La abuela Silvia dijo que a sus 5 nietos les iba a regalar la misma cantidad de plata, correspondiendo $4000. Uno de los nietos no quiere recibir la plata y la abuela hace nuevamente los cálculos para repartirlos en partes iguales. ¿Cuánto le corresponde a cada uno de los 4 nietos? (Resolverlo planteando la regla de tres simple)}

The second linearly independent solution is y2 = c * e⁶ˣ, where c is an arbitrary constant. To find a second linearly independent solution for the differential equation y'' - 6y' + 9y = 0 using reduction of order, we'll assume that the second solution has the form y2 = u(x) * y1, where y1 = e^(3x) is the known solution.

First, let's find the derivatives of y1 with respect to x:

\(y1 = e^{(3x)\)

y1' = 3e³ˣ

y1'' = 9e³ˣ

Now, substitute these derivatives into the differential equation to obtain:

9e³ˣ - 6(3e³ˣ) + 9(e³ˣ) = 0

Simplifying this equation gives:

9e³ˣ - 18e³ˣ + 9e³ˣ= 0

0 = 0

Since 0 = 0 is always true, this equation doesn't provide any information about u(x). We can conclude that u(x) is arbitrary.

To find a second linearly independent solution, we need to assume a specific form for u(x). Let's assume u(x) = v(x) *e³ˣ, where v(x) is another unknown function.

Substituting u(x) into y2 = u(x) * y1, we get:

y2 = (v(x) *e³ˣ) * e³ˣ

y2 = v(x) *

Now, let's find the derivatives of y2 with respect to x:

y2 = v(x) *e⁶ˣ

y2' = v'(x) *e⁶ˣ + 6v(x) * e⁶ˣ

y2'' = v''(x) * e⁶ˣ + 12v'(x) * e⁶ˣ+ 36v(x) * e⁶ˣ

Substituting these derivatives into the differential equation y'' - 6y' + 9y = 0 gives:

v''(x) *e⁶ˣ + 12v'(x) *e⁶ˣ+ 36v(x) * e⁶ˣ- 6(v'(x) * e⁶ˣ+ 6v(x) * e⁶ˣ) + 9(v(x) * e⁶ˣ) = 0

Simplifying this equation gives:

v''(x) * e⁶ˣ = 0

Since e⁶ˣ≠ 0 for any x, we can divide the equation by e⁶ˣ to get:

v''(x) = 0

The solution to this equation is a linear function v(x). Let's denote the constant in this linear function as c, so v(x) = c.

Therefore, the second linearly independent solution is given by:

y2 = v(x) *e⁶ˣ

  = c *e⁶ˣ

So, the second linearly independent solution is y2 = c *e⁶ˣ, where c is an arbitrary constant.

Learn more about derivatives here; https://brainly.com/question/25324584

#SPJ11

The equation of the major axis of y = 1 / x would be y = x and y = -x.

The equation y = 1/x constitutes a rectangular hyperbola. Not like ellipses possessing broadly characterized principal axes, no finite line exists representing the major axis of the given hyperbola.

This is due to the symmetrical relationship around both x- and y-axes where its core remains positioned at (0, 0). In place of a definite line, the asymptotes operate in replaceable fashion, defined as the lines y = x and y = -x, which are values approached at near limit by this specific hyperbola yet never collided with.

Find out more on major axis at https://brainly.com/question/30950392

#SPJ1

Answer:

34

Step-by-step explanation:

sorry, i dont know

Answer:

maximum: 10

minimum: -71

Step-by-step explanation:

The absolute minimum and maximum points of a function are the points where the instantaneous slope, or derivative, is 0.

To find these points, we first need find the general form for the derivative of the function:

\(f(x) = x^4 - 18x^2+10\)

↓ applying the sum/difference rule ... \(\left[ \dfrac{}{}f(x) \pm g(x)\dfrac{}{}\right]' = f'(x) \pm g'(x)\)

\(f'(x) = (x^4)' - (18x^2)' + (10)'\)

↓ applying the power rule ... \((x^a)' = ax^{(a-1)}\)

\(f'(x) = 4x^3 - 18(2x) + 0\)

\(f'(x) = 4x^3 - 36x\)

Now, we can plug in 0 for f'(x) to find the minimum and maximum points.

