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The largest area that can be enclosed will be 2812.5 square meters.

The perimeter of a rectangle is given as:

2L + 2W  ∴ L = length and W = width

As the farmer does not want to fence the side along the river, then the formula will be:

P = L + 2w

Now

150 = L + 2w

L = 150 - 2w

Here the area is LW

Area = (150 - 2W)(W)

After solving we get

150 - 2W = 0 or W = 0

150 - 2W = 0

2W = 150

W = 75

Now, there are two solutions whether 0 or 75

Let's find their average 0+75 / 2 = 37.5

Now L = 150 - 2(37.5)

L = 150 - 75

L = 75

As the dimensions are L = 75 and W = 37.5

Area = L x W = 75 x 37.5 = 2812.5 square meters

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The complete question is:

Farmer Ed has 150 meters of fencing and wants to enclose a rectangular play that borders a river. If farmer Ed does not fence in the side along the river, find the length and width of the plot that will maximize the area. What is the largest area that can be enclosed?

The classical probability of rolling a seven with two dice is 6/36 or 1/6.

The best probability to determine the outcome of rolling seven with two dice is the classical probability.

Classical probability is based on the assumption that all outcomes in a sample space are equally likely, and it involves counting the number of favorable outcomes and dividing by the total number of possible outcomes.

In the case of rolling two dice, there are 36 possible outcomes, each with an equal chance of occurring. The number of ways to roll a seven is 6, as there are six combinations of dice rolls that add up to seven: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1). Therefore, the classical probability of rolling a seven with two dice is 6/36 or 1/6.

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The direction field produced by the differential equationy' = (y - 1)(y + 2)matches the given direction field y' = (y - 1)(y + 2).

The given differential equation produces the following direction field.  The differential equation that produces the given direction field is y' = (y - 1)(y + 2)

To show this analytically, we can consider the slope of the direction field at various points. At points where y = 1, y' is negative, and at points where y < 1, y' is negative.

Similarly, at points where y = -2, y' is positive, and at points where y > -2, y' is positive.

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Answer:

160 days

Step-by-step explanation:

If it takes 8 days with 10 women to make 3 tree houses, then the rate of woman per tree house is 3/80. Multiplying this by 6 and dividing by 36, you get a rate of 1/160 or 160 days. Hope this helps!

Answer:

Step-by-step explanation:56*12=672

Answer:

This is a linear function and you have to rewrite the equation to the standard form y= mx+q, so y= -4x + 3 where -4 is m and tells you the slope of the function while 3 tells you where it intercepts the y axis. Now you have to write the points of the function taking some x values and obtaining the relative y. For example if x is 0 then y= 3-4(0) which is equal to 3. If x is 1 y is -1, if X is 2 then y is -5 and you continue like that until you want. However, to draw the line you could just stop to two points.

The inequality - 2 · x + y > - 4 represents the figure on Cartesian plane.

In this problem we have a picture with a representation of a linear inequality of the form:

y > m · x + b

Where:

By analytic geometry, a line can be generated from the knowledge of the location of two points on Cartesian plane. First, determine the equation of the line:

m · 0 + b = - 4

2 · m + b = 0

b = - 4

2 · m = - b

m = - b / 2

m = 2

Second, write the inequality:

y > 2 · x - 4

- 2 · x + y > - 4

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The child passes through 18π radians in the course of the carousel ride.

To determine the number of radians the child passes during the 6-minute ride on the carousel, we need to know the distance traveled in terms of radians.

Since there are 20 horses spaced evenly around the carousel, each horse is separated by an angle of 360/20 = 18 degrees or π/10 radians.

Therefore, during one rotation of the carousel, the child passes through 20π/10 = 2π radians. And since the carousel completes one rotation every 40 seconds, the angular velocity is 2π/40 = π/20 radians per second.

To find the total distance traveled in radians during a 6-minute ride, we need to multiply the angular velocity by the time elapsed.

6 minutes is equal to 360 seconds,

so the child passes through π/20 x 360 = 18π radians during the ride.

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Answer:

The answet is C.

