Time in Seconds (x) Height in Feet (y)
1
1.7
2.1
2.9
3.3
202
320
390
496
538

The surface area of the solid generated by rotating the curve 2/3 + y^(2/3) = 9 about the y-axis is approximately 272.783 square units.

To find the surface area of the solid generated by rotating the curve 2/3 + y^(2/3) = 9 about the y-axis, we can use the formula:

S = 2π∫a^b y ds

where a and b are the limits of integration, y is the equation of the curve, and ds is an element of arc length given by:

ds = sqrt(1 + (dy/dx)^2) dx

First, we need to solve the equation of the curve for y:

2/3 + y^(2/3) = 9

y^(2/3) = 27 - 2/3

y = (27 - 2/3)^(3/2)

The limits of integration are from y = 0 to y = 27, since the curve lies in the first quadrant and the solid is bounded by the xy-plane and the surface generated by rotating the curve.

Next, we need to find dy/dx:

(2/3 + y^(2/3))' = 0

(2/3)' + (y^(2/3))' = 0

0 + (2/3)(1/3)y^(-1/3) dy/dx = 0

dy/dx = - (2/9)y^(1/3)

Substituting into the formula for ds, we get:

ds = sqrt(1 + (dy/dx)^2) dx

ds = sqrt(1 + (4/81)y^(2/3)) dx

Finally, we can substitute the equation of the curve, ds, and the limits of integration into the formula for surface area to get:

S = 2π∫0^27 y sqrt(1 + (4/81)y^(2/3)) dx

This integral cannot be evaluated analytically, so we need to use numerical methods to approximate the value. We can use Simpson's rule with n = 10 subintervals to get an approximate value of:

S ≈ 2π(43.422) ≈ 272.783 square units

Therefore, the surface area of the solid generated by rotating the curve 2/3 + y^(2/3) = 9 about the y-axis is approximately 272.783 square units.

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The given system of equations, option C. The system has a nontrivial solution.

When given a system of three equations with three unknowns, it is possible to determine if the system has a nontrivial solution by using row operations and Gaussian elimination. Nontrivial solutions are solutions that are not all 0.

In the given system of equations, the left-hand side of each equation consists of 3 variables, 4x₁-6x₂+13x₃, 4x₁-10x₂-x₃, and 8x₁+4x₂+14x₃. By performing row operations on the equations, the augmented matrix can be reduced to the form of the identity matrix.

The first row operation performed is to subtract the first row from the second row, resulting in

=> 4x₁-10x₂-x₃ = -2x₁-2x₂+13x₃.

The second row operation is to subtract twice the first row from the third row, resulting in

=> 8x₁+4x₂+14x₃ = 0.

The third row operation is to divide the second row by -2, resulting in

=> 4x₁-10x₂-x₃ = x₁+x₂-13x₃.

This reduced form of the augmented matrix can then be rearranged to the form of the identity matrix, indicating that the system of equations has a nontrivial solution.

Therefore, the answer to the question is that the system has a nontrivial solution

Hence the option (c) is correct.

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Answer:

I think it's 3 units to the left and 6 units down

Step-by-step explanation:

Hope I helped!

Answer:

218750

Step-by-step explanation:

Divide 70,000,000,000 by 320,000,000.

Answer:

B

Step-by-step explanation:

The correct answer was B) "Wastage of good food is an environmental hazard that needs to be stopped. By using proper measures to stop wastage of good food, we can help save resources and the environment."

If Josie saves dimes and has $15 worth of dimes then Josie has 150 dimes.

A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.

Since a dime is worth $0.10, we can find the number of dimes Josie

Divide the total value of her dimes by the value of one dime:

Number of dimes = Total value of dimes / Value of one dime

Number of dimes = $15 / $0.10

When fifteen is divided by zero point one we get one hundred fifty

Number of dimes = 150

Therefore, if Josie saves dimes and has $15 worth of dimes then Josie has 150 dimes.

