Marcus has a square shaped garden that has an area of 4(x^2-y^2) square feet. If the garden has four equal sections, what is the area of each section?

The solution of the given initial value problem, x'' + 33.64x = 4cos(6t), with x(0) = x'(0) = 0, can be expressed as a sum of the homogeneous solution and the particular solution.

To find the solution, we start by solving the homogeneous equation, x'' + 33.64x = 0. The characteristic equation associated with this homogeneous equation is \(r^2 + 33.64 = 0\), which yields the roots

r = ±i√33.64. Thus, the homogeneous solution can be expressed as

x_h(t) = A*cos(√33.64*t) + B*sin(√33.64*t),

where A and B are constants determined by the initial conditions.

Next, we need to find the particular solution for the forced oscillation. Since the right-hand side of the equation is of the form Acos(ωt), where ω = 6, we assume a particular solution of the form x_p(t) = C*cos(ω*t + φ), where C and φ are constants to be determined. Taking the derivatives, we have x_p''(t) = -ω^2*C*cos(ω*t + φ) and x_p'(t) = -ω*C*sin(ω*t + φ). Substituting these into the original equation, we obtain -ω^2*C*cos(ω*t + φ) + 33.64*C*cos(ω*t + φ) = 4*cos(ω*t).

To satisfy this equation, the coefficient of the cosine term must be 4, while the coefficient of the sine term must be zero. This gives us two equations: -ω^2*C + 33.64*C = 4 and -ω*C = 0. Solving these equations, we find C = 4/(33.64 - ω^2) and φ = 0. Therefore, the particular solution is x_p(t) = (4/(33.64 - ω^2))*cos(ω*t).

Finally, we combine the homogeneous solution and the particular solution to obtain the complete solution:

x(t) = x_h(t) + x_p(t) = A*cos(√33.64*t) + B*sin(√33.64*t) + (4/(33.64 - ω^2))*cos(ω*t).

By substituting the initial conditions x(0) = x'(0) = 0 into this equation, we can determine the values of A and B. With the obtained values, the final solution for the initial value problem can be expressed in terms of the given constants and the trigonometric functions involved.

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Based on the information provided regarding same as cash loans, Chelsea won't be charged interest for the first 6 months of the loan, nor will she have to make payments for the first 6 months. (Option D)

A Same-As-Cash Loan refers to a short-term lending solution in which no interest or monthly payment are required to be paid during a set “Same-As-Cash” period. At the end of a predetermined period, the loan is paid off. Hence, the customer owes no interest or monthly payments during a set promotional period and pays the same amount on the loan as they would have paid up front with cash. These are interest deferred loans in which the loans interest still accrues during that promotional period, however if the customer pays off the entire principal balance before the period ends, they are not required to pay that interest. The advantage of these loans is that customers may spend the same amount they would have if they had paid with cash up front. Hence, if Chelsea opts for loan that offered 6 months, same as cash, there would be no requirement of payment or interest charged for the 6 months.

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The domain on which the graph described as in the image is increasing is to be determined; (-4, ∞).

It follows from the task content that the domain for which the function described by the graph is increasing is to be determined.

Since the graph is a quadratic function which opens upward and whose minimum point is at; x = -4.

Also, since a graph of a function, f(x) is increasing when f'(x) > 0.

Therefore, by observation the graph is increasing on the domain defined by; (-4, ∞).

Put simply, the function is increasing in the Domain; x > -4.

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Answer:

Obtuse

Step-by-step explanation:

Since the angle is higher than 90 degrees (which would be labeled as a box in the corner), the angle of A is obtuse

Answer:

obtuse

Step-by-step explanation:

obtuse - larger than a right angle/90°

right angle- would have the box in the inner corner to show its a right angle

acute - smaller than a right angle/90°

Answer:

B

Step-by-step explanation:

The annual rate of return for the investment in the new oil well should approximately be 90.28%

To calculate the annual rate of return for the investment in the new oil well, we need to consider the net cash flows over its useful life. The net cash flow is the difference between the annual revenues and expenses, taking into account the initial cost and salvage value.