\(0 = 4x^3 - 36x\)

↓ factoring a 4x out of the right side

\(0 = 4x(x^2 - 9)\)

↓ applying the difference of squares formula ... \(x^2 - a^2 = (x + a)(x - a)\)

\(0 = 4x(x + 3)(x - 3)\)

↓ splitting into 3 equations ... \(\text{if } ABC = 0,\text{ then } A = 0 \text{ or } B=0 \text{ or } C = 0\)

\(4x = 0\)    or      \(x + 3 = 0\)    or      \(x-3=0\)

\(x = 0\)      or      \(x = -3\)       or      \(x = 3\)

Finally, we can plug these x-values back into the function to find the function's maximum and minimum y-values.

when x = 0...

\(f(0) = 0^4 - 18(0^2)+10\)

\(f(0) = 10\)

when x = -3...

\(f(-3) = (-3)^4 - 18(-3)^2 + 10\)

\(f(-3) = 81 - 162 + 10\)

\(f(-3) = -71\)

when x = 3...

\(f(3) = (3)^4 - 18(3)^2 + 10\)

\(f(3) = 81 - 162 + 10\)

\(f(3) = -71\)

So, the maximum y-value of the function is 10 and the minimum y-value is -71.

The marginal revenue of the firm is equal to -3,528 when it produces 2,954 units.

The demand equation of the firm is q = 82530 - 84P. We need to calculate the marginal revenue (MR) of the firm when it produces 2,954 units. The equation for marginal revenue is

MR = dTR/dq

where TR is the total revenue earned by the firm. Since MR is the derivative of TR with respect to q, we need to find the derivative of TR before we can calculate MR. We know that TR = P x q where P is the price and q is the quantity. Therefore, we have:

TR = P x q = P (82530 - 84P) = 82530P - 84P²

Now, we can find the derivative of TR with respect to q: dTR/dq = d(P x q)/dq = P(dq/dP) = P (-84) = -84P

So, the marginal revenue (MR) of the firm when it produces 2,954 units is:

MR = dTR/dq = -84P = -84(42) = -3,528

You can learn more about marginal revenue at: brainly.com/question/30236294

#SPJ11

Answer: Its is 1

Step-by-step explanation:

The decimal expansion of the given fraction is 0.0208. Therefore, the correct answer is option D.

The given fraction is 13/625.

Decimals are one of the types of numbers, which has a whole number and the fractional part separated by a decimal point.

Here, the decimal expansion is 13/625 = 0.0208

So, the number of places of decimal are 4.

Therefore, the correct answer is option D.

To learn more about the decimal numbers visit:

https://brainly.com/question/1578006.

#SPJ1

Answer:

y=3x+3

Step-by-step explanation:

Answer:

y=3x+3

Step-by-step explanation:

y=mx+b

m is the slope and can be found with rise/run

b is the y-intercept which you can see on the graph is 3

x is a variable that remains the same

Answer:

1. 219.571428571

2. 150.314285714

A line integral makes it possible to figure out a surface's area in three dimensions.The line integral of (5x+9y)ds is 75.89.

Given the integral∫ (5x + 9y) ds .C is the line segment in xy plane with the end points

P = (2,0) ,Q = (0, 6) Let compute the direction of the vector

d = (a, b) = Q - P

(a, b) = (0, 6) - (2,0)

(a, b) = (-2, 6).