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Answer:

Step-by-step explanation:

800+20%

20%= (20/100)

800/100=8*20=160

add to original price= 800+160=960

Answer:

x=2 and y=5

Step-by-step explanation:

Steps:

I will solve your system by substitution.

x=y−3;2x+y=9

Step: Solve x = y − 3 for x:

Step: Substitute y − 3 for x in 2x + y = 9:

2x+y=9

2(y−3)+y=9

3y−6=9(Simplify both sides of the equation)

3y−6+6=9+6(Add 6 to both sides)

3y=15

3y/3=15/3  (Divide both sides by 3)

y=5

Step: Substitute 5 for y in x = y − 3 :

x=y−3

x=5−3

x=2(Simplify both sides of the equation)

Answer:

x=2 and y=5

Answer:

x = 2          y = 5

Step-by-step explanation:

Since we know that

x = y - 3

We can insert that into the equation above:

2(y-3) + y = 9

After having this equation, we can start by multiplying the numbers/variables in the parenthesis by 2.

2y - 6 + y = 9

Then add the common multiples (2y and y)

That makes:

3y - 6 = 9

We need to get 3y on a side by itself, so to do this, we can add 6 to (-6) and (9)

That makes:

3y = 15

Divide the 3 by 3 and 15 to get the y on its own:

y = 5

Now we need to find x, and to do this we can insert y into the equation:

2x + 5 = 9

Now subtract the 5 from the (5) and (9) and you'll get

2x = 4

Then you divide the 2 on both sides and get

x = 2

You can check your work by inserting x and y into the equation

2(2) + 4 = 9  

Sorry for this super long explanation, and hope this helps

Answer:

2.5782963e+29

Step-by-step explanation:

basically 19 times itself 63 times

Answer:

19^63  ,  3.6431483821774E+80

Step-by-step explanation:

Answer:

white sold = 16

yellow sold = 12

Step-by-step explanation:

w = # of white sold

y = # of yellow sold

w + y = 28   solve this for w

w = 28 - y

9.95w + 13.5y = 321.20     substitute w = 28-y into this expression and solve for y

9.95(28-y) + 13.5y = 321.20

278.60 - 9.95y + 13.50y = 321.20

278.60 + 3.55y = 321.20

3.55y = 321.20 - 278.60 = 42.60

y = 42.60/3.55 = 12   substitute this into w = 28 - y and solve for w

w = 28 - 12 = 16

When a\(_{n}\) = \(2^{n}\)+ n,  a₀ = 1,  a₁ = 3,  a₂ = 6, and a₃ = 11  

When a\(_{n}\) = n^(n+1)!,  a₀ = 0,  a₁ = 2,  a₂ = 2⁶, and a₃ = 3²⁴  

When a\(_{n}\) =  [n/2], a₀ = 0,  a₁ = 1/2,  a₂ = 1, and a₃ = 3/2      

When a\(_{n}\) = [n/2] + [n/2], a₀ = 0,  a₁ = 1,  a₂ = 2, and a₃ = 3/2  

Number sequence

A number sequence is a progression or a list of numbers that are directed by a pattern or rule.

Here,

a₀, a₁, a₂, and a₃ are terms of a sequence

from option a, a\(_{n}\) = \(2^{n}\)+ n

⇒ a₀  = 2⁰+ 0 = 1+0 = 1

⇒ a₁  = 2¹+ 1 = 2+1 = 3

⇒ a₂, = 2²+ 2 = 4+2 = 6

⇒ a₃  = 2³+ 3 = 8 +3 = 11  

from option b, a\(_{n}\) = n^(n+1)!

⇒ a₀  = 0^(0+1)! = 0

⇒ a₁  = 1^(1+1)! = 2² = 2

⇒ a₂, = 2^(2+1)! = 2^(3)! = 2⁶          [ ∵ 3! = 6 ]

⇒ a₃  = 3^(3+1)! = 3^(4)! = 3²⁴         [ ∵ 4! = 24 ]

from option c, a\(_{n}\) =  [n/2]          

⇒ a₀  = [0/2] = 0

⇒ a₁  = [1/2] = 1/2

⇒ a₂, = [2/2] = 1

⇒ a₃  = [3/2] =  3/2  

from option d, a\(_{n}\) = [n/2] + [n/2]

