ssume that a company gets x tons of steel from one provider, and y tons from another one. Assume that the profit made is then given by the function P(x,y) = 9x + 8y - 6 (x+y)²
The first provider can provide at most 5 tons, and the second one at most 3 tons. Finally, in order not to antagonize the first provider, it was felt it should not provide too small a fraction, so that x≥2(y-1)
1. Does P have critical points? 2. Draw the domain of P in the xy-plane. 3. Describe each boundary in terms of only one variable, and give the corresponding range of that variable, for instance "(x, 22) for x € (1, 2)". There can be different choices.

The new limits of integration are from u=0 to u=6sin(6) after the substitution u=6x is applied. The integral evaluates to (1/6)[cos(6sin(6))+1].

Let us assume the substitution u = 6x.

First, we need to find the new limits of integration by substituting u=6x into the original limits of integration:

When x=0, u=6(0) = 0.

When x=sin(6), u=6sin(6).

Therefore, the new limits of integration are from u=0 to u=6sin(6).

Next, we need to express the integral in terms of u by substituting x back in terms of u:

When x=0, u=6(0) = 0, so x=u/6.

When x=sin(6), u=6sin(6), so x=u/6.

Therefore, we have:

∫0sin(6) dx = (1/6) ∫0⁶ sin(6u/6) du

Simplifying, we get:

(1/6) ∫0⁶ sin(u) du

which evaluates to:

(1/6) [-cos(u)] from 0 to 6sin(6)

Plugging in the limits of integration, we get:

(1/6) [-cos(6sin(6)) + cos(0)]

which simplifies to:

(1/6) [-cos(6sin(6)) + 1]

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The new limits of integration are from u=0 to u=6sin(6) after the substitution u=6x is applied. The integral evaluates to (1/6)[cos(6sin(6))+1].

Let us assume the substitution u = 6x.

First, we need to find the new limits of integration by substituting u=6x into the original limits of integration:

When x=0, u=6(0) = 0.

When x=sin(6), u=6sin(6).

Therefore, the new limits of integration are from u=0 to u=6sin(6).

Next, we need to express the integral in terms of u by substituting x back in terms of u:

When x=0, u=6(0) = 0, so x=u/6.

When x=sin(6), u=6sin(6), so x=u/6.

Therefore, we have:

∫0sin(6) dx = (1/6) ∫0⁶ sin(6u/6) du

Simplifying, we get:

(1/6) ∫0⁶ sin(u) du

which evaluates to:

(1/6) [-cos(u)] from 0 to 6sin(6)

Plugging in the limits of integration, we get:

(1/6) [-cos(6sin(6)) + cos(0)]

which simplifies to:

(1/6) [-cos(6sin(6)) + 1]

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AnsTHE OTHER GUY GOT IT RIGHT SORRY I DID THE MATH WRONG :( Step-by-step explanation:

Answer:

5.2 miles

Step-by-step explanation:

Distance left to ride = 26.8miles - 6 miles = 20.8 miles

There are 4 days left, so on average,

Hassan has to ride:

\( \frac{20.8}{4} \\ = 5.2mi\)

The angle is decreasing at a rate of 0.0133 radians per second.

The height of the kite from the ground is y = 75 feet.

The kite moves horizontally at a speed of dx/dt = 4 ft/s

The length of the string L = 150 feet

The formula for the sine angle is:

sin ( θ ) = 75/150

sin ( θ ) = 1/2

The horizontal displacement (x) is calculated using the following tangent ratio:

tan θ = 75/x

1 / tanθ = x/75

cot θ = x/75

Differentiating the above equation with respect to t.

- csc² ( θ ) × dθ/dt  = 1/75 × dx/dt

Substituting the values in the equation,

- csc² ( θ ) × dθ/dt  = 1/75 × 4

- csc² ( θ ) × dθ/dt = 4/75

Now,

csc θ = 1/sin θ = 2

So,

- 2² × dθ/dt = 4/75

dθ/dt = - 1/75

dθ/dt = 0.0133

Hence, the angle is decreasing at a rate of 0.0133 radians per second.

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Answer: 13/25

Step-by-step explanation: it is equal to 52% which is greater than 50%

50% is greater than 13/25. To compare these two values, you can convert both of them to a common denominator, such as 50%. 50% is equal to 1/2, so 13/25 is equal to 52/50, which is less than 1/2 or 50%. Alternatively, you can also express both fractions as decimals and compare the two values that way. 50% is equal to 0.5, and 13/25 is equal to 0.52, so 50% is still greater than 13/25.

