can u answerr for me pls

Answer:

\(y(x)=3e^{\frac{x}{6}}+\frac{12}{7}xe^{\frac{x}{6}}\) (See attached graph)

Step-by-step explanation:

To solve a second-order homogeneous differential equation, we need to substitute each term with the auxiliary equation \(am^2+bm+c=0\) where the values of \(m\) are the roots:

\(36y''-12y'+y=0\\\\36m^2-12m+1=0\\\\(6m-1)^2=0\\\\6m-1=0\\\\6m=1\\\\m=\frac{1}{6}\)

Since the values of \(m\) are equal real roots, then the general solution is \(y(x)=C_1e^{m_1x}+C_2xe^{m_1x}\).

Thus, the general solution for our given differential equation is \(y(x)=C_1e^{\frac{x}{6}}+C_2xe^{\frac{x}{6}}\).

To account for both initial conditions, take the derivative of \(y(x)\), thus, \(y'(x)=\frac{C_1}{6}e^{\frac{x}{6}}+\frac{C_2}{6}e^{\frac{x}{6}}+C_2e^{\frac{x}{6}}\)

Now, we can create our system of equations given our initial conditions:

\(y(x)=C_1e^{\frac{x}{6}}+\frac{C_2}{6}xe^{\frac{x}{6}}\\ \\y(0)=C_1e^{\frac{0}{6}}+\frac{C_2}{6}(0)e^{\frac{0}{6}}=3\\ \\C_1=3\)

\(y'(x)=\frac{C_1}{6}e^{\frac{x}{6}}+\frac{C_2}{6}e^{\frac{x}{6}}+C_2e^{\frac{x}{6}}\\\\y'(0)=\frac{C_1}{6}e^{\frac{0}{6}}+\frac{C_2}{6}e^{\frac{0}{6}}+C_2e^{\frac{0}{6}}=\frac{5}{2}\\ \\\frac{C_1}{6}+\frac{C_2}{6}+C_2=\frac{5}{2}\)

We then solve the system of equations, which becomes easy since we already know that \(C_1=3\):

\(\frac{C_1}{6}+\frac{C_2}{6}+C_2=\frac{5}{2}\\\\\frac{3}{6}+\frac{C_2}{6}+C_2=\frac{5}{2}\\\\3+C_2+6C_2=15\\\\7C_2=12\\\\C_2=\frac{12}{7}\)

Thus, our final solution is:

\(y(x)=C_1e^{\frac{x}{6}}+C_2xe^{\frac{x}{6}}\\\\y(x)=3e^{\frac{x}{6}}+\frac{12}{7}xe^{\frac{x}{6}}\)

Step-by-step explanation:

To work out the height of the cuboid, we need to use the formula:

Volume = Length x Width x Height

We have been given the volume and the length, so we can substitute those values into the formula:

540 = 6 x Width x Height

Now we need to convert the width from millimeters to centimeters, so we divide it by 10:

150mm ÷ 10 = 15cm

Substituting this value into the formula:

540 = 6 x 15 x Height

Simplifying:

540 = 90 x Height

Dividing both sides by 90:

6 = Height

Therefore, the height of the cuboid is 6cm.

Answer:

1)   13    **Explained below **

2)   4    **Explained below **

3)   6

4)   8

5)   15

6)   2.64575    **Explained below **

Step-by-step explanation:

All 6 problems can be solved using the Pythagorean theorem using the following two rules

If x is the hypotenuse and a, b are the shorter sides then
\(x = \sqrt{a^2 + b^2}\)

If x is one of the shorter sides and a (or b) is the other shorter side and c is the hypotenuse then

\(x = \sqrt{c^2 - a^2\\\)  if a is the other shorter side

\(x = \sqrt{c^2 - b^2\\\)  if b is the other shorter side

I will just demonstrate for  #1 , #2 and #6. You can figure out the reasoning behind the rest.