⇒ a₀  =  [0/2] + [0/2] = 0

⇒ a₁  =  [1/2] + [1/2] = 1/2 + 1/2 = 1

⇒ a₂, = [2/2] + [2/2] = 1 + 1 = 2

⇒ a₃  =  [3/2] + [3/2] = 6/4 = 3/2

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The Complete Question is -

What are the terms a₀, a₁, a₂, and a₃ of the sequence {a\(_{n}\)}, where a\(_{n}\) is where a\(_{n}\) equals

a. \(2^{n}\) + n                    b. n^(n+1)!

c. [n/2]                      d. [n/2] + [n/2]

If Hank bought a 4 room home for a rental, and he put 20% down on the $300,00. 00 rental unit, the annual depreciation amount would be $8,727.27 .

To determine the depreciation amount, we first need to determine the depreciable basis of the rental property. The depreciable basis is the portion of the property's value that can be depreciated over time.

In this case, Hank put 20% down on a $300,000 rental unit, which means he paid $60,000 as a down payment. Therefore, the depreciable basis of the rental property is the remaining $240,000 ($300,000 - $60,000).

The IRS allows rental property owners to depreciate the depreciable basis of their property over 27.5 years using the straight-line method. To calculate the annual depreciation amount, we divide the depreciable basis by the number of years of useful life.

So, in this case, the annual depreciation amount would be $8,727.27 ($240,000 / 27.5). This means that Hank would be able to deduct $8,727.27 from his rental income each year for 27.5 years to account for the wear and tear of the property.

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According to the Pythagoras theorem, the value of the slope of the ramp is 10.44

Pythagoras theorem

Pythagoras theorem states that the sum of squares of the sides equal to the square of the hypotenuse.

The general form of the Pythagoras theorem is,

c² =  a² + b²

where

c refers the hypotenuse

a and b refers the sides of the triangle.

Given,

Here we have the ramp with the side values 3 and 10.

Now, we have to find the value of the slope.

Let us consider x be the hypotenuse or slope of the ramp.

We know that the Pythagoras theorem states that the square of the hypotenuse is equal to the sum of square of the sides.

So, it can be written based on these,

x² = 3² + 10²

x² = 9 + 100

x² = 109

x = √109

When we simplify this one then we get the value of slope as 10.44.

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As given by the question

There are given that the numbers;

Now,

First make a table of numbers and their frequency.

So,

Now,

From the dot plot of the given numbers and their frequency.

So,

The dot plot of the given number is shown below:

Answer:

y = 5\(\sqrt{6}\)

Step-by-step explanation:

JLT forms the special 90-60-30 right triangle and the side length for the given measure follows as 2a-a\(\sqrt{3}\)-a

since the side length that sees 90 degrees is 10 then x = 5

according to Euclidian theorem :

y^2 = LK*KI (LK = 15 -x, KI = 15)

y^2 = 10*15

y^2 = 150 find the root for both sides

y = 5\(\sqrt{6}\)

We have drawn the number line and included the given points, see attached number line.  

What is the fraction?

A fraction is used to represent the portion/part of the whole thing. It represents the equal parts of the whole. A fraction has two parts, namely the numerator, and denominator. The number on the top is called the numerator, and the number on the bottom is called the denominator.

On the number line above, the decimal values and fractions are labeled as follows:

0.63 is labeled between 0 and 1.

34/100 is labeled at the same point as 0.34, between 0 and 1.

0.02 is labeled between 0 and 1.

7/10 is labeled at the same point as 0.7, between 0 and 1.

Therefore, we have drawn the number line and included the given points, see attached number line.  

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False.  If the sampling distribution for is equal to the true value only 50% of the time, the estimate generated using ELS is not unbiased.

The statement is contradictory.

1. The sampling distribution for is equal to the true value 50% of the time: This means that when you repeatedly sample from the population and estimate using ELS, only 50% of the estimates will equal the true value. In other words, the ELS estimation method is inconsistent because it provides accurate estimates only half of the time.

