Find h as indicated in the figure.

It is necessary to compute in the volume of the rotated region while taking into account that each cross section piece is raised up by a height of h = 4 - y. Scale the results by 62.4 lb/ft3 as well.

The given parabolic region's volume of revolution about the y-axis is a parabolic cylinder. This solid is revolved, and it has circular disks as its cross section. The differential volume of one such disk situated at a differential height y above the x-axis must be determined. The weight of water in this volume can then be calculated by multiplying this volume by the density of water. The depth of this volume is then determined from the tank's top surface. Determine how much differential work is needed to lift this water layer to the top surface. Integrate this differential work now to calculate the overall effort needed to empty the tank.

Rotating the curve x=3y about the y-axis creates the region. Keep in mind that 62.5 = (125 / 2) As a result, using the disk method,

[tex]\int_{0}^{3} \left(\frac{125}{2} \pi (4-y) (3\sqrt{y})^2\right)\, dy \\ &=\int_{0}^{3} \left(\frac{1125}{2} \pi (4-y) y\right)\, dy &\text[/tex]

Integrate in relation to:

[tex]y\text{]} \\ &=\left(-\frac{1125}{2} \pi \left(\frac{y^3}{3}-2 y^2\right)\right)\bigg|_{0}^{3} \\ &=\frac{10125 \pi }{2} \\ &\approx 16045.7 \end{align*} \)[/tex]

To know more about Integration, refer to this link:

https://brainly.com/question/22008756

#SPJ4

The money will double in value in approximately 11.6 years.

From the question, we have the following parameters that can be used in our computation:

When the money doubles, the amount is

A = 900 * 2

A = 1800

The compound interest formula is given as

A = P(1 + r/n)^nt

Also from the question, we have

n = 12

This is so because the loan is compounded 12 times in a year as a result of being compounded monthly

Solving further, we replace the variables with their values in the above equation

1800 = 900 * (1 + (6%)/12)^(t*12)

Divide both sides by 900

2 = (1 + (6%)/12)^(t*12)

Also, we have

2 = (1.005)^(t*12)

Take the logarithm of both sides

12t = log(2)/log(1.005)

Evaluate the quotients

12t = 139

Divide both sides by 12

t = 11.6

Hence, the number of years is 11.6 years

Read more about compound interest at:

brainly.com/question/2455673

#SPJ1

Answer:

(1,2) and (4,2)

(2,6) and (6,6)

Step-by-step explanation:

(when a line is horizontal the slope is 0)

[tex]slope = \frac{rise}{run} [/tex]

[tex]rise = y1 - y2[/tex]

[tex] = 2 - 2 \\ = 0[/tex]

[tex]run = x2 - x1 \\ = 4 - 1 \\ = 3[/tex]

[tex]slope = \frac{0}{3} \\ = 0[/tex]

second option

[tex]rise = 6 - 6 \\ = 0[/tex]

run=6-2

=4

slope= 0/4

=0

please Heart this....

The one poison dart frog is 1/4 inch longer than the other.

What is Poison dart frog?

A family of frogs known as the Dendrobatidea that are indigenous to tropical Central and South America go by the common name "poison dart frog." These species are nocturnal and frequently have colorful bodies. These aposematic species have a bright coloration that is linked to the species' toxicity.

Given: Mary saw two poison dart frogs.

One was 7/8 inch long and the other was 5/8 inch long.

So, 7/8 - 5/8 = 2/8 = 1/4

Hence, the one poison dart frog is 1/4 inch longer than the other.

To know more about poison dart frog, click on the link

https://brainly.com/question/28695006

#SPJ1

The number of routes that Paula can take using graph theory is; E: 4

We will observe that out of the 12 cities, 6 of them possess 3 edges going in/out of them.

The 6 cities are such that there are 2 at the top, 2 at the bottom, and 1 on each side.

In graph theory terms, we can say that they are of degree 3.

Thus, at least 1 edge connecting to each of these cities cannot therefore be used. Furthermore, the same concept applies to the start and end points, due to the fact that we don't want to return to them.

There are 6 + 2 = 8 vertices that we can tell have 1 unused edge, and then we have 17 - 13 = 4 unused edges to work with due to the fact that we have 17 edges in total, and as such must use exactly 13 of them).

Finally, we notice that at each of the 2 cities marked with an O on a path in the image attached, that there are 2 possibilities such that it's either we continue straight and cross back over that same path later, or we will make a left turn, and then turn rightward when we approach the junction again.

This gives us a total of;

2 * 2 = 4 possible different routes

Read more about Number of routes at; https://brainly.com/question/13209100

#SPJ1

w is less than 75.

What do you mean by algebraic expression?

An expression constructed using integer constants, variables, and algebraic operations is known as an algebraic expression (addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number)

An equation that only uses algebraic expressions is known as an algebraic equation.