#1. x is the hypotenuse, 5 and 12 are legs(shorter sides)

\(x = \sqrt{5^2 + 12^2}\\\\x = \sqrt{25 + 144}\\\\x = \sqrt{169}\\\\x = 13\\\\\)

# 2. x is one of the shorter sides (leg)

5 is the hypotenuse and 3 is the other shorter side

\(x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{5^{2} - 3^{2}}\\\\x = \sqrt{25 - 9}\\\\x = \sqrt{16}\\\\x = 4\)

#6  hypotenuse is 4, short side = 3

\(x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{4^{2} - 3^{2}}\\\\x = \sqrt{16 - 9}\\\\x = \sqrt{7}\\\\x = 2.64575\\\\\)

Let

x ------> number of student tickets that the drama club must sell

so

we have

and

the values of x lie on the interval [48.5,52]

therefore

all possible values for the number of student tickets are on the interval

[49,52]

Answer: 17500 meters

Step-by-step explanation: 7 times 2.5 is 17.5 and one meter is 0.001 kilometers so

17.5 in meters is 17500.

Answer:

you can get 4 pieces

Step-by-step explanation:

2.5+2.5+2.5+2.5=10. or 2.5×4=10

Answer:It´s asking what the vale of P(4,3) is equal to and it´s P(4, 3) = 24

Step-by-step explanation:

Given statement solution is :- Interpreting the steady matrix:

The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.

The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.

The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.

To analyze the steady matrix for this situation, let's consider the two groups of customers: those who turn in tickets and those who do not turn in tickets.

Let's denote the proportion of customers who turn in tickets as X and the proportion of customers who do not turn in tickets as Y.

According to the given information:

40% of the customers who turn in tickets do not turn in tickets the following week. This means that 60% of the customers who turn in tickets will turn in tickets again the following week.

30% of the customers who do not turn in tickets will turn in tickets the following week. This means that 70% of the customers who do not turn in tickets will continue not turning in tickets the following week.

Based on these percentages, we can construct the steady matrix:

java

Copy code

     |  Customers turning in tickets (X) | Customers not turning in tickets (Y) |

----------|----------------------------------|--------------------------------------|

Next week 0.6 0.3

This week 0.4 0.7

Interpreting the steady matrix:

The value 0.6 in the top left cell represents the proportion of customers who turn in tickets this week and will turn in tickets again next week.

The value 0.3 in the top right cell represents the proportion of customers who turn in tickets this week but will not turn in tickets next week.

The value 0.4 in the bottom left cell represents the proportion of customers who do not turn in tickets this week but will turn in tickets next week.

The value 0.7 in the bottom right cell represents the proportion of customers who do not turn in tickets this week and will continue not turning in tickets next week.

These values describe the transition probabilities between the two customer groups. For example, if there are 100 customers in total, 60 of them will turn in tickets next week, and 40 of them will not. Similarly, 30 customers who turn in tickets this week will not do so next week, while 70 customers who do not turn in tickets this week will continue to not turn them in next week.

The steady matrix provides a snapshot of the probabilities of transitioning between the two states (turning in tickets or not turning in tickets) in the long run, assuming these probabilities remain constant over time.

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Answer:

$12.55

Step-by-step explanation:

25-6.75=18.25

18.25-3.70=14.55

14.55-2=12.55

Miguel has $12.55 left

Answer:

Step-by-step explanation:

The graph is all points to the left from -1, where -1 is not included

Answer:

Step-by-step explanation:

\( step - 1 : define\)

\( \sin( {30}^{o} ) = \frac{a}{12} \)

\( step - 2 : solve\)

Check the picture below.

so is more or less the figure of a rectangular prism with a right-cylinder underneath that has a radius of 1, since it has a diameter of 2.

now, if we just get the volume of the prism, and then the volume of half of the cylinder, because only half-cylinder is really inside the prism, and then subtract that half-cylinder volume from that of the prism, what's leftover is the volume of the figure only.

\(\stackrel{\textit{volume of a cylinder}}{V=\pi r^2 h}\hspace{5em}\stackrel{\textit{volume of half a cylinder}}{V=\cfrac{1}{2}\pi r^2 h} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE volumes}}{\stackrel{prism}{(4)(4)(8)}~~ - ~~\stackrel{half~cylinder}{\cfrac{1}{2}\pi (\underset{r}{1})^2(\underset{h}{8})}}\implies 128~~ - ~~4\pi ~~ \approx ~~\text{\LARGE 115.43}~cm^3\)

Answer:  A) 480

Step-by-step explanation:

x=20 substitute in the two equations

48(20)+37

24(20)+37

since the question said fewer , then you should subtract

48(20)+37 - 24(20)+37 = (960+37) - (480+37)

=923 - 443= 480

Students will have 517 hats to sell, that is 480 fewer than determined.