The net cash flow for each year is calculated as follows: Net Cash Flow = Annual Revenues - Annual Expenses - Depreciation

Using the given values, we can calculate the net cash flows for each year:

Year 1: $131,925 - $81,000 - $47,400 = $3,525

Year 2-9: $131,925 - $81,000 = $50,925

Year 10: $131,925 - $81,000 + $11,000 = $61,925

Now, we can calculate the total net cash flows over the 10-year period: Total Net Cash Flows = Year 1 + Year 2-9 + Year 10

= $3,525 + ($50,925 * 8) + $61,925

= $427,825

To determine the annual rate of return, we divide the total net cash flows by the initial investment: Annual Rate of Return = (Total Net Cash Flows / Initial Investment) * 100%

= ($427,825 / $474,000) * 100%

= 90.28%

Therefore, the annual rate of return for the investment in the new oil well is approximately 90.28%. This indicates the profitability of the investment over its useful life.

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Answer:

Sure! Let’s solve this equation step by step.

(7000).03 + (x).05=830

First, we can simplify the left side of the equation:

210 + 0.05x = 830

Next, we can subtract 210 from both sides:

0.05x = 620

Finally, we can divide both sides by 0.05 to solve for x:

x = 12400

So the solution to the equation (7000).03 + (x).05=830 is x = 12400.

Opciones:

A) (-8, -7)

B) (0, 1)

C) (0, 2)

D) (3, 4)

Responder:

(0, 2)

Explicación paso a paso:

Dado :

y = (x + 1)

Para probar qué puntos no pertenecen; aplicamos la ecuación a las opciones dadas para ver cuál de las opciones no se ajusta a la ecuación:

(x = -8, y = - 7)

y = (x + 1)

y = - 8 + 1

y = - 7

(x = 0, y = 1)

y = 0 + 1

y = 1

(x = 0, y = 2)

y = 0 + 1

y = 1

El punto (0, 2) no pertenece

(x = 3, y = 4)

y = 3 + 1

y = 4

The points (0,2) do not belong to the given equation y = x + 1.

A linear equation is an equation in which the highest power of the variable is always 1. The standard form of a linear equation in one variable is of the form Ax + B = 0.

The given equation is y = x + 1

To prove which points do not satisfy the given equation, we apply the given option to the equation.

1. (x = -8, y = - 7)

y = (x + 1)

y = - 8 + 1

y = - 7

Hence, The given points belong to the equation.

2. (x = 0, y = 1)

y = 0 + 1

y = 1

Hence, The given points belong to the equation.

3. (x = 0, y = 2)

y = 0 + 1

y = 1

Hence, The given points don't belong to the equation.

4. (x = 3, y = 4)

y = 3 + 1

y = 4

Hence, The given points belong to the equation.

Therefore, option 3 is correct in that point(0,2) does not belong to the given equation.

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Answer:

134 :)

Step-by-step explanation:

\(\:\: \:\: \:\star\) We are asked to find out the distance between (1,5) and (-6,-2).We know the formula to find the distance between two points is given by -

\( \:\: \star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\\)

As per question, points are -

Now that we are given the points, so we can put them into the formula and solve for distance between them.Which is -

\(\:\: \:\: \:\star \underline{ \sf{ Distance = \sqrt{ (y_2 -y_1)^2 + (x_2-x_1)^2}}}\\\)

\( \longrightarrow \sf Distance_{(AB)} = \sqrt{ (-2-5)^2 + (-6-1)^2 }\\\)

\(\:\:\:\:\:\longrightarrow \sf Distance_{(AB)}= \sqrt{ (-7)^2 + (-7)^2 }\\\)

\(\:\:\:\:\longrightarrow \sf Distance_{(AB)} = \sqrt{ 49+49 }\\\)

\(\: \:\:\:\: \:\longrightarrow \sf Distance _{(AB)}= \sqrt{ 98}\\\)

\(\: \:\:\: \:\longrightarrow \sf Distance_{(AB)} = \sqrt{49 \times 2}\\\)

\(\:\: \:\: \:\:\longrightarrow \sf\underline{ Distance_{(AB)} = 7√2}\\\)

\(\: \:\:\: \:\:\longrightarrow \sf Distance_{(AB) }= 9.89949......\\\)

\(\: \:\:\: \:\:\longrightarrow \sf \underline{Distance_{(AB) }= 9.9\:(Approx)}\\\)

Therefore, the distance between (1,5) and (-6,-2) is 7√2 or, 9.9 ( Approx).

Answer:

The distance between A and B is 2.6

Step-by-step explanation:

We know that there are 2 whole numbers from -1 to 0 and 0 to 1. Then we can add the 0.3 from both sides. 0.3 plus 0.3 is 0.6.