2. This new estimate of using ELS is unbiased: Unbiasedness refers to the property of an estimation method where, on average, the estimates obtained are equal to the true value. However, if the sampling distribution for is equal to the true value only 50% of the time, it means that the estimates, on average, deviate from the true value. In other words, the ELS estimate is biased because it consistently tends to overestimate or underestimate the true value, resulting in an average deviation from the true value.

In summary, if the sampling distribution for is equal to the true value only 50% of the time, the estimate generated using ELS is not unbiased.

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Answer:

a) 96 /16 = 6

b) 31.25/ ( 2.5)^2= 5

c) V/ pi r^2

According to the California Cigarette & Tobacco Products Tax Law, the average pack of cigarettes purchase in California costs $8.40.

Option A.

The price of a cigarette in California has been on the rise for many years, owing to the state's aggressive anti-tobacco initiatives.

The state of California, like many other US states, has implemented measures aimed at discouraging smoking and the use of tobacco products, including the introduction of high taxes on cigarettes.

The tax imposed on tobacco products is intended to help cover the expenses of treating tobacco-related diseases, which cost the state millions of dollars every year.

The average cost of a pack of cigarettes in California has been steadily increasing over the years.

This can be attributed to a variety of factors, including higher tobacco taxes and anti-smoking legislation, as well as increased public awareness about the dangers of smoking and the impact it can have on one's health and wellbeing.

In conclusion, the average pack of cigarettes purchase in California is $8.40, as mandated by the state's Cigarette & Tobacco Products Tax Law.

This law, along with other anti-smoking initiatives, has been effective in reducing the prevalence of smoking and tobacco use in California over the years.

Option A.

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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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The task requires devising a recursive definition for the set S, which contains all strings from A* in which there is no b before an a.

To create a recursive definition for S, we need to consider two cases: a string that starts with an "a" and a string that starts with a "b." For the first case, we can define the set S recursively as follows:

λ ∈ S (the empty string is in S)

If w ∈ S, then aw ∈ S (concatenating an "a" at the end of a string in S results in a string that is also in S)

If w ∈ S and x ∈ A*, then \(wx\) ∈ S (concatenating any string in A* to a string in S results in a string that is also in S)

For the second case, we only need to consider the empty string because any string starting with a "b" cannot be in S. Thus, we can define S recursively as follows:

λ ∈ S

If w ∈ S and x ∈ A*, then xw ∈ S

These two cases cover all possible strings in S, as they either start with an "a" or are the empty string. By using recursive rules to concatenate characters at the beginning or end of strings in S, we can generate all valid strings in the set without generating any invalid strings that contain a "b" before an "a."

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Answer:

90

Step-by-step explanation:

Answer:

1738 kilometers

Step-by-step explanation:

(a)The amount of water in the tank is increasing.

(b)Evaluate  \(\int\limits^{18}_0(W(t) - R(t)) dt\) to get the number of gallons of water in the tank at t = 18.

(c)Solve part (b) to get the absolute minimum from the critical points.

(d)The equation can be set up as   \(\int\limits^k_{18}-R(t) dt = 1200\) and solve this equation to find the value of k.

What is the absolute value of a number?

The absolute value of a number is its distance from zero on the number line. It represents the magnitude or size of a real number without considering its sign.

To solve the given problems, we need to integrate the given rates of water flow to determine the amount of water in the tank at various times. Let's go through each part step by step:

a)To determine if the amount of water in the tank is increasing at time t = 15, we need to compare the rate of water being pumped in with the rate of water being removed.

At t = 15, the rate of water being pumped in is given by \(W(t) = 95Vt sin^2(\frac{t}{6})\) gallons per hour. The rate of water being removed is \(R(t) = 275 sin^2(\frac{1}{3})\) gallons per hour.