The correct option is B.

A linear equation is an algebraic equation where each term has an exponent of 1 and when this equation is graphed, it always results in a straight line.

Given,

Total hats = Left hats of last year + 20 boxes of hats newly ordered

Total hats

f(x) = 48x + 37

where x is number of boxes

But number of hats per box changes,

h(x) = 24x + 37

fewer no. of hats than determined

f(x) - h(x) = 48x + 37 - 24x - 37

f(x) - h(x) = 24x

No. of boxes = 20

No. of hats fewer than determined = 24 × 20 = 480

And no. of hats available

h(20) = 480 + 37

h(20) = 517

No. of hats available to sell = 517

Hence, 517 hats are available to sell that is 480 fewer hats than determined

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Answer:

3.8

Step-by-step explanation:

6 - 2 1/5 = 6 - 11/5

= 6-2.2

=3.8

The difference between the 6 and 2 1/5 will be 3.8

A fraction represents a part of a number or any number of equal parts. There is a fraction, containing numerator(upper value) and denominator(lower value).  When the numerator is less than the denominator, the fraction is called proper fraction, otherwise it is called improper fraction. A proper fraction is also called fraction which is less than 1. A mixed fraction contains a sum of whole number and a proper fraction.

So, WE need to find the difference between the 6 and \(2 \frac{1}{5}\).​

First we need to convert the mixed fraction into simple fraction.

\(2 \frac{1}{5}\) = 11/5

Therefore, the difference between them will be;

6 -  \(2 \frac{1}{5}\)  = 6 - 11/5

= 6 - 2.2

= 3.8

Hence, the difference between the 6 and \(2 \frac{1}{5}\) will be 3.8

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On solving the provide question, we can say that - the quadratic equation \((6a^2 + 4b)(a^2 - b)\) = -4

A quadratic equation is x ax2+bx+c=0, which is a quadratic polynomial in a single variable. a 0. The Fundamental Theorem of Algebra ensures that it has at least one solution since this polynomial is of second order. Solutions may be simple or complicated. An equation that is quadratic is a quadratic equation. This indicates that it has at least one word that has to be squared. The formula "ax2 + bx + c = 0" is one of the often used solutions for quadratic equations. where are numerical coefficients or constants a, b, and c. where the variable "X" is unidentified.

here, we have

\((6a^2 + 4b)(a^2 - b)\)

a = 0 and b = 1

-4

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Answer:

greater

Step-by-step explanation:

The value of y at x =15 is 9.

Two variables are said to be in Direct Variation when increasing one variable the other also increases.

The direct variation is represented by

y ∝ x

y = kx

where k is the proportionality constant

the value of y =12 , x = 20

12 = k * 20

12/20 = k

k = 0.6

The equation becomes

y = 0.6 x

The value of y at x = 15 is

y = 0.6 * 15

y =9

Therefore, the value of y at x =15 is 9.

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a.) The value of pulses exported by US in billion would be=30 billion.

b.) The ratio of wheat export of UK to maize export of IND would be= 6:5

For question a.)

To calculate the pulses, the following steps should be taken as follows:

From the bar chart, the value of pulses in billions = 30 billions.

For question b.)

The ratio of wheat export at UK and maize export at IND would be calculated as follows:

The quantity of wheat export at UK = 24

The quantity of maize export at IND = 20

Therefore, the ratio of wheat to maize = 24:20= 6:5

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Answer:

p=4

q=2

s=1

t=1/2

Step-by-step explanation:

8,p,q,s,t,1/4

number of terms=6

first term a=8

last term a_{n}=1/4

\(a_{n}=ar^{n-1}\\\frac{1}{4}=8(r)^{6-1}\\\frac{1}{32}=r^5\\(\frac{1}{2})^5=r^5\\r=\frac{1}{2}\\p=8\times r=8 \times (\frac{1}{2})=4\\q=pr=4 \times(\frac{1}{2})=2\\s=qr\\s=2 \times (\frac{1}{2})=1\\t=sr\\=1 \times (\frac{1}{2})=\frac{1}{2}\)

Move it to the left 4 times, move it up once

Answer:

1. c; 2. a; 3. b

Step-by-step explanation:

A(3,-1) translated to (3-4, -1+1)=(-1,0); then reflecting to x=1 (in this case, y doesn't change, and only x value change. x=-1 is 2 unit left side of x=1 line, so new reflected x value would be 2 unit right side of x=1 line, which is 3) gives (3,0).

