4.7. Use (4.23) to find the Fourier coefficients for the exponential form for the signals of Figure P4.7. fourier series coefficients formula Ck = 1/T0 ∫ T0 x(T)e^jkw0L dt

The rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

The volume of a sphere is given by the formula V = 4/3πr³, where r is the radius of the sphere. To find the rate at which the volume is changing, we need to take the derivative of this equation with respect to time, using the chain rule.

dV/dt = 4/3π(3r²) dr/dt

We know that the radius of the snowball is decreasing at a constant rate, so we can find the value of dr/dt by using the information given in the problem. The radius is decreasing from 34 cm to 18 cm in 30 minutes, which means that:

dr/dt = (34 - 18) cm / 30 minutes = -0.5333 cm/min

Now that we know the rate at which the radius is changing, we can substitute it into the equation for dV/dt and find the rate at which the volume is changing.

We know that the radius is 6 cm at the instant the volume is changing, so we can substitute that into the equation:

dV/dt = 4/3π(3r²) dr/dt = 4/3(π)(3)(6 cm)²(-0.5333 cm/min) = -241.27 cm³/min

So, the rate at which the volume of the snowball is changing at the instant the radius is 6 cm is -241.27 cm³/min.

Note that the negative sign indicates that the volume is decreasing.

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Answer:

4. f(-2)=g(-2)

Step-by-step explanation:

Both lines intersect at the x-value of -2, thus they have the same y-value.

Length of the shorter diagonal of the parallelogram will be 18.46 feet

Let the Parallelogram ABCD with BD and AC as it’s diagonal

According to the question,

AB = 17 feet

AD = 11 feet

As the opposite sides of a parallelogram are parallel and equal

Therefore, AB = CD = 17 feet

                AD = BC = 11 feet

Also the longer diagonal, BD = 22 feet

In triangle BCD, using cosine formula

\(BD^{2}\) = \(CD^{2}\) + \(BC^{2}\)- 2BC.CD.CosC

\(22^{2}\) = \(17^{2}\) + \(11^{2}\) - 2(11)(17)Cos C

484 = 289 + 121 - 374CosC

-0.197 = Cos C

C = arc Cos(-0.197)

Therefore, C = \(110^{0}\)

Now ∠C + ∠D = \(180^{0}\)

101+  ∠D = 180

∠D = \(79^{0}\)

Now, in triangle ADC

\(AC^{2}\) = \(AD^{2}\) + \(CD^{2}\) - 2AD.CD.CosD

 \(AC^{2}\) = \(11^{2}\) + \(17^{2}\) - 2(11)(17)Cos79

\(AC^{2}\) = 121 + 289 - 374Cos79

\(AC^{2}\) = 410 -364(.19)

\(AC^{2}\) = 340.84

AC = sqrt(340.84)

AC = 18.46

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Answer:

t1/2=1m => 30days

A0=500g =0.5kg

t=8m = 240days

A=?

λ=ln2÷t1/2

λ=0.6931÷30

λ=0.0231033333

A=A0×e^-λ×t

A=0.5×e^-0.0231033333×240

A=1.953125grams

Given:

There are given two suppliers X and Y.

Where,

X offers a mechanic a part of 35% off the retail price of $68.20 and Y offers at 20% over the wholesale cost of $37.50.

Explanation:

To find the best offers, we need to find their percentages one by one.

So,

First, find the offer amount from supplier X.

So,

Then,

Now,

For the Y suppliers:

Then,

So,

The best deal for supplier Y is because they offer $23.87.

Final answer:

Hence, the correct option is B with $23.87

Answer:

x= -2; y= -2

Step-by-step explanation:

The opposite sides of a parallelogram are congruent, and therefore we can make two observations:

9=-9x-9
19=-10y-1

Then we can just solve each of the equations to get x and y:

9 = -9x - 9
+ 9       +9

18=-9x

----------
-9

-2=x

19=-10y-1
+1        +1

20=-10y
------------

-10

-2=y

Answer:

30 quarts

Step-by-step explanation:

4 quarts = 1 gallon

7.5 gallons * 4 quarts/ 1 gallon = 30 quarts

The maximum number of tickets the theater can sell is 39,572.

The maximum number means the greatest amount of something possible.

The theater sale each weekend is 761 tickets.

There are eight weekend days in a month and in case the month starts with a Saturday or a Sunday there can be an additional weekend.

To calculate the maximum number of tickets the theater can sell in 1 year, we can multiply the maximum number of tickets sold per weekend by the number of weekends in a year, which is 52.