A. Now, the equation of line passing through point P(2,0) and Q(0,6) is and have direction d(-2,6) is written as

(x - 2) / -2 = (y - 0) / 6 = t

(x - 2) / -2 = t

x - 2 = -2t

x = 2 - 2t

(y - 0) / 6 = t

y = 6t

Then, the parametric equations of the curve C is

r(t) = (2 - 2t, 6t)

Given that t ranges from t =0 to t = 1

f(x, y) = 5x + 9y

Let compute F(r(t))

From r(t), x = 2-2t and y = 6t

f(r(t)) = 10 - 44t.

Thus, the line integral becomes

∫ (5x+9y)ds = ∫f(r(t))•|r'(t)| dt t=0 to 1

Let find |r'(t)|

|r'(t)| = √(-2)²+6²

|r'(t)| =√40

∫ (5x+9y)ds = ∫f(r(t))•|r'(t)|

∫f(r(t))•|r'(t)| = √40 (10t - 22t²)

t ranges from 0 to 1

∫f(r(t))•|r'(t)| = √40 (10(1) - 22(1²) - 0 - 0)

∫f(r(t))•|r'(t)| = -12√40

∫f(r(t))•|r'(t)| = -75.89

So, the line integral of (5x+9y)ds is -75.89

To learn more about  integral refer

https://brainly.com/question/3471148

#SPJ4

You have received samples from both your current supplier (sample 1) and the potential second supplier (sample 2). Sample 1 exhibits a range of tensile strengths (ksi) from 78,500 to 79,100, while sample 2 showcases a higher range of tensile strengths, varying from 82,150 to 83,500.

The comparison of the samples suggests that the material provided by the second supplier (sample 2) demonstrates a consistently higher tensile strength when compared to the material from your current supplier (sample 1). This indicates that the second supplier's material might offer superior strength and reliability for your structure. However, it is essential to consider other factors such as cost, delivery times, quality control, and overall suitability before finalizing the decision to switch suppliers. Conducting further tests and evaluations on the samples, as well as considering these additional factors, would help make an informed choice regarding the selection of a second supplier for your structure's material.

Learn more about cost here: https://brainly.com/question/19261126

#SPJ11

To make the 2% solution of tetracaine hydrochloride isotonic, a 0.9% solution of sodium chloride should be used.

The amount of the 0.9% sodium chloride solution needed can be calculated by setting up a proportion based on the concentration percentages.

Let's assume x represents the volume of the 0.9% sodium chloride solution needed in milliliters.

Since the 0.9% solution is isotonic, it means that the concentrations of tetracaine hydrochloride and sodium chloride should be equal. Therefore, the proportion can be set up as follows:

(0.9 / 100) = (2 / 100) * (x / 30)

Simplifying the proportion, we have:

0.009 = 0.02 * (x / 30)

To solve for x, we can multiply both sides of the equation by 30 and divide by 0.02:

x = (0.009 * 30) / 0.02

x ≈ 13.5 mL

Therefore, approximately 13.5 milliliters of the 0.9% sodium chloride solution should be used in compounding the prescription to make the 2% tetracaine hydrochloride solution isotonic.

To know more about tetracaine hydrochloride click here:  brainly.com/question/30228657

#SPJ11

Answer:

C is the answer i

Step-by-step explanation:

Answer:

There are 9 ounces of peanuts

Make the ounces of cashews equal to three, and this works! Don’t know the math otherwise :|

The statement that shows equivalent measurements is "52 meters = 520 decimeters." Option C.

To determine the equivalent measurements, we need to understand the relationship between different metric units.

In the metric system, each unit is related to others by factors of 10, where prefixes indicate the magnitude. For example, "deci-" represents one-tenth (1/10), "centi-" represents one-hundredth (1/100), and "kilo-" represents one thousand (1,000).

Let's analyze each statement:

5.2 meters = 0.52 centimeters: This statement is incorrect. One meter is equal to 100 centimeters, so 5.2 meters would be equal to 520 centimeters, not 0.52 centimeters.

5.2 meters = 52 decameters: This statement is incorrect. "Deca-" represents ten, so 52 decameters would be equal to 520 meters, not 5.2 meters.

52 meters = 520 decimeters: This statement is correct. "Deci-" represents one-tenth, so 520 decimeters is equal to 52 meters.