B(7,1) --> (3,2) --> (-1,2)

C(5,-4) --> (1,-3)--> (1,-3)  

Answer:

1. D

2. AE (with a line above the 2 letters)

3. AC (with an arrowpointing to the right above the 2 letters)

4. B, A, and C

The slope in the equation p = 52 + 0.04w represents the rate of change in the water bill payment for each additional unit of water consumed.

Specifically, the slope of 0.04 indicates that for every increase of one unit in the number of water units (w), the water bill payment (p) will increase by 0.04 dollars.

This means that the slope represents the incremental cost of each additional unit of water.

In practical terms, the slope of 0.04 implies that for every additional unit of water consumed, the water bill will increase by $0.04.

This indicates a constant rate of increase in the water bill for each additional unit of water used.

It's important to note that the slope remains constant throughout the equation, suggesting a linear relationship between the amount of water consumed and the corresponding bill payment.

Therefore, The slope, in this case, is the coefficient of the variable w, which is 0.04.

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The probable question may be:

What is the meaning of the slope in the equation p = 52 + 0.04w, which models the relationship between the water bill payment p in dollars and the number of units of water w ?

The expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2) Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

The property of exponents that must be applied to the expression p^(1/2) to derive p as the result is the Power of a Power Property.

The Power of a Power Property states that when a power is raised to another power, the exponents are multiplied.

For instance, consider the expression p^(1/2). We can apply the Power of a Power Property to this expression as follows: p^(1/2) = (p^(1/2))^1 By applying the Power of a Power Property, the exponent (1/2) is multiplied by the exponent 1, giving a result of 1/2.

Therefore, the expression becomes: p^(1/2) = p^(1/2 * 1) = p^(1/2)Now we can simplify p^(1/2) as p^1/2 which equals the square root of p.

So we have derived p as the result using the Power of a Power Property.

In summary, we must apply the Power of a Power Property to the expression p^(1/2) to derive p as the result.

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Answer:

Step-by-step explanation:

let x be necromancers and y be wizards

if you know the amount of wizards and want to find the amount of necromancers. you just use y + 6

but if you know the amount of necromancers and want to find out the amount of wizards you just do x - 6

Answer:

140°

Step-by-step explanation:

Since we know that a circle is 360 degrees, and we are given three angles, we can subtract what we know from 360 to get ∠PTQ:

360 = 120 + 60 + 40 + ∠PTQ

360 = 220 + ∠PTQ

-220   -220

140 = ∠PTQ

∠PTQ = 140°

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Answer:

\(x=7\)

Step-by-step explanation:

\(3x+2x+4=39 \\ \\ 5x+4=39 \\ \\ 5x=35 \\ \\ x=7\)

Answer:

60 (0.25)

Step-by-step explanation:

Answer:

The 95% Confidence Interval for the difference between the two population mean completion times =

(0.081, 1.919)

Step-by-step explanation:

Confidence Interval for difference between two means =

μ1 -μ2 ± z × √ σ²1/n1 + σ²2/n2

Where

μ1 = mean 1 = 12 mins

σ1 = Standard deviation 1 = 2 mins

n1 = 100

μ2= mean 2 = 11 mins

σ2 = Standard deviation 2 = 3 mins

n1 = 50

z score for 95% confidence interval = 1.96

μ1 -μ2 ± z × √ σ²1/n1 + σ²2/n2

= 12 - 11 ± 1.96 × √2²/100 + 3²/50

= 1 ± 1.96 × √4/100 + 9/50

= 1 ± 1.96 × √0.04 + 0.18

= 1 ± 1.96 × √0.22

= 1 ± 1.96 × 0.469041576

= 1 ± 0.9193214889

Confidence Interval

= 1 - 0.9193214889

= 0.0806785111

≈ 0.081

1 + 0.9193214889

= 1.9193214889

≈ 1.919

Therefore, the 95% Confidence Interval for the difference between the two population mean completion times =

(0.081, 1.919)

Answer:

Some unhealthy methods is eating too much, sleep, and not working out everyday

Step-by-step explanation:

these are unhealthy because it increase stress and harm on your body