Answer:

x = 26, y = 120

Step-by-step explanation:

First we will find x.

We know that 3x-18 = 2x+8 because they are corresponding angles

Now we can solve for x

3x-18 = 2x+8 | subtract 2x from both sides

x-18 = 8 | add 18 to both sides

x = 26

Now we can find y. We know that 3x-18 and y are supplementary (add up to 180) since they are a linear pair (adjacent angles that form a line)

This means we can solve for y using the following :

3x-18 + y = 180 | substitute x for 26

3(26)-18 + y = 180 | simplify

60 + y = 180 | subtract 60 from both sides to isolate y

y = 120

- Kan Academy Advance

The population of the town in 2040 will be 9384.

According to the question,

We have the following information:

From 2006 to 2010, the population of a town declined to 22,000. The population is expected to continue to decline at a rate of 2.8% each year.

Rate of decline = 2.8/100

Rate of decline = 0.028

Number of years = 30 years (time between 2010 and 2040)

We know that the following formula is used to find the future population:

Future population = present population\((1-I)^{n}\) where I is the rate of decline and n is the number of years

Future population = 22000\((1-0.028)^{30}\)

Future population = 9384.49

Future population = 9384

Hence, the population of the town in 2040 will be 9384.

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Answer:x=2

Step-by-step explanation:

Answer:

x = 2

Step-by-step explanation:

6 (5x) = (x +14) + (x+17) + (8x+9)

30x = 14 + 17 + 9 + 2x + 8x

20x = 40

x = 40/20

x = 2

The Process Capability Index (Cpk) is 0.24

The process capability index (Cpk) for the organic yogurt processing plant can be calculated as follows:

Cpk = min[(USL - μ) / (3σ), (μ - LSL) / (3σ)]

Where:

- USL is the upper specification limit (16.9 ounces)

- LSL is the lower specification limit (15.1 ounces)

- μ is the process mean (16.0 ounces)

- σ is the process standard deviation (1.25 ounces)

To calculate Cpk, we need to consider the specifications and the process performance. The formula compares the process variation to the specification limits. The numerator represents the distance between the process mean and the nearest specification limit, while the denominator represents three times the process standard deviation.

In this case, the process mean (μ) is 16.0 ounces, the upper specification limit (USL) is 16.9 ounces, and the lower specification limit (LSL) is 15.1 ounces. The process standard deviation (σ) is 1.25 ounces.

By plugging these values into the Cpk formula, we can determine the smaller value between the two ratios, representing the capability of the process to meet the specifications. This Cpk value indicates how well the process fits within the specification limits, with higher values indicating better capability.

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Step-by-step explanation:

3+5=8

40÷8=5

5x5=25 girls

5x3=15

Answer:

the number of girls are 16

We have found the Laplace transform of y(t) in terms of C{3}(s). We could use inverse Laplace transform to obtain y(t) in terms of t.

To find the Laplace transform of the differential equation 2y' - 35y = sin(6t), we apply the Laplace transform to both sides of the equation:

L[2y' - 35y] = L[sin(6t)]

Using the linearity of the Laplace transform and the derivative property, we get:

2L[y'] - 35L[y] = 6/ (s²2 + 6²2)

Applying the initial conditions, we get:

Y(s) = L[y(t)] = C{3}(s)

Y'(s) = L[y'(t)] = sY(0) - y(0) = 3s - 6

Substituting these expressions into the Laplace transformed differential equation, we get:

2(3s - 6) - 35C{3}(s) = 6/ (s²2 + 6²2)

Simplifying, we can solve for C{3}(s):

C{3}(s) = [2(3s - 6) - 6/ (s²2 + 6²2)] / 35

C{3}(s) = (6s - 12 - 3/(s²2 + 6²2)) / 35

Therefore, the Laplace transform of y(t) is:

Y(s) = C{3}(s) = (6s - 12 - 3/(s²2 + 6²2)) / 35

Thus, we have found the Laplace transform of y(t) in terms of C{3}(s). We could use inverse Laplace transform to obtain y(t) in terms of t.

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To find the minimum score of the top 2.5% of students, we need to calculate the z-score corresponding to the 97.5th percentile and then convert it back to the original SAT score scale.

First, let's calculate the z-score using the formula:

z = (x - μ) / σ

where x is the SAT score, μ is the mean (1175), and σ is the standard deviation (120).

To find the z-score corresponding to the 97.5th percentile, we need to find the z-score value that leaves 2.5% in the tail of the distribution (to the right).

Using a standard normal distribution table or a statistical calculator, we find that the z-score corresponding to the 97.5th percentile is approximately 1.96.

Now we can solve for x (the SAT score) in the z-score formula:

1.96 = (x - 1175) / 120

Multiply both sides by 120:

1.96 * 120 = x - 1175

235.2 = x - 1175

Add 1175 to both sides:

235.2 + 1175 = x

1410.2 = x

Therefore, the minimum score of the top 2.5% of students is approximately 1410.

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The value of the probability P(Not N) is 7/8

The given parameters are:

Sections = 8

N section = 1

The sections that are not N is calculated using:

Not N = Sections - N

This gives

Not N = 8 - 1 = 7

The probability is then calculated using:

P(Not N) = Not N/Sections

This gives

P(Not N) = 7/8

Hence, the value of the probability P(Not N) is 7/8

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The length of each side is 26 meters, 32.5 meters and 32.5 meters.

Let, ABC is an isosceles triangle BC is the base and AB and AC are two equal sides.

By the property of triangle, the perirmeter P is equal to the sum of all three sides.

Let the sides are 4x, 5x, 6x.

P = 4x + 5x + 5x

91 = 14x

x = 6.5

Substitute the values in the assumed sides,

A = 4 × 6.5 = 26

B = 5 × 6.5 = 32.5

C = 5 × 6.5 = 32.5

The base of triangle is 26 meters and the two equal sides are 32.5 meters.

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Answer:

81.76in^2

Step-by-step explanation:

Given data

Lenght of book=  11.2 inches

WIdth of book= 7.3 inches

We know that Area= Length* Width

Area= 11.2*7.3

Area= 81.76 in^2

Hence the area of the front of the book is is 81.76in^2

Answer: 6

Step-by-step explanation:

Just some simple ratios

P = Pizza People = Pl

P: Pl

2 : 9

x: 27

We want to find x.

Since 27/9 is equal to 3, we multiply 2 by 3 as well!

2x3=6, our desired amount.

The given endpoint sum is expressed in sigma notation as;∑[(1 + i/30)²]*(1/30)i = 0,1,2,..,29

Express the following endpoint sums in sigma notation but do not evaluate them. L30 for f(x) = x^2 on [1,2]The objective is to represent the given endpoint sum in sigma notation. The given endpoint sum is: L30 for f(x) = x² on [1, 2]The formula for the endpoint sum is given by;∑f(x)*Δx From the question, the following are the given details:Interval: [1,2]Number of Sub-intervals: 30 Function: f(x) = x²

Here, the interval is divided into 30 equal sub-intervals of length;Δx = (2 - 1)/30= 1/30 Thus, the endpoint sum is; L30 for f(x) = x² on [1, 2]= f(1)*Δx + f(2)*Δx+ f(1 + Δx)*Δx+ f(2 - Δx)*Δx+ f(1 + 2*Δx)*Δx+ …..+ f(2 - 2*Δx)*Δx= f(1)*Δx + f(2)*Δx+ f(1 + Δx)*Δx+ f(2 - Δx)*Δx+ f(1 + 2*Δx)*Δx+ …..+ f(2 - 2*Δx)*Δx We know that the function f(x) = x²Therefore, we can substitute this in the expression.

L30 for f(x) = x² on [1, 2]= (1)^2*(1/30) + (2)^2*(1/30)+ (1 + 1/30)^2*(1/30)+ (2 - 1/30)^2*(1/30)+ (1 + 2*(1/30))^2*(1/30)+ …..+ (2 - 2*(1/30))^2*(1/30)Now, we represent this endpoint sum in sigma notation.∑f(x)*Δx = ∑[(1 + iΔx)²]*Δxi = 0,1,2,..,29

Note: the first interval starts at 0 and not 1, as we begin counting from zero instead of one.Thus, the given endpoint sum is expressed in sigma notation as;∑[(1 + i/30)²]*(1/30)i = 0,1,2,..,29

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The endpoint sums of L30 for f(x) = x² on [1,2] can be expressed in sigma notation as:  (1/30)[ f(1) + f(1+1/30) + f(1+2/30) + ... + f(1+29/30) ]

The Riemann sum equation is A=f (xi) A is the area beneath the curve on the interval being evaluated, and f(xi) f (x I is the height of each rectangle (or the average of the two heights in the case of a trapezoid). x is the width of each rectangle or trapezoid.