Step-by-step explanation:

First, you have to find the angle of ACB using Sine Rule, sinθ = opposite/hypotenuse :

\( \sin(θ ) = \frac{oppo.}{hypo.} \)

\(let \: oppo. = 4 \\ let \: hypo. = 5\)

\( \sin(θ) = \frac{4}{5} \)

\(θ = {\sin( \frac{4}{5} ) }^{ - 1} \)

\(θ = 53.1 \: (1d.p)\)

Given that line AB is parallel to line CD so ∠C = 90°. Next, you have to find the angle of ACD :

\(ACD = 90 - 53.1 = 36.9\)

Lastly, you can find the length of CD using Cosine rule, cosθ = adjacent/hypotenuse :

\( \cos(θ) = \frac{adj.}{hypo.} \)

\(let \: θ = 36.9 \\ let \: adj. = 5 \\ let \: hypo. = CD\)

\( \cos(36.9 ) = \frac{5}{CD} \)

\(CD \cos(36.9) = 5\)

\(CD = \frac{5}{ \cos(36.9) } \)

\(CD = 6.25 units\: (3s.f)\)

IBM's Cost of Equity based on DGM is 11.46%.

Dividend growth model (DGM) refers to a valuation model used to estimate the price of an investment using predicted dividends and expected growth rates of dividends over a particular period. The equation for DGM is as follows:

P = D1 / (Ke - G)

where:

P = The price of the stock

D1 = The expected dividend to be paid at the end of the year

Ke = The cost of equity

G = The expected dividend growth rate

Therefore, to determine IBM's Cost of Equity based on DGM we can use the given information as follows:

D1 = $4.50

G = 8.00%

Ke = ?

P = $130

Therefore,

Ke = (D1 / P) + G

Ke = ($4.50 / $130) + 0.08

Ke = 0.0346 + 0.08

Ke = 0.1146

Ke = 11.46%

Therefore, IBM's Cost of Equity based on DGM is approximately 11.46%

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\(-(5\cdot(-4))=-(-20)=20\)

Distributive property works only for addition.

\(a(b+c)=ab+ac\) but \(a(bc)=abc\), not \(ab+ac\) or something like that.

Answer:

\(-(-5\times(-4))=-(-20)=20\)

Step-by-step explanation:

Notice that the product within the brackets is:

\(5\times(-4)=-20\)

Then, by first evaluating the product within the brackets, we get the following:

\(-(5\times(-4))=-(-20)\)

Finally, note that the negative of negative twenty is twenty as follows:

\(-(-20)=20\)

*Note on your mistake:

You cannot distribute the negative sign to each component of a product.

This can only happen if the expression within the bracket is a sum, for instance:

\(-(5+(-4))=-5+4\)

Main Answer:

The given equation describes a plant with an input signal i(t) and an output signal y(t). The transfer function G(s) represents the dynamics of the plant in the Laplace domain.

Explanation:

The given equation can be interpreted as a mathematical representation of a dynamic system, commonly referred to as a plant, which is characterized by an input signal i(t) and an output signal y(t). The plant's behavior is governed by a transfer function G(s) that relates the Laplace transform of the input signal to the Laplace transform of the output signal.

In the first equation, i(t) › = [ 2 ] ² (0+ [ 1 ] (0) + [ 2 ] 4 (0) (t) u(t) d(t), the input signal is represented by i(t). The term [ 2 ] ² (0) indicates the initial condition of the input signal at t=0. The term [ 1 ] (0) represents the initial condition of the first derivative of the input signal at t=0. Similarly, [ 2 ] 4 (0) (t) represents the initial condition of the second derivative of the input signal at t=0. The u(t) term represents the unit step function, which is 0 for t<0 and 1 for t≥0. The d(t) term represents the Dirac delta function, which is 0 for t≠0 and infinity for t=0.

In the second equation, y(t) = [n² - 2π 2-π] x(t) + u(t) ㅠ, the output signal is represented by y(t). The term [n² - 2π 2-π] x(t) represents the multiplication of the Laplace transform of the input signal x(t) by the transfer function [n² - 2π 2-π]. The term u(t) represents the unit step function that accounts for any additional input or disturbances.

The transfer function G(s) = s² + (2π)s / (s² - π² - 2π) describes the dynamics of the plant. It is a ratio of polynomials in the Laplace variable s, which represents the complex frequency domain. The numerator polynomial s² + (2π)s represents the dynamics of the plant's zeros, while the denominator polynomial s² - π² - 2π represents the dynamics of the plant's poles.

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Answer:

523 inches

Step-by-step explanation:

got it right on edg

Answer:

Hill 1: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2: F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 3: F(x) = 4(x - 2)(x + 5)

Step-by-step explanation:

Hill 1

You must go up and down to make a peak, so your function must cross the x-axis six times. You need six zeros.

