3x-2+5x+3+c

Put alike terms together

14x-4= 3x+5x-2+3+c

14x-4= 8x+1+c

Make c the subject of the formula

c= 14x-4-8x-1

c= 14x-8x-4-1

c= 6x-5

Answer:

volume of a cylindrical water tank = 70,650cm³

Step-by-step explanation:

volume of cylinder, V = πr²h

where π = 3.14

h = 100cm

r = ?

given is diameter = 30cm

r = d/2 = 30/2 = 15cm

substituting the values in the formula,

V = 3.14 * 15² * 100

= 3.14 * 225 * 100

= 70,650cm³                        

Answer:

How much space it would take up: 706.86 square centimeters of floor space and extend vertically to a height of 100 cm

Volume: 706,500 cm³

Step-by-step explanation:

How much space it would take up:

To determine the space occupied by a cylindrical water tank in a room, we need to consider its dimensions and the area it covers on the floor.

The diameter of the tank is given as 30 cm, which means the radius is half of that, 15 cm.

To calculate the space it occupies on the floor, we need to find the area of the circular base. The formula for the area of a circle is A = πr², where A is the area and r is the radius.

A = π(15 cm)²

A = π(225 cm²)

A ≈ 706.86 cm²

So, the circular base of the tank occupies approximately 706.86 square centimeters of floor space.

The height of the tank is given as 100 cm, which represents the vertical space it occupies in the room.

Therefore, the cylindrical water tank would take up 706.86 square centimeters of floor space and extend vertically to a height of 100 cm in the room.

Volume:

To calculate the volume of a cylindrical water tank, we can use the formula V = πr²h, where V is the volume, r is the radius, and h is the height.

First, we need to find the radius by dividing the diameter by 2:

Radius = 30 cm / 2 = 15 cm

Now we can calculate the volume:

V = π(15 cm)²(100 cm)

V = 3.14 * 225 cm² * 100 cm

V = 706,500 cm³

Therefore, the cylindrical water tank will occupy a volume of 706,500 cm³ or 706.5 liters.

Answer:

\( x = 10.4 \)

Step-by-step explanation:

Since ∆ABD is similar to ∆CBE, therefore, the ratio of their corresponding side lengths would be equal to each other. Thus:

\( \frac{BD}{BE} = \frac{AD}{CE} \)

BD = 12 cm

BE = x

AD = 27 cm

CE = 23.4 cm

Plug in the values

\( \frac{12}{x} = \frac{27}{23.4} \)

Cross multiply

\( x \times 27 = 23.4 \times 12 \)

\( 27x = 280.8 \)

Divide both sides by 27

\( x = 10.4 \)

Answer:1.325

Step-by-step explanation:

Answer:

13.27 cm

Step-by-step explanation:

I am using (xy) to mean the length of the side xy

7^2 + (xy)^2 = 15^2

49 + (xy)^2 = 225

(xy)^2 = 225-49

(xy)^2 = 176

Side (xy) = sqrt(176) = 13.2664991614 = 13.27 cm

Answer:

4

Step-by-step explanation:

(x - h)² + (x - k)² = r²

r is the radius of the circle. We are given r as 16. So,

r² = 16

√r² = √16

r = 4

And we have our final answer!

Answer:

4

Step-by-step explanation:

(x - h)² + (x - k)² = r²

r is the radius of the circle. We are given r as 16. So,

r² = 16

√r² = √16

r = 4

This is the final answer!

Answer:

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

Given function:

Graph it first (see attached).

Test the graph for symmetry.

We know the odd degree parent function y = x³ has an origin symmetry, whilst even degree functions may have axis symmetry.

The given function is a translation of cubic function 5 units up so the center of symmetry has translated as well. Therefore correct answer is 4.

Answer:

4. no origin symmetry

Step-by-step explanation:

Functions are symmetric with respect to the x-axis if for every point (a, b) on the graph, there is also a point (a, −b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the y's with (−y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the x-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y &= x^3 + 5\\&\textsf{Replace $y$ for $(-y)$}: \quad &-y &= x^3 + 5\\&\textsf{Simplify}: \quad &y &= -x^3 - 5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the x-axis.

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

Functions are symmetric with respect to the y-axis if for every point (a, b) on the graph, there is also a point (-a, b) on the graph:

To determine if a graph is symmetric with respect to the x-axis, replace all the x's with (−x).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the y-axis.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$}: \quad &y&=(-x)^3+5\\&\textsf{Simplify}: \quad &y&=-x^3+5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the y-axis.

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

Functions are symmetric with respect to the origin if for every point (a, b) on the graph, there is also a point (-a, -b) on the graph:

To determine if a graph is symmetric with respect to the origin, replace all the x's with (−x) and all the y's with (-y).  If the resultant expression is equivalent to the original expression, the graph is symmetric with respect to the origin.

\(\begin{aligned}&\textsf{Given}: \quad &y&=x^3+5\\&\textsf{Replace $x$ for $(-x)$ and $y$ for $(-y)$}: \quad &(-y)&=(-x)^3+5\\&\textsf{Simplify}: \quad &-y&=-x^3+5\\&&y&=x^3-5\end{aligned}\)

Therefore, since the resultant expression is not equivalent to the original expression, it is not symmetric with respect to the origin.