So, 761 tickets x 52 weekends = 39,572 tickets

Therefore, the maximum number of tickets the theater can sell in 1 year is 39,572 tickets.

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Given that "a" is an approximate value for a quantity with a true value of "t" and a relative error of "r," we need to prove that "a" can be expressed as "t(1+r)" using the definitions of these terms.

The relative error "r" is defined as the absolute difference between the true value "t" and the approximate value "a," divided by the true value "t." Mathematically, this can be expressed as r = |t - a| / t.

To prove that a = t(1 + r), we start by rearranging the definition of relative error:

r = |t - a| / t

Multiply both sides by t:

rt = |t - a|

Since the absolute value of t - a is equal to a - t (as the true value "t" is assumed to be larger than the approximate value "a"), we can rewrite the equation as:

rt = a - t

Rearranging the equation, we have:

a = t + rt

Factoring out t, we get:

a = t(1 + r)

Thus, we have proven that "a" can be expressed as "t(1 + r)" based on the definitions of "a," "t," and "r." This equation shows the relationship between the approximate value "a," the true value "t," and the relative error "r."

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The volume of the given object would be the addition of the volume of the cone and the volume of the rectangular prism = 3,648 in³.

The volume of cone = v = πr²h/3

where π = 3

r = 8/2 = 4ft

h = 12ft

Volume = 3× 4² × 12/3

= 576/3 = 192ft³

The volume of the rectangular prism = l×w×h

where;

l = 7ft

w = 2ft

h = 8ft

volume = 7×2×8 = 112ft³

Therefore the volume of the object = 192+112 = 304ft³

To convert to inches the following is carried out;

1 ft = 12 inches

304 ft = 304× 12 = 3,648 in³

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The total quantity demanded, q = q1 + q2, should be set such that the total cost is minimized and the price is maximized. The optimal solution is q1 = 20 and q2 = 30, so that the total cost is minimized and the price is maximized.

To maximize the company's profit, we must find the optimal quantity of q1 and q2 that minimizes the total cost and maximizes the price. We start by finding the total quantity demanded, q: q = q1 + q2. We can then use this equation to relate the price, p, and the total quantity, q, by substituting the equation for q into the equation for price: p = 50 - 0.04q. Next, we use the cost functions for each plant to find the total cost: C = C1 + C2. We can then use calculus to find the minimum total cost by taking the partial derivatives of C with respect to q1 and q2 and setting them equal to zero.Finally, we can use the equations for price and total cost together to find the optimal values for q1 and q2 that maximize the company's profit. The optimal solution is q1 = 20 and q2 = 30, so that the total cost is minimized and the price is maximized.

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Answer: 62

Step-by-step explanation: In the red empty spot, the #5 would go there and in the blue spot the #6 would go there. 8x2=16 and 16+16= 32: t=This is for the to rectangle shapes on both sides. Now for the square in the middle, since the red spot is 5 and the blue is 6, 5x6= 30. So, 30+32=62.

Answer:

x = 3

Step-by-step explanation:

The angle measuring 5x and the angle measuring 165° are a linear pair, so they are supplementary. Their measures add to 180°.

5x + 165 = 180

5x = 15

x = 3

64 is the number of bit strings that are of length 7 having at least four 1s. This can be obtained by finding each of the required combination and adding them.  

If length of the string is n, then there are 2ⁿ bit stings of length n.

We apply combination formula for this,

                ⇒    ⁿCr = n!/(n-r)!r!                        

At least four 1s is 4, 5, 6, 7,  

⇒ ⁷C₄ + ⁷C₅ + ⁷C₆ + ⁷C₇ = 35 + 21 + 7 + 1

⇒ ⁷C₄ + ⁷C₅ + ⁷C₆ + ⁷C₇ = 64

Hence 64 is the number of bit strings that are of length 7 having at least four 1s.      

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Answer:

17 lunches

Step-by-step explanation:

False. In statistical process control (SPC), the mean and the standard deviation serve different purposes and are not interchangeable.

The mean, often denoted as μ, represents the central tendency or average of a set of data points. It provides information about the typical or expected value of the process under consideration.

The mean is commonly used as a reference point in SPC to monitor and control the process performance. Control charts, which are a fundamental tool in SPC, typically plot the mean of the process data over time to detect any shifts or trends.

On the other hand, the standard deviation, often denoted as σ, is a measure of the dispersion or variability of the data points around the mean. It provides insights into the spread or consistency of the process. The standard deviation is not used as a substitute for the mean in SPC; rather, it is used to calculate control limits on control charts.