Also, the end behaviour must have F(x) ⟶ -∞ as x ⟶ -∞ and F(x) ⟶ -∞ as x⟶ ∞. You need a negative sign in front of the binomials.

One possibility is

F(x)  = -(x + 4)(x + 3)(x + 1)(x - 1)(x - 3)(x - 4)

Hill 2

Multiplying the polynomial by -½ makes the slopes shallower. You must multiply by -2 to make them steeper. Of course, flipping the hills converts them into valleys.

Adding 3 to a function shifts it up three units. To shift it three units to the right, you must subtract 3 from each value of x.

The transformed function should be

F(x)  = -2(x +1)(x)(x -2)(x -3)(x - 6)(x - 7)

Hill 3

To make a shallow parabola, you must divide it by a number. The factor should be ¼, not 4.

The zeroes of your picture run from -4 to +7.

One of the zeros of your parabola is +5 (2 less than 7).

Rather than put the other zero at ½, I would put it at (2 more than -4) to make the parabola cover the picture more evenly.

The function could be

F(x) = ¼(x - 2)(x + 5).

In the image below, Hill 1 is red, Hill 2 is blue, and Hill 3 is the shallow black parabola.

The length of the base of the rectangle is approximately 18 millimeters.

To find the length of the base of the rectangle, we can use the formula for the area of a rectangle: A = bh, where A is the area, b is the length of the base, and h is the height.
We are given that the area of the rectangle is 370.8 square millimeters and the height is 20.6 millimeters. Substituting these values into the formula, we get:
370.8 = b(20.6)
To solve for b, we can divide both sides of the equation by 20.6:
b = 370.8/20.6
b ≈ 18
Therefore, the length of the base of the rectangle is approximately 18 millimeters.
It's important to note that the units of the answer are millimeters, which is consistent with the units of the given height and area. Additionally, we rounded the answer to the nearest millimeter since the height and area were given to only one decimal place.

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Answer:

8 inches from beginning to end

Step-by-step explanation:

8 inches because 1 times 8 is 8

Answer:

1.8m/s

Step-by-step explanation:

Given:

speed;

v = 5t² - 2t + 2                 ---------------(i)

(i) First, find the acceleration a by differentiating the speed equation in equation (i) with respect to t as follows;

a = \(\frac{dv}{dt}\)

a = \(\frac{d}{dt} [5t^2 - 2t + 2]\)

a = 10t - 2              ---------------------(ii)

(ii) Next, find the moment (time) when the acceleration is zero. This is done by substituting a = 0 into equation(ii) as follows;

0 = 10t - 2

Solve for t

10t = 2

t = 2 / 10 = 0.2

Therefore, at t = 0.2s, the acceleration is zero.

(iii) Now, find the velocity at time t = 0.2s when the acceleration is zero. This is done by substituting the value of t = 0.2s into equation (i) as follows;

v = 5(0.2)² - 2(0.2) + 2

v = 0.2 - 0.4 + 2

v = 1.8

Therefore, the speed at the moment when acceleration is zero is 1.8m/s

NB: Since the units of measurement are not given, the S.I units are used. Hence m/s for speed.

As per the unitary method, the amount saved by Aaron after one year is  $780

We can use the following formula to find out how much Aaron saves per month:

Amount saved per month = Total amount saved / Number of months

We can use this formula to find out how much Aaron saves per month for each period:

For the first period (3 months):

Amount saved per month = 195 / 3

= 65

For the second period (4 months):

Amount saved per month = 260 / 4

= 65

For the third period (6 months):

Amount saved per month = 390 / 6

= 65

For the fourth period (7 months):

Amount saved per month = 455 / 7

= 65

We can see that Aaron saves $65 per month, regardless of the time period. Therefore, we can use this value to find out how much he will save in one year (12 months):

Amount saved in 1 year = Amount saved per month x Number of months

= 65 x 12

= 780

Therefore, we can predict that Aaron will save $780 after one year.

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The coordinates of point P' would be (-2, 0). To calculate this, we use the scaling and translation transformation equations.

The scaling transformation formula is (x, y) → (x', y') = (kx, ky), where k is the scale factor. In this case, k = 2/3. Therefore, the coordinates of point P' would be (2/3x, 2/3y).

