Solve the differential equation y" + 4y' - 5y = 2x - 1 by first finding the particular solution, Yp, and then finding the general solution. You may use the results from the previous problem.

Answer: \(\frac{13}{24}\)

Step-by-step explanation: 11/12 - 3/8

1. First, we will find a common denomenator. It needs to be the least common factor, or the answer will not be in its simplist form. Let's take a look at the multiples of 12 and 8.

12: 12, 24, 36, 48, 60, 72, 84, 96

8: 8, 16, 24, 32, 40, 48, 56, 64, 72

2. Next, we will choose the smallest common multiple. That would be 24.

3. Now, we will work this out.

11/12 = 22/24

3/8 = 9/24

4. Subtract.

22/24 - 9/24

= 13/24

= \(\frac{13}{24}\)

I found the denomenators by multiplying.

Hope this answer helped!

Answer:

Let's find the equation of motion for Steve.

First, the things we know:

He hikes at a steady pace, so we can model this with a linear equation:

Distance = speed*time + initial position

or:

D(t) = S*t + p.

Where we make the assumption that the waterfall is our position 0m and the t = 0h is when he starts hiking.

Now we have two data points:

"After 2 hours he is 13 miles from the  waterfall"

We can represent this with the point (2h, 13mi)

"After 4 hours he is 6 miles from the waterfall."

We can represent this with the point (4h, 6mi).

The speed will be equal to the quotient between the total distance and the total time, this is:

S = (6mi - 13mi)/(4h - 2h) = -7mi/2h = -3.5 mph.

Then we can write the equation as:

D(t) = -3.5mph*t + p.

And we know that, when t = 2h, we have D(2h) = 13mi, replacing those in our equation we can find the value of p.

13mi = -3.5mph*2h + p

13mi = -7mi + p

13mi + 7mi = 20mi = p

Then the equation of motion is:

D(t) = -3.5mph*t + 20mi.

Whit this equation we can find the total time that Steeve needs to reach the waterfall.

Remember that the waterfall is at the position 0m, then he will arrive at the waterfall when:

  D(t) = 0m = -3.5mph*t + 20mi

  3.5mph*t = 20mi

                t = 20mi/3.5h = 5.7h

So he will get to the waterfall 5.7 hours after he begins hiking.

Answer:

Candy = $ 0.5

Soda = $ 4.0

Step-by-step explanation:

x + 2y = 5

x + 4y = 6

2y = 1

y = 1/2

= two candies were added and the price increased by 1 dollar, meaning that the a single candy is 0.5 dollar

1 candy = 0.5

x + 2(0.5) = 5

x + 1 = 5

x = 4

The value of a(t) is -1 and b(t) is 55 + \(e^t\)

No, the given equation y' - y = 55 + \(e^t\) is not in the standard form of a first-order linear differential equation.

In the method for solving a first-order linear differential equation, an integrating factor is a function used to transform the equation into a form that can be easily solved.

For an equation in the standard form y' + a(t)y = b(t), the integrating factor is defined as:

μ(t) = e^∫a(t)dt

To solve the equation, you multiply both sides of the equation by the integrating factor μ(t) and then simplify. This multiplication helps to make the left side of the equation integrable and simplifies the process of finding the solution.

To put it in standard form, we need to rewrite it as y' + a(t)y = b(t).

Comparing the given equation with the standard form, we can identify:

a(t) = -1

b(t) = 55 + \(e^t\)

Therefore, The value of a(t) is -1 and b(t) is 55 + \(e^t\)

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Answer:

Step-by-step explanation:

% means p/100

100(5/25)=20%

Answer:

The probability of picking the first boy is 14/26 and the probability of picking another boy is 13/25.

Step-by-step explanation:

Answer:

w = 17.4º OR 17 2/5º

Step-by-step explanation:

5w - 3 = 90º

5w = 90º - 3

5w = 87º

w = 17.4º OR 17 2/5º

Hope that helps, and sorry if it's wrong!

Answer:

Part A:

B. rhombus

Part B:

C. Opposite sides are parallel and congruent

Answer:

57.2

Step-by-step explanation:

This is a right triangle so we can use trig ratios.