The left endpoint Riemann sum for a function f(x) on the interval [a, b] with n subintervals of equal width Δx = (b-a)/n is given by:

Ln = Δx [ f(a) + f(a+Δx) + f(a+2Δx) + ... + f(a + (n-1)Δx) ]

Here, we have f(x) = x², a = 1, b = 2, and n = 30. Therefore,

Δx = (b-a)/n = (2-1)/30 = 1/30

a + iΔx = 1 + i/30

Hence, the left endpoint Riemann sum L30 for f(x) = x^2 on [1,2] is:

L30 = (1/30)[ f(1) + f(1+1/30) + f(1+2/30) + ... + f(1+29/30) ]

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Answer:

\(5m^3-3m^2+9m-7\)

Step-by-step explanation:

since there are only two variables, there are only two solutions

Answer:  Total Pay = 6X

Step-by-step explanation:  This assunes the question wants to know how to calculate Pablo's earning for a given tutoring time.

Pablo's rate is $6/hr.  Set X to the number of hours of tutoring.  Pablo's total pay would be:

Total Pay = 6X

The solution for the given differential equation y′ + 7y′ + 10y = 40t + 68, with the initial conditions

y(0) = 12 and

y′(0) = -21, is

y(t) = 14e^(-5t) - 2e^(-2t) - 2t + 14.

To find the solution for y(t), we can use the method of solving linear homogeneous differential equations. Here's how to solve it:

1. Rewrite the given differential equation in standard form: y′ + 7y′ + 10y = 40t + 68.

2. The characteristic equation for this differential equation is obtained by setting the coefficients of the derivatives to zero: r^2 + 7r + 10 = 0.

3. Solve the characteristic equation by factoring or using the quadratic formula. In this case, we can factor it as (r + 5)(r + 2) = 0.

Therefore, the roots are r = -5 and

r = -2.

4. The general solution for the homogeneous part of the differential equation is given by y_h(t) = C1e^(-5t) + C2e^(-2t), where C1 and C2 are constants.

5. To find the particular solution for the non-homogeneous part, we can use the method of undetermined coefficients. Since the right-hand side is a linear function, we can assume a particular solution of the form y_p(t) = At + B.

6. Substitute the assumed particular solution back into the original differential equation and solve for the coefficients A and B. In this case, we have y′ + 7y′ + 10y = 40t + 68.

7. Differentiate y_p(t) to find y′_p(t), and substitute both y_p(t) and y′_p(t) into the differential equation. This will give us two equations in terms of A and B.

8. Solve the resulting equations for A and B. In this case, you'll find that A = -2 and

B = 14.

9. The particular solution for the non-homogeneous part is y_p(t) = -2t + 14.

10. The general solution for the entire differential equation is given by y(t) = y_h(t) + y_p(t), where y_h(t) is the homogeneous solution and y_p(t) is the particular solution.

11. Substitute the initial conditions y(0) = 12 and

y′(0) = -21 into the general solution to find the values of the constants C1 and C2. In this case, you'll find that C1 = 14 and C2 = -2.

12. Finally, plug in the values of C1, C2, and the particular solution y_p(t) into the general solution to obtain the final solution for y(t).

Conclusion:
The solution for the given differential equation y′ + 7y′ + 10y = 40t + 68, with the initial conditions

y(0) = 12 and

y′(0) = -21, is

y(t) = 14e^(-5t) - 2e^(-2t) - 2t + 14.

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In the morning, the train went 170 miles. in the afternoon the train went 50 more miles. The Train ended up going 220 miles in total.

In the morning, the train traveled 170 miles.

In the afternoon, it traveled an additional 50 miles.

To find the total distance traveled by the train, we need to add the distance traveled in the morning and the distance traveled in the afternoon:

Total distance = Distance traveled in the morning + Distance traveled in the afternoon

Total distance = 170 miles + 50 miles

Total distance = 220 miles

So, the train ended up traveling a total of 220 miles.