Answer: See below

Step-by-step explanation:

For the line on top, we know the slope is negative because it is going down. We can find the slope by counting how much the point goes down and to the right. Y-intercept is the point on the y-axis.

slope: -3

y-intercept: 2

Now that we have the slope and y-intercept, we know the equation is y=-3x+2.

For the second line, we know the slope is positive because it is going up. Since slope is rise/run, we can see it rises 1 unit and runs to the right by 2 units. Y-intercept is the point on the y-axis.

slope: 1/2

y-intercept: -5

With our slope and y-intercept, we know our equation.

y=1/2x-5

When the sample contains proportions of items/events/people that are different from those of the population. When surveying the entire population is time-consuming.

In statistics, the term "sampling" refers to the act of choosing a portion of people or observations from a larger population in order to infer or derive information about the population as a whole. To create a representative sample that properly represents the features and distribution of the population is the aim of sampling.

The results of the research can be biased when the sample comprises proportions of things, events, or individuals that are different from those of the population, making the conclusions less trustworthy and accurate.

It might not be viable or practical to survey the entire population if it takes too much time, in which case a sample could be required.

Hence, the correct answer are: When the sample contains proportions of items/events/people that are different from those of the population.

When surveying the entire population is time-consuming.

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Answer:

*When the population is small.(A)

*When the sample contains proportions of items//events/people that are different from those of the population. (C)

Step-by-step explanation:

I took the Unit Test.

Answer:s

Step-by-step explanation:

i can see you

Answer:

2240 liters

Step-by-step explanation:

448 multplied by 5 is equal to 2240 liters.

8 multplied by 5 is 40.

40 multplied by 5 is 200.

400 multplied by 5 is 2000.

2000 + 200 + 40 = 2240.

Answer:

1.3859

Step-by-step explanation:

The formula for Margin of Error is given as:

Margin of Error = Critical value × Standard Error

Critical value = z score

In the question, we are given a confidence interval of 95%.

Z score for a 95% confidence level is given as: 1.96

Hence, critical value = 1.96

Standard Error = σ / √n

Where n = number of samples = 98 chicken eggs

σ = Standard deviation = 7 milligrams

Standard Error = 7/√98

Standard Error = 0.7071067812

Hence, Margin of Error = Critical value × Standard Error

Margin of Error = 1.96 × 0.7071067812

Margin of Error = 1.3859292911

Therefore, the margin of error corresponding to a 95% confidence interval for the true mean cholesterol content, μ, of all such eggs is approximately 1.3859

Answer:

Option D.

Step-by-step explanation:

Domain and range of inverse function:

The domain of the inverse function(x values) is the range(y values) of the original function.

The range of the interse function(y values) is the domain of the original function(x values).

Original function:

Domain: \(x \geq 0\)

Range: \(y \leq -1\)

Inverse function:

x values in the domain of the inverse function are the y values in the range of the original function. So

Domain: \(x \leq 1\)

Same for range(exchange of y and x).

Range: \(y \geq 0\)

The answer is given by option D.

The angles that are 118 degrees are ∠1 , ∠3, ∠5 and ∠7.

When parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, vertically opposite angles etc.

Therefore, let's find the angle relationship in the line and find the angles that are 118 degrees.

Hence,

∠3 = 180 - 62 = 118 degrees(angles on a straight line)

∠1 ≅ ∠3 (vertically opposite angles)

∠7 ≅ ∠3 (alternate interior angles)

∠5 ≅ ∠7 (vertically opposite angles)

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The graph of g(x) is obtained from the graph of f(x) by the following transformations:

- A horizontal stretch by a factor of 9. This is because the graph of g(x) is 9 times wider than the graph of f(x).

- A vertical translation down by 2 units. This is because the graph of g(x) is 2 units lower than the graph of f(x).

In other words, to obtain the graph of g(x) from the graph of f(x), we stretch the graph horizontally by a factor of 9 and then translate it down by 2 units.

Here is a more detailed explanation of the transformations:

- Horizontal stretch by a factor of 9: To stretch the graph horizontally by a factor of 9, we multiply all of the x-coordinates by 9. This means that every point on the graph of f(x) will be moved 9 units to the right on the graph of g(x).

- Vertical translation down by 2 units: To translate the graph down by 2 units, we subtract 2 from all of the y-coordinates. This means that every point on the graph of f(x) will be moved 2 units down on the graph of g(x).

Given:

In a triangle, a segment connecting the midpoints of two sides of the triangle

Required:

We need to find the name of that segment

Explanation:

Here E is the midpoint of AB

D is the midpoint of AC

Final answer:

ED is called midsegment

2 by 7 + – is equals to 1 so we can say that x.

x=1-2/7

x=7/7-2/7

x=5/7

-10 + 5.47722~
=4.523~
round to nearest tenth = 4.5

Answer:

-4.5

Step-by-step explanation:

\(\sqrt{30}\) is approximately 5.47722557505.  You can find this number with a calculator.

-10 + 5.47722557505 = -4.52277442495

To add a negative and a positive number, you subtract the absolute values and take the sign of the number that has the larger absolute value.  Absolute value just means thinking of both numbers as positive numbers.

Helping in the name of Jesus.