We are asked to find a side when we know a angle adjacent to that side. And we are given a side opposite of that angle. We can use Tangent to find the side length.

\( \tan(40) = \frac{48}{x} \)

Take the reciprocal of both sides.

\( \frac{1}{ \tan( 40) ) } = \frac{x}{ 48} \)

Multiply both sides by 48.

\( x = \frac{1}{ \tan(40) } \times 48\)

\(x = 57.2\)

ToTo find the equation of the tangent to the curve at the given point, we first need to find the coordinates of the point and the slope of the tangent. 1. Find the coordinates of the point (x, y) at t = 1: x = e√1 = e^1 = e y = 1 - ln(1^4) = 1 - ln(1) = 1 So the point is (e, 1). 2. Find the derivatives dx/dt and dy/dt: dx/dt = (d/dt) e√t = e√t * (1/2) * t^(-1/2) = (1/2) * e√t * t^(-1/2) dy/dt = 1 - (1/t) 3. Find the slope of the tangent at t = 1: dx/dt (1) = (1/2) * e^1 * 1^(-1/2) = e/2 dy/dt (1) = 1 - (1/1) = 0 4. Calculate the slope dy/dx at the point (e, 1): dy/dx = (dy/dt) / (dx/dt) = 0 / (e/2) = 0 5. Use the point-slope form to find the equation of the tangent: y - y1 = m(x - x1) y - 1 = 0(x - e) So the equation of the tangent is y(x) = 1.




The given curve is x = e√t and y = t - ln t4. To find an equation of the tangent to the curve at the point corresponding to the given value of the parameter t = 1, we will use the formula of the slope of the tangent at the given point.

Most of the times, a tangent is defined as a straight line that touches the curve at only one point. It is at a point on a curve where its gradient is equal to that of the curve itself. The slope of the tangent at a point on the curve is equal to the value of the derivative at that point.

So, let's differentiate y with respect to t to obtain the derivative of y. Then we will substitute t = 1 in the derivative to get the slope of the tangent.dy/dt = 1 - 1/t4Let t = 1,dy/dt = 1 - 1/14 = 13/4So, the slope of the tangent at the point t = 1 is 13/4.Now, to find an equation of the , we need a point on the tangent. The given point on the tangent is (e, y) where y = t - ln t4 and t = 1.

Substituting t = 1 in the equation of y,y = 1 - ln 14Thus, the point on the tangent is (e, 1 - ln 14).Using the point-slope form of the equation of a straight line,y - y1 = m(x - x1)where m is the slope of the tangent and (x1, y1) is the given point on the tangent.

Substituting the values,m = 13/4, x1 = e and y1 = 1 - ln 14,y - (1 - ln 14) = (13/4)(x - e)Expanding the above equation,y - 1 + ln 14 = 13/4 x - 13/4e.

Thus, the equation of the tangent to the curve at the point corresponding to t = 1 is y - 1 + ln 14 = 13/4 x - 13/4e.

Therefore, the correct option is C. y - 1 + ln 14 = 13/4 x - 13/4.

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The ordered pairs which correctly lists all of the x-intercepts of the graphed function include the following: C. (1, 0), (2, 0), and (–3, 0).

In Mathematics, the x-intercept can be defined as the point at which the graph of a particular function crosses the x-coordinate (x-axis) and the value of "y" is equal to zero (0).

By critically observing the given graphed function (see attachment), the x-intercept is given by the following ordered pairs:

This ultimately implies that, this function would cross the x-coordinate (x-axis) at points (1, 0), (2, 0), and (-3, 0).

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The Sine Ratio is written as \(\frac{Perpendicular }{Hypoynuse}\) , then the maximum possible value of a Sine Ratio is 1 .

What is Sine Ratio ?

In a Right Triangle , the Sine of angle is defined as the ratio of length of the opposite side divided by the length of the hypotenuse .

we know that the domain for the Sine function is ⇒ all real numbers ;

and the range of Sine function is ⇒  [-1,1] ;

so , from the range we can conclude that , the maximum value is 1 .

Therefore , the maximum value of Sine ratio is = 1 .