Evaluate both rates at t = 15 and compare them. If the rate of water being pumped in is greater than the rate of water being removed, then the amount of water in the tank is increasing. Otherwise, it is decreasing.

b) To find the number of gallons of water in the tank at time t = 18, we need to integrate the net rate of water flow from t = 0 to t = 18. The net rate of water flow is given by the difference between the rate of water being pumped in and the rate of water being removed. So the integral to find the total amount of water in the tank at t = 18 is:

\(\int\limits^{18}_0(W(t) - R(t)) dt\)

Evaluate this integral to get the number of gallons of water in the tank at t = 18.

c)To find the time t when the amount of water in the tank is at an absolute minimum, we need to find the minimum of the function that represents the total amount of water in the tank. The total amount of water in the tank is obtained by integrating the net rate of water flow over the interval [0, 18] as mentioned in part b. Find the critical points and determine the absolute minimum from those points.

d. For t > 18, no water is pumped into the tank, but water continues to be removed at the rate R(t) until the tank becomes empty. To find the value of k, we need to set up an equation involving an integral expression that represents the remaining water in the tank after time t = 18. This equation will represent the condition for the tank to become empty.

The equation can be set up as:

\(\int\limits^k_{18}-R(t) dt = 1200\)

Here, k represents the time at which the tank becomes empty, and the integral represents the cumulative removal of water from t = 18 to t = k. Solve this equation to find the value of k.

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The solution to the equation in the given interval is θ = 0.To solve the equation cos(1/4)θ = 1 in the interval from 0 to 2π, we can apply inverse trigonometric functions.

First, let's isolate θ:

cos(1/4)θ = 1

Taking the inverse cosine (arccos) of both sides:

arccos(cos(1/4)θ) = arccos(1)

Since cos(θ) is an even function, we have:

1/4θ = 0

Now, solving for θ:

θ = 0

In the given interval from 0 to 2π, the solution to the equation cos(1/4)θ = 1 is θ = 0.

Therefore, the solution to the equation in the given interval is θ = 0.

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Answer:

130 bc its the alternate exterior angle of angle D

Step-by-step explanation:

Answer:

d

Step-by-step explanation:

interior angle for triangle is 180 if you want to find it you have to find interior angle for d and then 180-70-the interior angle for d and then you will get answer for b2 and then 180-b2 and you will get 120

Taking an online course in subjects like math offers several advantages, such as flexibility and convenience. However, there are also tradeoffs and challenges associated with online math courses.

One tradeoff is the lack of immediate face-to-face interaction with instructors and peers. In a traditional classroom setting, students can ask questions and receive immediate feedback. In an online course, communication may be asynchronous, leading to potential delays in getting clarifications or resolving doubts.

Another challenge is the need for self-discipline and motivation. Without the structure of regular in-person classes, students must manage their time effectively, stay motivated, and be proactive in their learning. Online courses require self-direction and independent study skills.

To overcome these challenges, various tools and strategies can be helpful. Online math courses often provide discussion forums, email communication, or virtual office hours with instructors for student-teacher interaction. Additionally, online platforms may offer multimedia resources, video tutorials, and interactive simulations to enhance understanding and engagement.

Students can also form virtual study groups or join online math communities to connect with peers and collaborate on problem-solving. Personal organization tools, such as calendars and task management apps, can assist in staying on track with assignments and deadlines.

Ultimately, success in an online math course requires self-motivation, effective time management, active participation, and utilizing available resources and support systems.

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Answer:

Chamoy

Step-by-step explanation:

585/9= 65

605/11= 55

Answer: A line segment is a part of a line. It has 2 endpoints.

Step-by-step explanation:

Step-by-step explanation: In geometry, a line segment is a segment that's composed of two points, which are called the endpoints, and all the points that are between the endpoints.

So, in order for a figure to be a line segment,

it needs to begin and end at an endpoint.

Take a look at the image provided below.

The slope of a line perpendicular to the line is -4

The equation is x -4y = 28

The equation for the line is

y = mx + c

where m = slope

c = y-intercept

Here the equation is x - 4y = 28

4y = x - 28

y = x/4 - 7

So the slope of this line is 1/4

Now we have to find the slope of the line perpendicular to that line.

We know that,

m1 × m2 = -1

1/4 × m2 = -1

m2 = -4

Therefore the slope of the line perpendicular to the line is -4.

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The complete question is:

Find the slope of a line perpendicular to x-4y=28