Control limits help identify when the process is exhibiting unusual variation that may indicate a special cause or a deviation from the desired performance.

In summary, the mean and the standard deviation are distinct statistical measures, each with its own role in SPC. They provide complementary information and should not be used interchangeably.

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Intellectual property is a crucial aspect of many contractual agreements, and patent registration is an important indicator of a country's innovation and competitiveness in the global market. The correct option is C. U.K.

According to the information presented in the lecture, the top three countries in patent registration as of 2017 are the United States, Japan, and China. These three countries account for the majority of patent filings globally and are known for their strong research and development capabilities.


It is worth noting that patent registration is not the only indicator of a country's intellectual property capabilities. Other factors such as copyright, trademarks, and trade secrets also play a crucial role in protecting and promoting innovation. Additionally, countries may have different approaches to intellectual property protection, with some emphasizing strong enforcement and others favoring more flexible regimes.

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Answer:

90

Step-by-step explanation:

90 degree angle is a perfect square

Answer:

B)  81

Step-by-step explanation:

Let \(a\) be the first term in the sequence, and \(r\) the common ratio between consecutive terms. Let \(a_n\) denote the \(n\)-th term in the sequence. The first several terms are

\(\{a, ar, ar^2, ar^3, \ldots\}\)

and so the \(n\)-th term is given by \(a_n = ar^{n-1}\).

Let \(S_N\) denote the \(N\)-th partial sum of the series,

\(\displaystyle S_N = \sum_{n=1}^N ar^{n-1} = a + ar + ar^2 + \cdots + ar^{N-1}\)

Multiply both sides by \(r\).

\(r S_N = ar + ar^2 + ar^3 + \cdots + ar^N\)

Subtract this from, then solve for, \(S_N\).

\(S_N - r S_N = a - ar^N \implies S_N = \dfrac{a(1 - r^N)}{1 - r}\)

We know the infinite series converges, so \(|r|<1\), which means the \(S_N \to \frac a{1-r}\) as \(N\to\infty\). And since we know the infinite sum is 25, we have

\(\dfrac a{1-r} = 25 \implies a + 25r = 25\)

Meanwhile, the sum of the first 2 terms is

\(a + ar = 16\)

Solve for \(r\).

\(a + ar = 16 \implies ar = 16 - a \\\\ \implies r = \dfrac{16}a - 1\)

Substitute this into the other equation and solve for \(a\), then again for \(r\).

\(a + 25\left(\dfrac{16}a - 1\right) = 25 \implies a + \dfrac{400}a - 25 = 25 \\\\ \implies a - 50 + \dfrac{400}a = 0 \\\\ \implies a^2 - 50a + 400 = 0 \\\\ \implies (a-10) (a-40) = 0 \\\\ \implies a = 10 \text{ or } a = 40\)

\(\implies r = \dfrac{16}{10} - 1 = \dfrac35 \text{ or } r = \dfrac{16}{40} - 1 = -\dfrac35\)

We're given that the ration is positive, so \(r=\frac35\) and \(a=10\).

i) The fifth term in the sequence is

\(ar^{5-1} = 10 \left(\dfrac35\right)^4 = \dfrac{162}{125} = 1.296\)

ii) The sum of the first 4 terms is

\(\displaystyle S_4 = \sum_{n=1}^4 ar^{n-1} = \frac{a(1 - r^4)}{1 - r} = \dfrac{10\left(1 - \left(\frac35\right)^4\right)}{1 - \frac35} = \dfrac{544}{25} = 21.76\)

Answer:

See below.

Step-by-step explanation:

So, here's how to break it down. Percentages can be turned into decimals, and vice versa, so we shall change 30% in 0.3. Next, we multiply 3.60 by 0.3. giving us 1.8. we subtract 1.8 from 3.6 and we are left with 1.8, which can be rounded up to two. I'm not sure where 2 came from other than estimation, but I did the math and got 1.8.

Answer:

For this one I think the answer would be A and E

Step-by-step explanation:

when seeing if the coordinates represent a function, make sure none of the inputs repeat and none of the outputs repeat.

hope this helps

Answer:

\(A_X=\frac{15x^2}{16}\)

Step-by-step explanation:

From the question we are told that:

Base of Flower bed \(b=\frac{x}{2}\)

Height of Flower bed \(h=\frac{x}{4}\)

Generally the equation for Area of garden left A_X is mathematically given by

 \(A_X=Area\ of\ Garden\ A_g\ - Area\ of\ flower\ bed\ A_f\)

Where

 \(A_f=b*h\)

 \(A_f=\frac{1}{2}*\frac{x}{2}*\frac{x}{4}\)

 \(A_f=\frac{x^2}{16}\)

Therefore

 \(A_X= A_g - A_f\)

 \(A_X=x^2-\frac{x^2}{16}\)

 \(A_X=\frac{15x^2}{16}\)

Answer:

28. Just divide 1876 by 67.

Step-by-step explanation:

Answer:

28 I believe

Step-by-step explanation:

Answer:

  a) see attached

  b) 15015 meters

Step-by-step explanation:

You want the voltage, current, resistance, and power for each component of the circuit shown in the diagram.

The relevant circuit relations are ...

Given current and resistance for element 1, we immediately know its voltage is ...

  V = IR = (4)(10) = 40 . . . . volts

Given the voltage on element 3, we know that parallel element 2 has the same voltage: 30 volts.

Given the voltage at T is 90 volts, the sum of voltages on elements 1, 2, and 4 must be 90 volts. That means the voltage on element 4 is ...

  90 -(40 +30) = 20

The current in elements 1, 4, and T are all the same, because these elements are in series. They are all 4 amperes.

That 4 ampere current is split between elements 2 and 3. The table tells us that element 2 has a current of 1 ampere, so element 3 must have a current of ...

  4 - 1 = 3 . . . . amperes

The resistance of each element is the ratio of voltage to current:

  R = V/I

Dividing the V column by the I column gives the values in the R column.

Note that power source T does not have a resistance of 22.5 ohms. Rather, it is supplying power to a circuit with an equivalent resistance of 22.5 ohms.

Power is the product of voltage and current. Multiplying the V and I columns gives the value in the P column.

Note that the power supplied by the source T is the sum of the powers in the load elements.

We found that the transmitter is receiving a power of 90 watts, so its operating frequency is ...

  (90 W)×(222 Hz/W) = 19980 Hz

Then the wavelength is ...

  λ = c/f

  λ = (3×10⁸ m/s)/(19980 cycles/s) ≈ 15015 m/cycle

The wavelength of the broadcast is about 15015 meters.

__

Additional comment

The voltage and current relations are "real" and used by circuit analysts everywhere. The relationship of frequency and power is "made up" specifically for this problem. You will likely never see such a relationship again, and certainly not in "real life."

Kirchoff's voltage law (KVL) means the sum of voltage rises (as at T) will be the sum of voltage drops (across elements 1, 2, 4).

Kirchoff's current law (KCL) means the sum of currents into a node is equal to the sum of currents out of the node. At the node between elements 1 and 2, this means the 4 amps from element 1 into the node is equal to the sum of the currents out of the node: 1 amp into element 2 and the 3 amps into element 3.

As with much of math and physics, there are a number of relations that can come into play in any given problem. You are expected to remember them all (or have a ready reference).

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Answer:

4x+68=180

4x=180-68

4x=112

4. 4

x= 28°

question 2 has been solved that way because 5x+70°=180 because they are on a straight line and angles on a straight line are 180°

200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

The absolute difference between the predicted and actual values must be determined, added together, and divided by the total number of periods.

Forecasted values are as follows: 1,500 and 1,400

Values in actuality: 1,200 and 1,500

Absolute differences:

|1,500 - 1,200| = 300

|1,400 - 1,500| = 100

Now, we calculate the MAD:

MAD = (300 + 100) / 2 = 400 / 2 = 200

Therefore, 200 is the mean absolute deviation. Therefore, choice three (200) is the right one.

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the return on equity (after tax) ratio for 2017 is 3.47% and for 2018 is 5.61%.To calculate the return on equity (ROE) ratio, we need to determine the net income and average stockholders' equity for both 2017 and 2018.

Net Income:
2017: $1,338
2018: $2,160

Average Stockholders' Equity:
2017: ($31,500 + $45,500) / 2 = $38,500
2018: ($31,500 + $45,500) / 2 = $38,500

ROE Ratio:
2017: $1,338 / $38,500 = 0.0347 or 3.47%
2018: $2,160 / $38,500 = 0.0561 or 5.61%

Therefore, the return on equity (after tax) ratio for 2017 is 3.47% and for 2018 is 5.61%.

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Answer:

$18

Step-by-step explanation:

If she starts with $50 and has $32 left when she's done then. 50-32= 18

So she spent $18 on clothing.

Answer:

I believe it is A because if you use the slope x it matches with the line.