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Answer:

The answer is x = 24 , y = 8√3

Hope it will help :)

Answer:

24\(x^{2}\) - 2x - 15

Step-by-step explanation:

f(x) = 4x + 3

g(x) = 6x - 5

(4x + 3) (6x - 5)

24\(x^{2}\) - 20x + 18x - 15

24\(x^{2}\) - 2x - 15

Answer:

0.0267m/s

Step-by-step explanation:

Given the following

Length of the wave = 10cm  = 0.1m

Time taken = 3.75seconds

Required

Wave speed in m/s

Speed = Distance/Time

Substitute the given values into the formula

Speed = 0.1/3.75

Speed = 0.0267m/s

Hence the speed of the wave in m/s is 0.0267m/s

Answer: 0.0267m/s

Step-by-step explanation: Hence the speed of the wave in m/s is 0.0267m/s because the Length of the wave = 10cm  = 0.1m

Wave speed in m/s

Speed = Distance/Time

Substitute the given values into the formula

Speed = 0.1/3.75

Speed = 0.0267m/s

Answer:

To find how much greater 4/5 is than 3/4 we can turn them into decimal values:

4/5 = 0.8

3/4 = 0.75

0.8 - 0.75 = 0.05

4/5 is 0.05 or 1/20 greater than 3/4

we will use the formula of tan(A+B)= (tanA+tanB)/(1-tanAtanB)

and tan(A-B)= (tanA-tanB)/(1+tanAtanB)

tan[(pie/4)+(x/2)]= [1+tan(x/2)]/[1-tan(x/2)] ......(1)

tan[(pie/4)-(x/2)]= [1-tan(x/2)]/[1+tan(x/2)]......(2)

now add the equation (1) and (2) which is LHS of question. So we get:

{[1+tan(x/2)]^2 + [1- tan(x/2)]^2}/1-tan^2(x/2)=2[1+tan^2(x/2)]/1-tan^2(x/2)= 2/cosx = 2secx =RHS

Hence proved.

Initial marked price of Shirt is Rs. 1000

First discount = 15%

New selling price = Rs. 850

Successive discount = 25%

Final selling price = 850 - (25/100) × 850 = Rs. 637.5

Answer:

This too easy yes or no? thanks for question.

Answer:

\(64\frac{1}{8}\)

Step-by-step explanation:

Convert mixed numbers to improper fractions, this is done by taking the denominator multiplying it by the whole number and adding that to the numerator. The denominator is kept the same

4 * 2 = 8 + 1 = 9

9/4

8 * 5 = 40 + 7 = 47

47/8

Use the LCM to be able to add both fractions. The LCM is 8

47/8 already has a denominator of 8, so only 9/4 has to be changed

9 * 2 = 18

4 * 2 = 8

Simplify

47/8 + 18/8

Add the numerators

47 + 18 = 65/8

Convert the improper fraction back to a mixed number

This is done by multiplying to the highest extent and placing the remainder as the numerator, the denominator is untouched.

8 * 8 = 64, we have a remainder of 1, which is the numerator. The denominator is untouched.

Simplify

64 1/8

The answer is 64 1/8

Answer:

6 times

Step-by-step explanation:

If there are total of 6 marbles and 3 are pink, then you will have a one half (or 50%) chance of picking a pink marble. Because you put the marble back each time, your chance of picking a pink marble remains the same every time.

So one half of 12 is 6. You are predicted to pick a pink marble 6/12 times.

Answer: Simplification of Fractions.

Step-by-step explanation:

Option B. $9,255.75, Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of

To find the present value of an infinite stream of cash flows, we can use the formula:

PV = CF / r

where PV is the present value, CF is the cash flow per period, and r is the interest rate per period.

In this case, CF = $100 (received at the end of each year forever) and r = 10%.

Plugging in the numbers, we get:

PV = $100 / 0.10 = $1,000

So the present value of the infinite stream of cash flows is $1,000.

However, we need to adjust for the fact that the cash flows are received at the end of each year, not at the beginning. To do this, we can use the formula:

PV = CF / (r - g)

where g is the growth rate of the cash flows, which in this case is 0 (since the cash flows are constant).