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Answer:

$265

Step-by-step explanation:

You add $435 and $625 and get $1060 dived that by four and you get

Answer: $1400 for the total 3 days

Step-by-step explanation:

A= (3,435)

B= (5,625)

625-435 190

M= ————— = —— = 95

5-3 2

Y- 435= 95(x-3)

Y - 435= 95x - 285

Y= 95x + 150

95(2) + 150

190 + 150

= $340 for Monday

Finally,

435 + 625 + 340= $1400 for 3 days

The radical expression \(\frac{\sqrt{200} }{28}\) can be simplified to \(\frac{\sqrt{25} }{7}\) or \(5*\frac{\sqrt{14} }{7}\)

To simplify the given radical expression, we can simplify the numerator and denominator separately. The square root of 200 can be simplified as follows: √200 = √(2 * 100) = √2 * √100 = 10√2.

Similarly, the square root of 28 can be simplified as follows: √28 = √(4 * 7) = √4 * √7 = 2√7.

Now, substituting these simplified values into the original expression, we have \(\frac{\sqrt{200} }{28}\) = \(\frac{10\sqrt{2} }{2\sqrt{7} }\)

To further simplify the expression, we can divide the common factor of 2 from both the numerator and denominator: \(\frac{10}{2}\) * \(\frac{\sqrt{2} }{\sqrt{7} }\) = 5 * \(\frac{\sqrt{2} }{\sqrt{7} }\)

Finally, we rationalize the denominator by multiplying the expression by (√7/√7): \(5*\frac{\sqrt{2} }{\sqrt{7} } *\frac{\sqrt{7} }{\sqrt{7} } =5\frac{\sqrt{14} }{7}\)

Therefore, the simplified form of the radical expression \(\frac{\sqrt{200} }{28}\) is \(\frac{\sqrt{25} }{7}\) or \(5*\frac{\sqrt{14} }{7}\)

The radical expression \(\frac{\sqrt{200} }{28}\) can be simplified to \(\frac{\sqrt{25} }{7}\) or \(5*\frac{\sqrt{14} }{7}\)

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The missing length in the triangle is 56 cm.

Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion .

Let us form a proportional equation to find the value of missing length

p/21 = 24/9

Apply cross multiplication

9p=21×24

9p=504

Divide both sides by 9

p=56

Hence, the missing length in the triangle is 56 cm.

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Lucy has $7 less than Kristine and $5 more than Nina together, the three have $35. Lucy has $11.

Let's denote the amount of money that Kristine has as K, the amount of money that Lucy has as L, and the amount of money that Nina has as N.

According to the given information, we can form two equations:

Lucy has $7 less than Kristine: L = K - 7

Lucy has $5 more than Nina: L = N + 5

We also know that the three of them have a total of $35: K + L + N = 35

We can solve this system of equations to find the values of K, L, and N.

Substituting equation 1 into equation 3, we get:

K + (K - 7) + N = 35

2K - 7 + N = 35

Substituting equation 2 into the above equation, we get:

2K - 7 + (L - 5) = 35

2K + L - 12 = 35

Since Lucy has $7 less than Kristine (equation 1), we can substitute K - 7 for L in the above equation:

2K + (K - 7) - 12 = 35

3K - 19 = 35

Adding 19 to both sides:

3K = 54

Dividing both sides by 3:

K = 18

Now we can substitute the value of K into equation 1 to find L:

L = K - 7

L = 18 - 7

L = 11

Finally, we can find the value of N by substituting the values of K and L into equation 3:

K + L + N = 35

18 + 11 + N = 35

N = 35 - 18 - 11

N = 6

Therefore, Lucy has $11.

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☁️ Answer ☁️

annyeonghaseyo!

Your answer is:

The first one:

Exact form: x = 5/2

Decimal form: x = 2.5

Mixed number form: x = 2 1/2

The second one:

y = 15.

The third one:

t = 4. Good luck on the rest

Hope it helps.

Have a nice day hyung/noona!~ ￣▽￣❤️

The probability that the amount dispensed per box will have to be increased is 0.

To answer this question, we need to know the target amount that should be distributed per carton.

Assuming that the target amount is also 1 pound, we can use the concept of the normal distribution to estimate the likelihood that we will have to increase the amount distributed per case.

hence the probability of having to increase the amount is 0.

z = (target volume - mean) / standard deviation

z = (1 - 1) / 0.2

z = 0

A Z-score of 0 indicates that the target volume is equal to the mean. A standard normal distribution table or calculator can be used to find the probability that the amount should be increased.

However, the target amount is equal to the mean value,

In summary, without knowing the target amount to be dispensed in each case, it is not possible to determine the potential for volume increases.

If the target amount is to be £1 and the mean and standard deviation is also £1 and 0.2 respectively, then the probability of having to increase the amount is 0.

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