I hope this helped and if it did I would appreciate it if you marked me brainliest, thank you and have a nice

day

Answer:

27 cm or 2in and 6cm!

Step-by-step explanation:

count the lines.

it's easier b or d I'm not sure

Answer:  

It would be D

Step-by-step explanation:

Answer:

13x

Step-by-step explanation:

hope this helps

The probability that a set of twins will be born on feb. 29 is 0.75%.

For the stated question-

Let the probability of having twins is P(A).

There is a 3% risk of having twins.

Thus,

P(A) = 3%

P(A) = 0.03.

Let the probability of coming leap day be P(B).

Leap Day only occurs once every four years.

Thus,

P(B) = 1/4

Thus, the chance that a set of twins will be born on feb. 29

= P(A).P(B)

= 0.03 x 1/4

= 0.0075

= 0.75%

Thus, the probability that a set of twins will be born on feb. 29 is 0.75%.

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Answer:

Step-by-step explanation:

C(x) = x² - 19x + 40 (cost equation)

9850 = x² - 19x + 40 (substitute 9850 for C(x))

Rearranging the equation, we get:

x² - 19x + 9810 = 0

We can use the quadratic formula to solve for x:

x = (-b ± sqrt(b² - 4ac)) / 2a

where a = 1, b = -19, and c = 9810

x = (-(-19) ± sqrt((-19)² - 4(1)(9810))) / 2(1)

x = (19 ± sqrt(19² - 4(1)(9810))) / 2

x = (19 ± sqrt(361 - 39240)) / 2

x = (19 ± sqrt(-38879)) / 2

Since the value under the square root is negative, there are no real solutions for x. This means that it's not possible to manufacture a number of units at a cost of $9850 using this cost equation.

Answer:

90

Step-by-step explanation:

5x10 = 50

18-10 = 8

8 is the height of the triangle

8x5 = 40

40/2 = 20

20+70 = 90

Answer:

who?

Step-by-step explanation:

Answer:

.>.

Step-by-step explanation:

Therefore, the formula for converting 35 liters to milliliters is 35000, with a conversion factor of 1000.

This is further explained below.

Generally,  The amount that is supplied in liters must be multiplied by 1000 in order to be converted to milliliters.

A conversion factor is a number that may be multiplied or divided to shift the units of measurement used for one set to another.

In situations when a conversion is required, the correct conversion factor that results in the same value must be used. For the purpose of converting inches to feet, for instance, the correct value for the conversion is 12 inches equaling 1 foot.

In conclusion, Therefore 35 liters to milliliters is given as 35000, conversion factor of 1000

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Answer:

1000ml and 1 liter

Step-by-step explanation:

Answer:

3/8x + y = 2 1/8

*im not entirely sure but this is what i got*

Step-by-step explanation:

y = -3/8x - 2 1/8

+3/8x     +3/8x

3/8x + y = 2 1/8

*hope this helped! : )*

Answer:

-4<-12

Step-by-step explanation:

Answer:

17/10

Step-by-step explanation:

Answer:17/10 or 1 and 7/10

Step-by-step explanation:

The selling price per kg of the mixed mangoes would be Rs 34.

To determine the selling price per kilogram (kg) when two varieties of mangoes are mixed in a specific ratio, we need to calculate the weighted average of their prices based on the given ratio.Let's assume the selling price per kg of the mixed mangoes is S.

Given that the two varieties are mixed in a ratio of 3:2, we can calculate the weighted average as follows:

(3 * Rs 30 + 2 * Rs 40) / (3 + 2) = (90 + 80) / 5 = Rs 170 / 5 = Rs 34

It's important to note that the selling price per kg is determined by the weighted average of the individual prices, taking into account the proportion or ratio in which they are mixed.

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Professor evaluation in this case is an example of a discrete random variable. A discrete random variable takes on a countable number of distinct values.

In this case, the scores 1, 2, 3, 4, and 5. The variable represents the outcome of a specific event (the evaluation of a professor) and can only assume these specific values. Each score has a certain probability associated with it, reflecting the likelihood of that score being given by the students.

As it is a discrete random variable, there is no intermediate value between the possible scores, and the probability distribution can be represented by a probability mass function.