Any mathematical operation that involves variables, such as addition, subtraction, multiplication, or division, can have its solutions calculated using algebraic expressions.

Given expression:

[tex]\frac{75}{w}=\frac{150}{100}[/tex]

⇒ w = [tex]\frac{75 \times 100}{150 }[/tex]

⇒ w = 50

Convert the value of w into percentage.

w = 50 × 100 % = 500%

Therefore, w is less than 75.

To learn more about the algebraic expression from the given link.

https://brainly.com/question/4344214

#SPJ4

The amount in his savings after 5 years will be  $1507.5.

We know simple interest (SI) is given by SI = (p×r×t)/100, where

p = principle, r = rate in percentage, and t = time in years.

Given, P = 1500, r = 0.1, t = 5 years.

∴ SI = (1500×0.1×5)/100.

SI = $7.5.

Now, We know Amount = principle + SI.

∴ Amount = 1500 + 7.5 = $1507.5

learn more about simple interests here :

https://brainly.com/question/11564235

#SPJ1

The solution set for the inequality - x < 2 is - x < 2.

What is  inequality?

In mathematics, inequalities specify the connection between two non-equal numbers. Equal does not imply inequality. Typically, we use the "not equal sign ()" to indicate that two values are not equal. But several inequalities are utilized to compare the numbers, whether it is less than or higher than.

An inequality in mathematics depicts the connection between two values in an unbalanced algebraic statement. A sign of inequality can be used to show that one of the two variables is larger than, more than or equal to, less than, or equal to another value.

-x<2

Multiply both sides by -1 (reverse the inequality)

(-x)(-1)>2(-1)

Simplify

x>-2

To learn more about inequality visit:https://brainly.com/question/28823603

#SPJ1

Answer: y = 11x + 31, the y - intercept is 31!

Step-by-step explanation:

The equation that models this situation is y = mx + b

We already have the slope, m, of 11.

since we have 2 coordinates, we can substitute all the known values into the equation.

==> 108 = 11 (7) + b

Multiply.

==> 108 = 77 + b

Take 77 from both sides

==> 108 - 77 = 77 - 77 + b

==> 31 = b

==> This means that the y intercept of this linear function is;

f(x) = 11x + 31

or

y = 11x + 31

Using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.

An operation is a function in mathematics that transforms zero or more input values into a clearly defined output value.

The operation's arity is determined by the number of operands.

Mathematical operations include addition, subtraction, multiplication, division, and finding the root.

So, the total cost of fencing is:

According to the given figure, the total length of fencing will be:

8m + 8m + 6m + 2m + 2m + 6m

32 m

Now, 4% more of the total fence:

4/32 * 100

1.28 m

Now the total fencing length:

32 + 1.28

33.28 m

We know that:
1m = 3.2 ft

33.28m = 109.18 ft

We are given that fencing of 4 feet costs: $27. Then,

109.18/4

27.295 * $27

$736.965

Rounding off: $737 approximately

Therefore, using some mathematical operations, we know that the total cost of the fencing will be $737 approximately.

Know more about mathematical operations here:

https://brainly.com/question/28937023

#SPJ1

Answer:

The above answers are incorrect.

Step-by-step explanation:

If the price of one of the goods decreases, the quantity demanded of that good will increase due to the substitution effect. This means that the consumer will choose to buy more of the cheaper good and less of the more expensive good. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.

In this case, if the price of one of the goods decreases from $10 to $8, the consumer will likely purchase more of that good and less of the other good, which is a substitution effect. The income effect may also come into play, as the consumer now has more disposable income due to the lower price of one of the goods. However, it is not possible to determine the exact quantity of each good that the consumer will purchase without further information.

Therefore, the correct answer is e. The above answers are incorrect.

The given statement is false. If a sample is selected using random sampling methods, the primary reason that the sample mean might be different from the corresponding population mean is not that the sample might be biased.

Because random sampling ensures that results obtained from the sample should approximate what would have been obtained if the entire population had been measured. And the simplest random sample allows all the units in the population to have an equal chance of being selected. In this case, the sample might not be biased.

Random sampling is a part of the sampling technique where each sample has an equal probability of being chosen. A sample chosen randomly is meant to be an unbiased representation of the total population.

Learn more about random sampling at: https://brainly.com/question/29852583

#SPJ4

a) The percentage of buyers that paid between $18,000 and $26,000 is; 95%

b) The middle 99.7% of car costs are between $16000 and $28000

c) The probability a car will cost less than $24,000 is; 68%

d) The probability a car will cost more than $26,000 is; 2.5%

The empirical rule of statistics states that 68% of data will be ± 1 standard deviations from the mean, 95% of data will be ± 2 standard deviations of the mean, and 99.7% of data will be ± 3 standard deviations from the mean.

a) We are given;

Mean; μ = $22000

Standard deviation; σ = $2000

$18,000 and $26,000 are both 2 standard deviations from the mean and so, the percentage of buyers is 95%.

b) Since the middle 99.7% of car costs, this is simply 3 standard deviations from the mean and as such it is between the values;

22000 - 3(2000) = $16000 and 22000 + 3(2000) = $28000

c) $24,000 is 1 standard deviation away from the mean and as such the probability will be 68% from empirical rule.

d) $26000 is 2 standard deviations from the mean and as such probability that a car will cost more than that is;

(100% - 95%)/2 = 5%/2 = 2.5%

Read more about empirical rule at; https://brainly.com/question/10093236

#SPJ1

Answer:

Yes

Step-by-step explanation:

16x^4 x 16x^2= 16x^8

Answer:

1

Step-by-step explanation:

anything to the power of 0 is 1

hopes this helps

The average amount that the roller coaster's height drops over each horizontal foot will be -5 feet.

The four basic mathematical operations are the addition, subtraction, multiplication, and division of two or even more integers. Among them is the examination of integers, particularly the order of actions, which is crucial for all other mathematical topics, including algebra, data organization, and geometry.

As per the given data in the question,

Slope = change in y/change in x

Slope = Δy/Δx

A 20-foot horizontal drop is present on a roller coaster.

So, Δx = 20-foot

The roller coaster is 100 feet tall when it is at the bottom of the drop.

So, Δy = -100 feet.

Now, the average rate of change will be,

= -100/20

= -5/1 = -5

To know more about arithmetic operations:

https://brainly.com/question/13585407

#SPJ1

The coordinates to plot the graph after solving the equation will be 0.33 and 1.2.

In math, graph science is the theory of geometric structures called graphs that are used to represent pairwise different objects. Vertices—also known as nodes or points—that are joined by edges make form a network in this sense.

Undirected graphs, where edges connect two vertices equally, and focused therapy, where edges connect two vertices unevenly, are distinguished.

As per the given expressions to plot, the graph is,

f(x) = 3x - 1 and,  (i)

h(x) = -4x - 5       (ii)

From equation (i),

f(x) = 3x - 1

3x = 1

x = 1/3

x = 0.33

From equation (ii)

h(x) = -4x - 5

-4x = 5

x = -5/4

x = 1.2

To know more about Graph:

https://brainly.com/question/17267403

#SPJ1

Answer:

look below

Step-by-step explanation:

To determine the upper-tail critical value of the test statistic for a chi-square test for independence in a contingency table, you can use a table of critical values for the chi-square distribution or you can use a statistical software package or calculator to compute the critical value.

In each of the following circumstances:

a. a=0.05, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.05.

b. a=0.01, r=5, c=6: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

c. a=0.01, r=5, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 5 degrees of freedom and an alpha level of 0.01.

d. a=0.01, r=3, c=4: The critical value would be the upper-tail critical value of the chi-square distribution with 3 degrees of freedom and an alpha level of 0.01.

e. α=0.01, r=6, c=5: The critical value would be the upper-tail critical value of the chi-square distribution with 6 degrees of freedom and an alpha level of 0.01.

It's important to note that the critical value is dependent on the degrees of freedom and the alpha level, so you will need to use the appropriate values for these parameters in order to determine the correct critical value.

The required equation of conic section that shows eclipse is  [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

An equation is a combination of different variables, in which two mathematical expressions are equal to each other.

Let the standard equation of conic section,

[tex]\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2}=1[/tex]      (1)

From the given diagram,

The center of the eclipse is (2, 4),

Here h = 2, and k = 4

The length of minor axis 2a = 8 ⇒ a = 4

The length of major axis 2b = 12  ⇒ b = 6

Substitute the values of a, b and h, k in equation (1)

[tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex]

The required equation of the given conic section is [tex]\frac{(x-2)^2}{4^2} + \frac{(y-4)^2}{6^2}=1[/tex].

The conic section represents the eclipse.

To know more about Equation on:

https://brainly.com/question/187506

#SPJ1

The distance between the bank and Hiroto's house on the map is 11.5 units.

A coordinate plane is a 2D plane that is formed by the intersection of two perpendicular lines known as the x-axis and y-axis. A coordinate system in geometry is a method for determining the positions of the points by using one or more numbers or coordinates.

The distance between the bank and Hiroto's house will be calculated as,

The coordinates are, B(-8,6) and H(3.5,6).

D=√(3.5-(-8))²+(6-6)²

D = √11.5²

D = 11.5

Therefore, the distance between the bank and Hiroto's house on the map is 11.5 units.