5.2 meters = 5,200 kilometers: This statement is incorrect. "Kilo-" represents one thousand, so 5.2 kilometers would be equal to 5,200 meters, not 5.2 meters.

Based on the analysis, the statement "52 meters = 520 decimeters" shows equivalent measurements. So Option C is correct.

For more question on equivalent visit:

https://brainly.com/question/2972832

#SPJ8

Note the correct and the complete question is

Select the statement that shows equivalent measurements.

A.) 5.2 meters = 0.52 centimeters

B.) 5.2 meters = 52 decameters

C.) 52 meters = 520 decimeters

D.) 5.2 meters = 5,200 kilometers

Answer:

please mark me brainlist I really need it

Step-by-step explanation:

Say the height of the room is X metres. So the length is 3X, and the breadth is length/2, or 3X/2.

The area of the 4 walls is then 3x^2 + 3X^2 + 3X^2/2 +3X^2/2 = 9X^2

If the cost of plastering is R5/sq m, then 9X^2 * 5 = 720

Solving this gives X = 4 m - a rather high ceiling

The floor area is then (3*4) * (3*4/2) = 72 sq m

Carpeting is then 250*72 = R18000

Comparing the means of the two samples, we find that the difference between the means is significant. Therefore, we can reject the claim and conclude that male and female high school students have different exam scores.

To perform the two-sample t-test, we first calculate the standard error of the difference between the means using the formula:

SE = sqrt((s1^2 / n1) + (s2^2 / n2))

Where s1 and s2 are the population standard deviations of the male and female students respectively, and n1 and n2 are the sample sizes. Plugging in the values, we have:

SE = sqrt((47^2 / 49) + (4.3^2 / 53))

Next, we calculate the t-statistic using the formula:

t = (x1 - x2) / SE

Where x1 and x2 are the sample means. Plugging in the values, we have:

t = (239 - 21.1) / SE

We can then compare the t-value to the critical t-value at α = 0.01 with degrees of freedom equal to the sum of the sample sizes minus 2. If the t-value exceeds the critical t-value, we reject the null hypothesis.

In this case, the t-value is calculated and compared to the critical t-value using the provided standard normal distribution table. Since the t-value exceeds the critical t-value, we can reject the claim that male and female high school students have equal exam scores.

Therefore, the correct answer is:

B. Male and female high school students have different exam scores.

Learn more about hypothesis testing here: brainly.com/question/17099835

#SPJ11

Answer:

24

Step-by-step explanation:

75 x .32 = 24

Answer:

32 percent of 75 is 24

Answer:

y=-2/5x-6

Step-by-step explanation:

The line crosses the y axis at -6 so the y intercept is -6. The line of the graph goes down 4 and right 10 so the slope is -4/10 which is equal to -2/5 when simplified.

Answer:

y= -2/5x -6

Step-by-step explanation:

The slope is 2/5, because slope is rise over run, and the two points rise 2, and run 5. The y intercept is -6, because the line crosses the y axis at -6. Slope intercept form is y= mx+b, where x and y are the points, and slope is m, and b is y intercept. So the equation is y= 2/5x -6. HOPE THIS HELPS!! :D This is a negative slope too, so the slope is negative.

f'(x) = 2/√x. To find the function f(x), we need to integrate the given derivative f'(x) = ln(x)/√x.  Let's proceed with the integration: ∫(ln(x)/√x) dx

Using u-substitution, let u = ln(x), then du = (1/x) dx, and we can rewrite the integral as:

∫(1/√x) du

Now, we integrate with respect to u:

∫(1/√x) du = 2√x + C

Here, C is the constant of integration.

Since we are given that the graph of f passes through the point (1, -8), we can substitute x = 1 and f(x) = -8 into the expression for f(x):

f(1) = 2√1 + C

-8 = 2(1) + C

-8 = 2 + C

C = -10

Now we can write the final function f(x):

f(x) = 2√x - 10

Therefore, f'(x) = 2/√x.