The translation transformation formula is (x, y) → (x', y') = (x + h, y + k), where h is the horizontal shift and k is the vertical shift. In this case, h = -2 and k = 0. Therefore, the coordinates of point P' would be (2/3x-2, 0).

We know that the coordinates of point P is (0, 0). Therefore, the coordinates of point P' would be (2/3 x - 2, 0) = (-2, 0).

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Answer:

Suppose that the batch has N liters of paint.

we know that the recipe is:

1/2 of red paint

1/3 of yellow paint

1/6 of white paint.

Then, out of the N liters, 1/2 is red.

This means that we must use:

N/2 liters of red paint.

And the same for the other two colors:

N/3 liters of yellow paint

N/6 liters of white paint.

When we add those 3, we have:

(N/2 + N/3 + N/6)  = (3*N/6 + 2*N/6 + N/6) = N.

Now, if for example N = 2

Then the batch has 2 liters of paint, this would mean that we must use:

2/2 liters of red paint

2/3 liters of yellow paint

2/6 liters of white paint.

Answer:

120 km

distance = speed * time

90 minutes can be converted to 1.5 hours

speed given 80 km/h and time given 1.5 hours

so distance =  80 * 1.5 = 120 km

Answer:

The panther will run 120 km in 90 mins

Step-by-step explanation:

An hour is 60 mins and you know in 1 hour the panther can run 80km

all you need to do is figure out how many miles an xtra 30 mins will be

60 minutes divided by 2 = 30 minutes and 80 km divided by 2 = 40km

Therefore 30 minutes = 40km

just add this to the original statement and you're good

60 mins + 30 mins = 90 mins

80km + 40km = 120km

The panther will run 120km in 90 mins

The value of the principal is \($10,000\).

The equation:

A = P(1 + 0.043t)

A represents the amount of money earned on a savings account with 4.3% annual simple interest, P represents the principal (initial amount of money), and t represents the time in years.

We are also given that the account balance is \($15160\) after 12 years.

To substitute these values into the equation and solve for the principal:

A = \($15160\)

t = 12

0.043 = 4.3%

\($15160\) = P(1 + 0.043(12))

\($15160\) = P(1 + 0.516)

\($15160\) = P(1.516)

P = \($10000\)

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Answer:

6

Step-by-step explanation:

substitute t and u with the number

15-9= 6

please like and rate and follow

Answer:

6

Step-by-step explanation:

If t = 15 and u = 9, then:

\(\large \textsf{$t-u = 15-9$}\\ \large \textsf{$\phantom{t-u}=6$}\)

Thus, the answer is 6

Shelby's new weekly wage would be £318.50  if she receives a pay increase  of 45p per hour.

What is Shelby's hourly rate based on the  weekly wage of £302.75?

Shelby's hourly rate can be determined as her weekly wage divided by the number of hours spent working per week, in essence, the hourly rate is based on the weekly wage and the number of hours since the total weekly wage can as well be determined as the hourly rate multiplied by the number of hours working per week

hourly rate=weekly wage/hours spent working per week

weekly wage=£302.75

hours spent working per week=35

hourly rate=£302.75/35

hourly rate=£8.65

her new hourly rate=£8.65+£0.45

her new hourly rate=£9.10

new weekly wage=35*£9.10

new weekly wage=£318.50

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Answer:

the answer is 3x as that is the slope

Answer:

3

Step-by-step explanation:

yeah < 3

Answer:

6 full bags of rice.

0.4 kg of rice will be left.

Step-by-step explanation:

The man can carry a max of 160 kg.

1 bag of rice weighs 25 kg.

160/25 = 6.4

He can carry 6 full bags of rice.

Yes, there will be rice left.

0.4 kg of rice will be left.

Answer:

He can carry 6 whole 2/5 of the rice and 3/5 of rice in one bag would be left.

Step-by-step explanation:

Man can carry = 160 kg

1 bag of rice = 25 kg

He can carry = \(\frac{160}{25}\)

=> \(6\frac{2}{5}\)

He can carry 6 whole 2/5 of the rice and 3/5 of rice in one bag would be left.

Answer:

3x(2)

=6x

Step-by-step explanation:

Answer:

\(6x^{2}\)

Step-by-step explanation:

x(3x)(2)

=x*3*x*2

=6*x2

=6x2

Answer:

the discount is for 8.40$

Answer:

Parabola

Step-by-step explanation:

Answer:

Step-by-step explanation: Xmin:

-10

Xmax:

10

Ymin:

-10

Ymax:

10