The blades of a windmill turn on an axis that is 40 feet from the ground. The blades are 15 feet long and complete 3 rotations every minute. Write a sine model, y = asin(bt) + k, for the height (in feet) of the end of one blade as a function of time t (in seconds). Assume the blade is pointing to the right when t = 0 and that the windmill turns counterclockwise at a constant rate.

a is the .
The vertical shift, k, is the... length of a blade, height of a windmill, or numbers of rotations per minute.
a =
k =

Final answer:

The combined width of the three tables is 14 feet 4 inches, calculated by first converting each table's width to inches, adding them together, and then converting the total back to feet and inches.

Explanation:

To find the combined width of the three tables placed side by side, you need to add the widths together. First, convert all measurements to inches, add them, and then convert back to feet and inches.

Table 1: 2 feet 9 inches = (2 × 12) + 9 = 24 + 9 = 33 inches

Table 2: 4 feet 8 inches = (4 × 12) + 8 = 48 + 8 = 56 inches

Table 3: 6 feet 11 inches = (6 × 12) + 11 = 72 + 11 = 83 inches

Now, add the inches: 33 + 56 + 83 = 172 inches.

To convert 172 inches back to feet and inches, divide by 12 (since there are 12 inches in a foot): 172 ÷ 12 = 14 feet 4 inches (since 172 divided by 12 is 14 with a remainder of 4).

Therefore, the combined width of the tables is 14 feet 4 inches.

I think it's 2(x+3).

Answer: 2(x+3)

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The individual pipes can fill the pool in 4 hours and 12 hours respectively then using both pipes together, it will take 3 hours to fill the pool.

Use the concept of fraction defined as:

A fraction is a part of the whole number and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called a fraction. It can be written in the form of p: q, which is equivalent to p / q.

Give that,

One pipe can fill the pool in 4 hours.

Another pipe can fill the pool in 12 hours.

The first pipe fills the pool in 4 hours,

So its rate is 1/4 of the pool per hour.

Similarly,

The second pipe fills the pool in 12 hours,

So its rate is 1/12 of the pool per hour.

To find the combined rate, when both pipes are used together,

Add their individual rates:

(1/4 + 1/12)  = 3/12 + 1/12 of the pool per hour.

(1/4 + 1/12)  = 1/3 of the pool per hour.

Now, to find the time it takes to fill the pool using both pipes,

Take the reciprocal of the combined rate,

1 / (1/3) = 3 hours.

Hence,

Using both pipes together, it will take 3 hours to fill the pool.

To learn more about fractions defined as:

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Orange juice contains some amount of sugar in it. There is 176 g of sugar present in a 2000 ml bottle of orange juice.

Given:

A 250 ml glass of orange juice contains 22 grams of sugar.

It is required to calculate the amount of sugar present in the 2000 ml bottle of juice.

Now, the amount of sugar present in 1 ml of juice will be,

[tex]\dfrac{22}{250}=\dfrac{11}{125}\rm \; g[/tex]

So, the amount of sugar in 2000 ml of juice will be,

[tex]\dfrac{11}{125}\times 2000=11\times 16\\=176\rm \; g[/tex]

Therefore, there is 176 g of sugar present in a 2000 ml bottle of orange juice.

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Paul must increase the temperature by 216 degrees Fahrenheit to boil his ice and be able to cook his pasta.

Paul needs to raise the temperature of the ice he has from -4 degrees Fahrenheit to the boiling point of water, which is 212 degrees Fahrenheit. To determine how many degrees Paul needs to change the temperature, we subtract the current temperature of the ice from the desired temperature to boil water. Here is the step-by-step calculation: Subtract -4 from 212. The result is that Paul needs to increase the temperature by 216 degrees Fahrenheit for the ice to reach the boiling point and cook his pasta.

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This question is solved using proportions.

Thus, to find the number of boxes, we use a rule of three.

1 box - 12 cookies.

x boxes - 168 cookies.

Applying cross multiplication:

[tex]12x = 168[/tex]

[tex]x = \frac{168}{12}[/tex]

[tex]x = 14[/tex]

Thus, 14 boxes can be packaged.

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Now, we find the amount of money she made.

Thus:

[tex]T = 14 \times 1.2 = 16.8[/tex]

She made $16.8.

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The coordinates of the points of intersections of [tex]l[/tex] and the curve are [tex](x_{1}, y_{1}) = (4,3)[/tex] and [tex](x_{2}, y_{2}) = (1.5, 8)[/tex].

According to the statement, we get the following nonlinear system of equations:

[tex]x\cdot y = 12[/tex] (1)

[tex]2\cdot x + y = 11[/tex] (2)

Now we proceed to solve for each variable by algebraic means. By (1):

[tex]y = \frac{12}{x}[/tex]

Then we apply the formula in (2):

[tex]2\cdot x + \frac{12}{x} = 11[/tex]

[tex]2\cdot x^{2}+12 = 11\cdot x[/tex]

[tex]2\cdot x^{2}-11\cdot x +12 = 0[/tex]

Roots are found by the quadratic formula and (1):

[tex]x_{1} = 4[/tex], [tex]y_{1} = 3[/tex]

[tex]x_{2} = 1.5[/tex], [tex]y_{2} = 8[/tex]

The coordinates of the points of intersections of [tex]l[/tex] and the curve are [tex](x_{1}, y_{1}) = (4,3)[/tex] and [tex](x_{2}, y_{2}) = (1.5, 8)[/tex].

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In 2006, 112.8 million households owned at least one TV set. About 5.8 million households owned 3 or more TV sets in 2006. What percentage of those owning atleast one TV set was this? Round to the nearest integer

5.8 / 112.8 = 0.051418 which is 5.1418 percent, rounds down to 5%.

The simplified form of the expression  [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] is [tex]6\sqrt{120}[/tex] which corresponds to answer choice A.

Given: [tex]2\sqrt{10} \times 3\sqrt{12}[/tex]

To find: simplify

We can break down the expression  [tex]2\sqrt{10} \times 3\sqrt{12}[/tex] and multiply the roots and whole numbers as follows:

[tex]\text{product is} = 2\sqrt{10} \times 3\sqrt{12} \\\text{product is} = 2 \times 3 \times \sqrt{10} \times \sqrt{12}\\\text{product is} = 6 \times \sqrt{120}\\\text{product is} = 6\sqrt{120}[/tex]

The simplified form of the given expression is 6√120, which corresponds to answer choice A.

Answer:

B) 6,700,000,000 people.

Step-by-step explanation:

We have been given that in 2008, there were [tex]6.7\times 10^9[/tex] people living on earth. We are asked to convert our given population in standard notation.

While changing scientific notation to standard notation we just move the decimal as many times as the exponent indicates. We can see that our exponent is 9, so we will move the decimal to 9 places right.

[tex]6.7\times 10^9=6.7\times 1000000000[/tex]

[tex]6.7\times 10^9=6700000000[/tex]

Therefore, there were 6,700,000,000 people living on earth and option B is the correct choice.

Answer:

B.)6,700,000,000

Step-by-step explanation:

SO when you have to transform from the scientific notation into standar notation, you just have to move the decimal point to the right the number of positions that the scientific notation has as the exponent, in this case it is 9, so you move one position the decimal point to the right to make the number 67, and then add 8 zero´s to the right:

6,700,000,000

As you can see you moved the decimal point 9 positions to the right.

So that´s how you can convert scientific notation to standard notation.

Please see attached document for the graphs:

The functions with the given graphs can't be solutions of the differential equation dy dt = et(y − 1)2.

(a) won’t work, since it has negative slope on portions of its solutions. The slope, e t (y − 1)2 , is a nonnegative function.

(b) won’t work, since it has positive slope at y = 1, where the slope must be flat.

Functions with given graphs cannot be solutions to the differential equation dy / dt = e^t(y-1)^2 because their graphs don't satisfy the conditions imposed by the equation, such as non-oscillatory behavior and non-linear variation with time.

The question pertains to why certain functions represented by their graphs cannot be solutions to the differential equation dy / dt = et(y-1)2. The explanation lies in the structure of the given differential equation and the properties of function graphs.

Equation dy / dt = et(y-1)2 is a non-linear first order differential equation. To be a solution to this equation, a function's graph must satisfy certain conditions imposed by the equation. However, if certain function graphs represent an undefined curve or if their graphs demonstrate oscillatory behavior, they do not satisfy these criteria.

For instance, the differential equation demands non-oscillatory behavior as seen in the general solution provided in the reference: Yn(x) = Ce-Bx +De+Bx. This form describes a gradual attenuation of y(x), i.e., it does not oscillate. Similarly, if a graph represents a function that varies non-linearly with time (like In[A] vs. Time), it does not represent a solution to the differential equation as well.

Thus, the inability of certain function graphs to satisfy the conditions required by the given differential equation is the reason they cannot be its solutions.

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Answer:

Lines e and f are parallel since their alternate exterior angles 75 ad 75 are congruent.

Step-by-step explanation:

Parallel lines mean that angle relationships exits where specific angles are congruent to each other. 75 and 75 are in the position of alternate exterior angles for lines e and f. Since they are congruent, these lines must be parallel. However, a and b have same side exterior angles which must add to 180. 75 + 115 does not equal 180. It equals 190. Therefore a and b cannot be parallel.

Answer:

E and F on edgenuidy

Step-by-step explanation:

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