Plugging in the numbers, we get:

PV = $100 / (0.10 - 0) = $1,000

So the present value of the infinite stream of cash flows received at the end of each year is also $1,000.

Therefore, the answer must include the present value of an infinite stream of cash flows. Only option (b) includes a value close to $1,000, which is the present value of the infinite stream of cash flows.

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The first scenario described is an example of a retrospective cohort study.  The second scenario suggests a retrospective cohort study as well. The third scenario represents a cross-sectional study, where researchers conduct a survey among high school students to assess the prevalence of obesity and diabetes.

1. In the first scenario, a retrospective cohort study is conducted by tracking individuals over a 20-year period. The study begins in 1960 and collects data on cigar smoking practices. After 20 years, the participants are followed up to determine if they developed any cancers. This type of study design allows researchers to examine the long-term effects of smoking Cuban cigars.

2. The second scenario involves a retrospective cohort study as well. The objective is to study the long-term neurological effects of a discontinued anesthetic agent. The researchers identify patients who received the drug before it was discontinued and then assess the occurrence of subsequent neurological disorders. This study design allows for the examination of the relationship between exposure to the anesthetic agent and the development of neurological disorders.

3. The third scenario represents a cross-sectional study. Researchers aim to assess the prevalence of obesity and diabetes among high school students during their junior year. They conduct a survey to gather information on the students' current weight, diabetes status, and other relevant factors. A cross-sectional study provides a snapshot of the population at a specific point in time, allowing researchers to examine the prevalence of certain conditions or characteristics.

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Answer: -21x+35+11y

Step-by-step explanation:

7(-3x+5) +11y

7x-3 7x5

-21x+35+11y

you can't add, subtract, or anything with this, so this will be your final answer.

Answer:

The Answer is $95

Step-by-step explanation:

Let x and y be the per hour price of both activities. This gives us two equations which are:

\((1)2x+5y=205\\(2)3x+3y=240\)

Now we divide equation (2) by 3 so we get the value of y:

\(x+y=80\\y=80-x\)

Then we substitute y into equation (1):

\(2x+5(80-x)=205\\-3x=205-400\\-3x=(-195)\\3x=195\\x=65\)

Now we insert the in the equation we got for y:

\(y=80-x\\y=80-65\\y=5\)

The code for 1 hour of parasailing and 2 hours of horseback riding:

\(=x+2y\\=65+2(15)\\=95\)

The twins are 6 years old, and the oldest sister is 13 years old (since they were born seven years after their older sister).

7.3% of women under the age of 35. 6.9% of females aged 35 to 37. 6.8% of women aged 38 to 40 were female. 5.1% of females aged 41 to 42.

Starting out, let's assign some variables.

Let x represent the sister's older sister's age in years.

The twins' age is then x – 7. (since they were born seven years after their older sister).

We are told that the product of the three siblings' ages is 2693 more than the sum of their ages. This can be expressed algebraically as:

x(x - 7)(x - 7) = x + (x - 7) + (x - 7) + 2693

Simplifying this equation gives:

x³ - 21x² + 98x - 2693 = 0

We can see that x = 13 is a root of the equation, since:

13³ - 21(13)² + 98(13) - 2693 = 0

This means that (x - 13) is a factor of the equation.

We can use polynomial division or synthetic division to divide the equation by (x - 13) and obtain a quadratic equation:

x² - 8x + 207 = 0

The solutions of this quadratic equation are:

x = (8 ± sqrt(8² - 4(1)(207))) / 2 = 4 ± sqrt(241)

Since x represents the age of the older sister, which must be a positive integer, the only valid solution is:

x = 13

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Answer:

\(y = 2x - - 3\)

That's the answer. Hope this helps

Please could you give me brainliest

Answer:

0.4

Step-by-step explanation:

hope this helps :)

Answer:

It 3.3

Step-by-step explanation:

This is because I divided the two number given in both triangles (3 and 2). With that I got 1.5 as the factor scale of both triangle. I then used 1.5 and dicided it with 5 and I got 3.3 as my answer.

I hope this helped