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Answer:

No, the package will not be labeled "heavy"

Step-by-step explanation:

1) if you multiply 1lb. and 12 oz. by the number of flower pots(I'll be using the variable P), then the expression will be (1lb.P) (12oz.P).

2) then after you get the answer for that, which is 6lb. 72oz. and after that you'll have to add the weight of the packaging, which is 5oz. which the answer is 6lb. 77oz.

3) after, you will then have to get the number of pounds from the ounces if there are more than 16, which there are, so after you get the answer out of that, which is 4 and then you would have 13oz. leftover.

4) you would then have to add your 4lb. to your 6 that you already have, which would be 10lb.

Final) so in the end, you would have 10lb. 13oz.

The expected value of the continuous random variable V is 5. The expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

To calculate the expected value of a continuous random variable V with a given probability density function (PDF), we integrate the product of V and the PDF over its entire range.

The PDF of V is defined as:

f(v) = 6/24 = 0.25 for 3 ≤ v ≤ 7, and 0 otherwise.

The expected value of V, denoted as E(V), can be calculated as:

E(V) = ∫v * f(v) dv

To find the expected value, we integrate v * f(v) over the range where the PDF is non-zero, which is 3 to 7.

E(V) = ∫v * (0.25) dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * ∫v dv, with the limits of integration from 3 to 7.

E(V) = (0.25) * [(v^2) / 2] evaluated from 3 to 7.

E(V) = (0.25) * [(7^2 / 2) - (3^2 / 2)].

E(V) = (0.25) * [(49 / 2) - (9 / 2)].

E(V) = (0.25) * (40 / 2).

E(V) = (0.25) * 20.

E(V) = 5.

Therefore, the expected value of the continuous random variable V is 5.

The expected value represents the average value or mean of the random variable V. It is the weighted average of all possible values of V, with each value weighted by its corresponding probability. In this case, the expected value of V is 5, indicating that, on average, we expect the value of V to be around 5.

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For the transformation at -78 °C, appropriate reagents include lithium aluminum hydride (LiAlH4) and diethyl ether.

At -78 °C, certain chemical reactions require the use of specific reagents to achieve the desired transformation. One commonly used reagent is lithium aluminum hydride (LiAlH4), which acts as a strong reducing agent. It is capable of reducing various functional groups, such as carbonyl compounds, to their corresponding alcohols.

Diethyl ether is typically employed as a solvent to facilitate the reaction and ensure efficient mixing of the reactants. Researchers often utilize this low temperature for reactions involving sensitive or reactive intermediates, as it helps control the reaction and prevent unwanted side reactions.

The use of LiAlH4 and diethyl ether provides a reliable combination for achieving the desired transformation at this temperature, enabling chemists to manipulate and modify compounds in a controlled manner.

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Answer:

-62.8 is the Answer fot the equation, Hope this helped

Answer:

B

Step-by-step explanation:

16 x 3/2 = 24

24 x 3/2 = 36

36 x 3/2 = 54

To evaluate the triple integral of 2x dV over the given region E, we need to integrate over all three variables, x, y, and z. We start by integrating with respect to z since there is no z dependence in the integrand. The limits of integration for z are from 0 to 0, which gives us zero.

Next, we integrate with respect to y. The limits of integration for y are from 0 to 2. For each value of y, x ranges from 0 to 4-y^2. So, the triple integral becomes:
Triple integral of 2x dV = ∫(from 0 to 2)∫(from 0 to 4-y^2)∫(from 0 to 0) 2x dz dx dy
Integrating with respect to z first gives us zero, so we can simplify the expression:
Triple integral of 2x dV = 0
The triple integral evaluates to zero since there is no z dependence in the integrand and the limits of integration for z are both zero. Therefore, the answer is just "0".
In summary, the triple integral of 2x dV over the given region E is zero.

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Answer:

7

Step-by-step explanation:

Criteria:

• same number of books on each shelf

 ⇒find a number that divides 58 and 145

• greatest number of books on each shelf

 ⇒find the greatest number that divides 58 and 145

Find the GCF of 58 and 145.

58 = 2 ⋅ 29

145 = 5 ⋅ 29The GCF of 58 and 145 is 29.

Each shelf will contain 29 books.

There are 203 total books (because 58 + 145 = 203).

Divide 203 by 29 to find the number of shelves there should be.

203 / 29 = 7

Therefore, there will be 7 shelves.