To know more about coordinate geometry follow

https://brainly.com/question/28565198

#SPJ1

The error student made was converting 6.5% to decimal

6.5% = 0.065

0.065 * 525.08 =  $34.13

information from the problem

A student is finding a 6.5% commission on $525.08 worth of sales

The question is a percentage problem, percentage deals with a fraction hundred and used as follows

6.5%

=  6.5 percent

= 6.5 / 100

= 0.065

The factor 0.065 of the commission on $525.08

= 0.065 * 525.08

= $34.13

The commission is $34.13

Learn more about percent here:

https://brainly.com/question/29230566

#SPJ1

Step-by-step explanation:

Set each binomial equal to 0, solve for x.

[tex](x + 5) = 0[/tex]

[tex]x = - 5[/tex]

[tex](x - 2) {}^{2} = 0[/tex]

[tex]x - 2 = 0[/tex]

[tex]x = 2[/tex]

The zeroes are -5, and 2(with a multiplicity of 2)

We have a degree of 3.

[tex](x + 5)(x {}^{2} - 4x + 4)[/tex]

the first term in each binomail when using FOIL, become x^3 since that is the highest degree, 3 is the degree of c.

The inequality that best represents Soro's situation regarding the number of bus rides he can take between now and the end of this month is :

50 - 2.5y ≥ 20.

        = 50 - 2.5y

To learn more about inequalities refer to :

https://brainly.com/question/25275758

#SPJ1

The perimeter of the pattern the same as the area of the pattern is 20 cm.

Perimeter of a square is the total length (distance) of the boundary of a square

In a square all the sides are of equal lengths.

Hence, perimeter of a square = 4l

We know that all the sides of a square are equal.

Perimeter of a Square

Perimeter of the square ABCD

                  = AB + BC + CD + AD

                  = 2 cm + 2 cm + 2 cm + 2 cm

                  = (2 × 4) cm

                 = 8 cm

Perimeter of a square is 4 times of s side.

Perimeter of a square = 4 × length of a side..

1st method:

Perimeter of a square PQRS

                 = side + side + side + side

                 = 5 cm + 5 cm + 5 cm + 5 cm

                = 20 cm:

2nd method

Perimeter of a square = 4 times side

                               = 4 × side

                               = 4 × 5 cm

                               = 20 cm

Therefore, Perimeter of a square = 4 × length of one side.

To learn more about Perimeter of a square visit:

https://brainly.com/question/11495285

#SPJ1

8,9,10 is the value from the given replacement set make-up the solution set for inequality.

In mathematics if a statement of an order relation greater or greatest then or equal to is called inequality. To compute the inequality:

if we replace m with 8 it will be 8+7 which is 15 and less then 18

for 9 its 9+7 which is 16 which is less then 18

and for 10 its 10+7 which is 17 which is less then 18

and for 11 its 11+7 is 18 which is equal to 18 so it would not apply to this equation.

To know more about inequality click-

https://brainly.com/question/19003099

#SPJ1

The proportional relationship of the table are as follows:

Proportional relationships are relationships between two variables where their ratios are equivalent.

A proportional relationship is one in which two quantities vary directly with each other. We say the variable y varies directly as x if:  

y = k x

for some constant k , called the constant of proportionality.

First table

k =hx

10 = 2x

x = 5

Hence,

k = 5h

h = 1 / 5 k

Second table

k = hx

5 = 4x

x = 5 / 4

Hence,

k = 5 / 4 h

Third table

k = hx

5 = 25x

x = 5 / 25

Hence,

k = 1 / 5 h

h = 5k

learn more on proportional relationships here:  https://brainly.com/question/8879344

#SPJ1

That is a geometric progression.

the common ratio is 1/2.(t2÷t1)

nth term= ar^n-1

16×1/2=8

tn=8^n-1

The simplification of the given expression is (x - 1)²/ (x-2)(x+3) which restrictions on the domain of this expression are x ≠ 1, 2, -3.

The expression is given in the question as:

(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)

To simplify the expression (x+3)(x-1)/(x-2) ÷ (x+3)/(x-1), we can start by multiplying the numerator and denominator of the first fraction by the denominator of the second fraction:

(x+3)(x-1)/(x-2) ÷ (x+3)/(x-1)

= (x+3)(x-1) / (x-2) × (x-1) / (x+3)

Then, we can simplify the expression by combining like terms:

= (x - 1)² (x+3)/ (x-2)(x+3)

= (x - 1)²/ (x-2)(x+3)

The restrictions on the domain of this expression are that x cannot be equal to 2 or -3, because these values would make the denominator equal to zero, which is not allowed in a fraction.

Therefore, the domain of the expression is all real numbers except x = 1, x = 2, and x = -3. We can express this as:

Domain: x ∈ R, x ≠ 1, x ≠ 2, x ≠ -3

Learn more about the domain and the range here:

brainly.com/question/21027387

#SPJ1