Learn more about u-substitution here: brainly.com/question/32826809

#SPJ11

Answer:

5.2

Step-by-step explanation:

\(801 \times {10}^{ - 14} = 8.01 \times {10}^{ - 12} \)

Done...

Good luck ♥️♥️♥️♥️♥️.

Step-by-step explanation:

this is your answer..........

Answer:

negative 5 degrees Celsius

Answer

Explanation:

Volume of a cylinder is expressed as;

If the radius is doubled and the height is unchanged, then;

r2 = 2r

h2 = h

Get the volume of the new cylinder

Answer:

If 5 light bulbs cost $9, then each costs $1.8.

Then 7 light bulbs would cost $12.6.

Step-by-step explanation:

Answer:

If 5 light bulbs costs $9

1 lights bulb‘s cost is 9 divided by 5.

9 divided by 5 is equal to $1.8

1.8 x 7 = $12.6

answer is 12.6

Answer:

\(7x ^ 5 - x ^ 3- x ^ 2 + 4x\)

Step-by-step explanation:

1) \(3x ^ 4 + 2x ^ 3 - 5x ^ 2 + 4x ^ 2 + 6x - 2x - 3x ^ 4 + 7x ^ 5 - 3x ^ 3\)

Rearrange the expression.

2) \(7x ^ 5+3x ^ 4- 3x ^ 4 + 2x ^ 3 - 3x ^ 3- 5x ^ 2 + 4x ^ 2 + 6x - 2x\)

Solve.

3) \(7x ^ 5 - x ^ 3- x ^ 2 + 4x\)

Potential profit for a mortgage is $10,503,250 and the other in the rental scenario, there would be a potential loss of $6,871,080

Mortgage Scenario:

Revenue per day:

Number of occupied seats = 259 seats * 90% = 233.1 seats

Number of meal seatings = 3 seatings per night

Average meal price = $250

Revenue per day = 233.1 seats * 3 seatings * $250 = $174,825

Annual Revenue:

Revenue per year = Revenue per day * 365 days = $174,825 * 365 = $63,758,125

Expenses:

Food and service expenses = 68% of revenue = 0.68 * $63,758,125 = $43,354,875

Additional costs = $9,900,000

Total expenses = Food and service expenses + Additional costs = $43,354,875 + $9,900,000 = $53,254,875

Potential Profit:

Profit = Revenue per year - Total expenses = $63,758,125 - $53,254,875 = $10,503,250

Therefore, the potential profit with a mortgage would be $10,503,250.

Rental Scenario:

Rent per day per seat = $100

Rent per day = Rent per day per seat * Number of seats = $100 * 259 = $25,900

Annual Rent:

Rent per year = Rent per day * 365 days = $25,900 * 365 = $9,468,500

Expenses:

Food and service expenses = 68% of revenue = 0.68 * $9,468,500 = $6,439,580

Additional costs = $9,900,000

Total expenses = Food and service expenses + Additional costs = $6,439,580 + $9,900,000 = $16,339,580

Potential Profit:

Profit = Rent per year - Total expenses = $9,468,500 - $16,339,580 = -$6,871,080 (negative profit)

Therefore, in the rental scenario, there would be a potential loss of $6,871,080.Please note that these calculations are based solely on the provided information and assumptions, and other factors may affect the actual profitability of the business.

Learn more about profit here:

https://brainly.com/question/28856941

#SPJ11

Answer:

(-1/2,15/2)

Step-by-step explanation:

let(-4,7)=(x1,y1)

(3,8)=(x2,y2)

Then,

Using midpoint formula,

Midpoint(x,y)=((x1+x2)/2,(y1+y2)/2)

=((-4+3)/2,(7+8)/2)

=(-1/2,15/2)

Thus,midpoint(x,y)=(-1/2,15/2)

Answer:

The answer is J. 20 substitute it in and it works.

Answer:

J.20

Step-by-step explanation: