Please help me with this question.

Please Help Me With This Question.

Answers

Answer 1

The solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

What is initial value problem?In multivariable calculus, an initial value problem is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given point in the domain.

Given is the initial value problem -

y''' + 10y'' + 25y' = 0

We can write the -

[tex]$25 \frac{d}{d x} y{\left(x \right)} + 10 \frac{d^{2}}{d x^{2}} y{\left(x \right)} + \frac{d^{3}}{d x^{3}} y{\left(x \right)} = 0$[/tex]

The given differential equation can be solved and written as -

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6)

Therefore, the solution of the given differential initial value problem is

y(x) = 1/25 e⁻⁵ˣ(6e⁵ˣ - 5x - 6).

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Related Questions

Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $220. Now the cost is $305. What is the percent increase? What would be the percent increase if the airline charges an additional $50 baggage fee with the new ticket price?

Answers

Considering the context of the question and the percentage analysis, it is concluded that a 38.64% charge has been hiked in the price of the ticket and if the extra $50 is charged for the baggage fee the hike is 61.36%.

White at is the Percentage?

A percentage is a number or ratio indicated as a fraction of 100. To get the percentage of any number, such number will be divided by the number of the whole and multiplied by 100. Hence, the percentage means, a part per hundred

In this case, Cari is searching online for airline tickets. Two weeks ago, the cost to fly from Hartford to Orlando was $220. Now the cost is $305

Hike in price = 305 - 220 = 85

Hike % = 85/220 * 100% = 38.64%

When the extra charge is $50 for extra baggage, the total price = is $355

Hike in price = 355 - 220 = 135

Hike % = 135/220 *100% = 61.36%

Hence, in this case, it is concluded that a 38.64% charge has been hiked in the price of the ticket and if the extra $50 is charged for the baggage fee the hike is 61.36%

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Look at the picture and answer the question thank you

Answers

Answer:

given that z=3 and w=2

10z+5w

now by putting the values of z and w

10(3) + 5(2)

30 + 10

40 is your correct answer

Need the solution for this, question I don’t know what formula to use

Answers

The value of the specified finite sum is -15.

The correct option is D.

What is subtraction?

Subtraction is a mathematic operation. Which is used to remove terms or objects in an expression.

Given:

The finite sum,

[tex]\sum^n_{k=1}{a_k = 5[/tex],

and [tex]\sum^n_{k=1}{b_k = 10[/tex].

Now,

[tex]\sum^n_{k=1}{a_k -2b_k = \sum^n_{k=1}{a_k -2\sum^n_{k=1}{b_k[/tex]

Substituting the values,

[tex]\sum^n_{k=1}{a_k -2b_k[/tex] = 5 - 20

                      = -15

Therefore, the value is -15.

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The top of a hill rises 64 feet above checkpoint -213. What is the altitude of the hill?

Answers

The altitude of the hill whose top rises 64 feet above checkpoint -213, is 277 feet above sea level.

What is the altitude?

The altitude refers to the vertical distance or height of an object or point in relation to sea level (true altitude) or ground level (absolute altitude).

The altitude of a hill refers to its height measured from the ground level or the sea level, as the case may be.

In this situation, we can compute the altitude of the hill as the difference between the rise of the hill or mountain above the checkpoint and the given checkpoint.

The rise of the top of a hill = 64 feet

Given checkpoint = -213

The altitude of the hill = 277 feet [64 - (-213)]

Thus, the position or altitude of the hilltop in relation to the ground or sea level is 277 feet.

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One aircraft has a capacity of 64 more seats than a second
aircraft. A third aircraft has 152 seats less than twice the seating
capacity of the second aircraft. If their total number of seats is
1900, find the number of seats for each aircraft.

Answers

Therefore, the number of seats for each aircraft is 752, 688, and 1224.

Define Unitary method.

The unitary method is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.

What is multiplication?

Multiplying in math is the same as adding equal groups. The number of items in the group grows as we multiply. Parts of a multiplication issue include the product, the two factors, and the product. The components in the multiplication problem 6 x 9 = 54 are the numbers 6 and 9, and the result is the number 54.

Let x be the number of seats for the second aircraft.

The first aircraft has x + 64 seats.

The third aircraft has 2x - 152 seats.

The total number of seats for all aircraft is x + (x + 64) + (2x - 152) = 1900.

Therefore, 3x = 2064, so x = 688.

The first aircraft has 688 + 64 = 752 seats.

The third aircraft has 2(688) - 152 = 1224 seats.

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If 692 = 4,761, then 4,761 / 69 =​

Answers

Answer: 69

Step-by-step explanation:

In the equation 692 = 4,761, we can see that 692 is being multiplied by some number to get 4,761. To find that number, we can divide 4,761 by 692:

4,761 / 692 = 69.

So, 4,761 / 69 = 69

In this case, 692 is being multiplied by 69 to get 4,761, so 69 is the value we get when we divide 4,761 by 69.

Alison made 21/2 glasses of fruity iced tea for 7 her friends. Considering that each friend drank an equal quantity, how many glasses were served per person

Answers

Answer:

You could convert 21/2 to a whole number by multiplying it by 2 and then dividing by 2, so 21/2 = 21/2 = 10.5, then dividing the total by the number of people that is 10.5 / 7 = 1.5 glasses/person.

Marco budgets $1,600 a month for expenses.
According to the graph, how much does he pay
for his credit card, groceries, and rent?
$1,008
$908
$1,142
$1,029

Answers

Marco pays $1008  for for his credit card, groceries, and rent.

What is Percentage?

percentage, a relative value indicating hundredth parts of any quantity.

Given that Marco budgets $1,600 a month for expenses.

According to the graph he pays 4% of credit card

Now let us find 4% of 1600

4/100×1600

0.04×1600

$64 Marco pays for credit card.

From graph, he pays 17% for groceries

17% of 1600

17/100×1600

0.17×1600=$272

$272 Marco pays for Groceries.

From graph, he pays 42% for rent

42/100×1600

0.42×1600=672

$672 Marco pays for Rent.

Hence, Marco pays $1008  for for his credit card, groceries, and rent.

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A can of soda can be modeled as a right cylinder. Ajay measures its height as 8.9 cm
and its radius as 1.9 cm. Find the volume of the can in cubic centimeters. Round your
answer to the nearest tenth if necessary.

Answers

Answer:

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

So, using the given measurements, we can substitute in the values and solve for the volume:

V = π(1.9 cm)^2(8.9 cm) = 301.958 cm^3

Rounded to the nearest tenth, the volume of the can is 301.9 cm^3.

Step-by-step explanation:

Given that sin(x)+cos(x)=2/5, compute the following.
sin^3(x)+cos^3(x)
PLEASE HELP URGENT

Answers

The computation of sin^3(x) + cos^3(x) is mathematically given as (2/5)(1 - sin(x)cos(x))

What is trigonometry?

Generally, The study of the connections between the lengths of the sides of triangles and the angles of those triangles is the subject of the mathematical discipline known as trigonometry.

Applications of geometry to astronomical research gave rise to the discipline in the Hellenistic civilization during the third century B.C.

To compute sin^3(x) + cos^3(x), we can use the identity:

sin^3(x) + cos^3(x) = (sin(x) + cos(x))(sin^2(x) - sin(x)cos(x) + cos^2(x))

We know that sin(x) + cos(x) = 2/5, so we can substitute this into the above equation: sin^3(x) + cos^3(x) = (2/5)(sin^2(x) - sin(x)cos(x) + cos^2(x))

We also know that sin^2(x) + cos^2(x) = 1, so we can substitute this into the above equation:

sin^3(x) + cos^3(x) = (2/5)(1 - sin(x)cos(x))

Then we can simplify the above equation:

sin^3(x) + cos^3(x) = (2/5)(1 - sin(x)cos(x))

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Height of a hot air balloon. As a hot air balloon began to ride, the ground crew drove 1.2mi to an observation station. The initial observation from the station estimated the angle between the ground and the line of sight to the balloon to be 30. Approximately how high was the balloon at that point

Answers

Answer:

0.7 mile high

Step-by-step explanation:

tan 30 = height /1.2

so height =1.2 *tan30 = 1.2*0.58 = 0.7

A toy rocket is launched from the ground at an angle of 45° and an initial velocity of 100 feet
per second. How far does the rocket travel in the air before hitting the ground?

A. 170.7 ft
B. 213.4 ft
C. 312.4 ft
D.423.1 ft

Answers

[tex]\textit{Horizontal Range}\\\\ R=\cfrac{(v_0)^2\cdot \sin(2\theta )}{g} ~~ \begin{cases} v_o=\textit{initial velocity}\\ \theta =\textit{initial angle}\\ g=gravity\\[-0.5em] \hrulefill\\ v_o=100\\ \theta =45^o\\ g\approx 32~\frac{ft}{s^2} \end{cases}\implies R\approx\cfrac{(100)^2 \sin(2\cdot 45^o)}{32} \\\\\\ R\approx\cfrac{10000\sin(90^o)}{32}\implies R\approx\cfrac{10000(1)}{32}\implies R\approx 312.5~ft[/tex]

Gerber Product's Gerber Mixed Cereal for Baby contains, in each serving, 60 calories and 11 grams of carbohydrates.† Gerber Mango Tropical Fruit Dessert contains, in each serving, 80 calories and 21 grams of carbohydrates.† If you want to provide your child with 340 calories and 75 grams of carbohydrates, how many servings of each should you use?
Gerber Mixed Cereal for Baby
serving(s)
Gerber Mango Tropical Fruit Dessert
serving(s)

Answers

3 of mixed cereal and 2 of tropical fruit

(Look at picture) thanks! <3

Answers

Answer:

The annual passenger revenue of the rail transport corporation was $930 million when:

R = 930

-20|t-15| + 1,010 = 930

-20|t-15| = 80

|t-15| = 4

So, we can see that t-15 = 4 and t-15 = -4 both lead to an annual revenue of $930 million dollars.

To find the values of t, we add 15 to both sides of the equation:

t-15 = 4 => t = 19

t-15 = -4 => t = 11

So, the years where the passenger revenue was $930 million are:

2011

2019

Which graph show y is less than or equal to 3x-4?

Answers

The graph that shows that y is less than or equal to 3x - 4 is plotted and attached

how to plot the graph

The graph is plotted by forming a table of value, then tracing eaching point in the table and marking the points of intersection of the x and y

The points intersections later joined with a line

The table of value is formed for x = -2, 0, and2

y ≤ 3x - 4

for x = -2, y ≤ 3 * -2 - 4 = -10

for x = 0, y ≤ 3 * 0 - 4 = -4

for x = 2, y ≤ 3 * 2 - 4 = 2

table of value

x      y

-2    -10

0     -4

2      2

The graph is attached, the line is a solid line since the inequality is less than or "equal to". The shading is below because it is less than

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Explain how you could use mental math to find the following sum. Then find the sum. Support your answer with a model

Answers

The mental math for the fraction is shown below.

What is Fraction?

The fractional bar is a horizontal bar that divides the numerator and denominator of every fraction into these two halves.

The number of parts into which the whole has been divided is shown by the denominator. It is positioned in the fraction's lower portion, below the fractional bar.How many sections of the fraction are displayed or chosen is shown in the numerator. It is positioned above the fractional bar in the upper portion of the fraction.

Given:

Model: 1 1/4 + 2 1/3 + 3 2/3 + 4 1/2 + 5 1/2 + 6 3/4

Now, if we use mental math then we can add the whole number first.

1 + 2 + 3 + 4 + 5 + 6 = 21

Now, add the fraction with same denominator

1/3 + 2/3 = 3/3 = 1

1/2 + 1/2 = 1

1/4 + 3/4 = 4/4 = 1

Finally add all of them

21 + 1+ 1 +1= 24.

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The announcer said, ‘Ingrid won the 100 metre race in 13.9 seconds.’

Her time was originally measured to 2 decimal places.

What was the slowest time she could have run?​

Answers

Answer:

So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.

Step-by-step explanation:

Ingrid's time of 13.9 seconds was originally measured to 2 decimal places, which means that her actual time could be rounded to 13.9 seconds. To find the slowest time she could have run, we need to find the greatest value that could have been rounded down to 13.9 seconds.

Since the time was measured to 2 decimal places, this means that the hundredths place is known and the thousandths place can be anything between 0 and 9. So the slowest time she could have run is 13.99 seconds, as any time greater than that would have been rounded up to 14 seconds.

Match the image to the scale factor from FG to F'G'.
Image 1
F
F
Image 2
F'
F
Image 3
F'
F
F
Image 4
F
F
Image 5
F'
12
12
8
6
18
12
12
12
12
24
G'
G
G
G'
G
G'
G
F

Answers

The scale factor for each of the dilation is given as -

K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2

What is scale factor?

Direct variation of a quantity {y} with respect quantity {x} means that the value of {y} increases as the the value of {x} increases. Mathematically -

y = Kx

K = y/x

where -

{K} is scale factor. It also tells by how many times is {y}, greater than {x}.

Given is a line segment and its dilated image.

The scale factor is given by -

K = y/x

[1] -

K₁ = 18/12 = 3/2

[2] -

K₂ = 8/12 = 2/3

[3] -

K₃ = 12/12 = 1

[4] -

K₄ = 6/12 = 1/2

Therefore, the scale factor for each of the dilation is given as -

K₁ = 18/12 = 3/2K₂ = 8/12 = 2/3K₃ = 12/12 = 1K₄ = 6/12 = 1/2

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Please help me find answer

Answers

The answer is option c

What are two things that are the same for an angle of elevation in an angle of depression

Answers

Answer:

sight line & horizontal line

Step-by-step explanation:

varsitytutrs

u) A man working in a firm gets monthly Salary of Rs 65 000 Read the tax rates given below and answer the following question (Annual income 450,000 Cupto 450.000) 450,001 -5,50,000 5,50,001 - 7.50,000 7,50, 001-20, 00,000 Soln Tax rate 1% 10%. 20%. 30%​

Answers

answer

The man's annual salary is Rs 780,000 (65,000 x 12 months). Since his annual salary is below Rs 5,50,000, the tax rate applicable to him is 1%. Therefore, his tax liability would be Rs 7,800 (780,000 x 1%).

The annual salary of the man is Rs 780,000 and his total taxes is given by the relation T = Rs 9,000

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Since the man's monthly salary is Rs 65,000, his annual salary would be:

Annual salary = Monthly salary x 12

Annual salary = 65,000 x 12

Annual salary = 780,000

His annual salary of Rs 780,000 falls in the third tax bracket which is from 750,001 to 2,000,000.

So, the tax rate applicable to him would be 30%.

To calculate the amount of tax he would have to pay, we can use the formula:

Tax amount = Tax rate x Taxable income

where taxable income is the income above the lower limit of the tax bracket.

In this case, the taxable income would be:

Taxable income = Annual income - Lower limit of tax bracket

Taxable income = 780,000 - 750,001

Taxable income = 29,999

So, the amount of tax he would have to pay would be:

Tax amount = 30% x 29,999

Tax amount = 8,999.7

Rounding this to the nearest rupee gives us:

Tax amount = Rs 9,000

Hence , the man would have to pay Rs 9,000 in taxes on his annual salary of Rs 780,000.

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I need some help answering this question right here

Answers

The given expression can be as 2 + i as a complex number standard form.

Complex numbers:

The combination of a number and an imaginary number is a complex number. Complex numbers are symbolized by the symbol z and have the form a + ib. a and b are said to be real numbers.

The imaginary portion of the complex number can be represented by the letter i called the iota.  

Here i² = -1

Here we have

 [tex]\frac{4 +\sqrt{16 - 4(5)}}{2}[/tex]    

The above expression can be simplified as follows

=>  [tex]\frac{4 +\sqrt{16 - 20}}{2}[/tex]  

=>  [tex]\frac{4 +\sqrt{- 4}}{2}[/tex]    

As we know, [tex]i^{2} = -1[/tex]  

=>  [tex]\frac{4 +\sqrt{i^{2} (2)^{2} }}{2}[/tex]  

=> [tex]\frac{4+2i}{2}[/tex]  

=> [tex]\frac{2(2+i)}{2}[/tex]  

= 2 + i  

Therefore,

The given expression can be as 2 + i as a complex number standard form.

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In the equation for the exponential function, f ( x ) = P ( 1 + r ) ^ x, how do we find r (rate of change) algebraically?

Answers

Answer:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

Step-by-step explanation:

Given exponential function:

[tex]f(x)=P(1+r)^x[/tex]

Replace f(x) with y:

[tex]y=P(1+r)^x[/tex]

Divide both sides by P:

[tex]\dfrac{y}{P}=(1+r)^x[/tex]

Take natural logs of both sides:

[tex]\ln \left(\dfrac{y}{P}\right)=\ln (1+r)^x[/tex]

[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)=x \ln (1+r)[/tex]

Divide both sides by x:

[tex]\dfrac{1}{x}\ln \left(\dfrac{y}{P}\right)=\ln (1+r)[/tex]

[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]

[tex]\ln \left(\dfrac{y}{P}\right)^{\frac{1}{x}}=\ln (1+r)[/tex]

Raise both sides to power of e:

[tex]\large\text{$e^{\ln \left(\frac{y}{P}\right)^{\frac{1}{x}}}=e^{\ln (1+r)}$}[/tex]

[tex]\textsf{Apply the power law}: \quad e^{\ln x}=x[/tex]

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}=1+r[/tex]

Subtract 1 from both sides:

[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1=r[/tex]

Therefore, the equation to find r is:

[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]

Solve for y. -10 - 8y = 2y - 5

Answers

Answer:

y = -1/2

Step-by-step explanation:

Pre-Solving

We are given the equation -10 - 8y = 2y - 5.

We want to solve this equation for y.

To do that, we need to isolate y on one side of the equation.

Solving

To start, add 10 to both sides.

-10 - 8y = 2y - 5

+10               +10

________________

-8y = 2y + 5

Subtract 2y from both sides.

-10y = 5

Divide both sides by -10.

y = -5/10

-5/10 can be simplified to -1/2.

Hence, y = -1/2.

In a right triangle, cos (9x) = sin (6x - 10)°. Find the larger of the triangle's two
acute angles.

Answers

The larger acute angle in the right triangle is 60°

What is a right triangle?

A triangle with at least one angle a right angle, is called a right triangle.

Given that, In a right triangle, cos (9x) = sin (6x - 10)°.

We know that, sine and cosine of an angle are supplementary.

Therefore,

9x+6x-10 = 90

15x = 100

x = 20 / 3

Therefore, sin(6(20/3)-10)°

= sin(30)°

And also,

cos(9(20/3)

= cos(60)°

Hence, the larger angle is in the triangle is 60°

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Solve the following equation: x = 6.0% X 99.5% X 1.3 X 1.6

Answers

Answer:

0.124176

Step-by-step explanation:

.06 x .995 x 1.3 x 1.6= 0.124176

You change a percent into a decimal by dividing it by 100%

Last season Rio's football team scored 50 goals in 20 matches.
This season they scored 60 goals in 25 matches.
work out the mean number of goals per match for each season

Answers

The mean number of goals for two seasons is 2.44 goals per match.

What is the weighted average?

When the average is not of any individual rather it is an average of two or more groups or sets it is called a weighted average.

To obtain the weighted average we multiply no. of individuals by their averages and sum the next group in the previous procedure and divide them by the total no. of individuals.

Given, Last season Rio's football team scored 50 goals in 20 matches.

This season they scored 60 goals in 25 matches.

Therefore, The mean number of goals per match for each season is,

= (50 + 60)/(20 + 25).

= 110/45.

= 2.44 goals per match.

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I will give brainliest, if you get this correct

1) What is the probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the I.D's of five students from among ten students of which four are not of legal age? ​

Answers

Answer: The probability that a waitress will refuse to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students from among ten students of which four are not of legal age is 0.288 or 28.8%.

Step-by-step explanation:

he probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated using the binomial probability formula.

The binomial probability formula is: P(x) = (n choose x) * p^x * (1-p)^(n-x)

Where:

x = the number of successful outcomes (in this case, the number of minors refused service)

n = the total number of trials (in this case, the number of IDs checked)

p = the probability of a successful outcome in a single trial (in this case, the probability that a randomly chosen student is a minor)

In this case:

x = 3 (the number of minors refused service)

n = 5 (the number of IDs checked)

p = 4/10 (the probability that a randomly chosen student is a minor)

So, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students can be calculated as:

P(3) = (5 choose 3) * (4/10)^3 * (6/10)^2 = (10/3) * (0.16) * (0.36) = 0.288

Therefore, the probability of a waitress refusing to serve alcoholic beverages to only three minors if she randomly checks the IDs of five students is 0.288 or 28.8%.

It's worth noting that this problem assumes that the waitress randomly chooses the 5 students, if the waitress doesn't pick them randomly the result may be different.

Caleb is doing an obstacle course in gym class. First, he runs 500 meters and jumps over a hurdle. Then, he crawls through a 20-meter tunnel. Finally, he dribbles a soccer ball 100 meters to the finish line. How many kilometers long is the obstacle course?

Answers

Answer: An obstacle course is a series of challenging physical obstacles that must be completed in order to finish the course. To find out how many kilometers long the obstacle course is, you need to add up the distance that Caleb runs, jumps crawls, and dribbles.

First, we need to convert the 500 meters to kilometers by dividing it by 1000.

500 meters / 1000 = 0.5 kilometers

Then, we need to add the distance that Caleb crawls through the tunnel, which is 20 meters.

20 meters = 0.02 kilometers

Finally, we need to add the distance that Caleb dribbles the soccer ball, which is 100 meters.

100 meters = 0.1 kilometers

To find the total distance of the obstacle course, we need to add the distance that Caleb runs, jumps, crawls, and dribbles:

0.5 + 0.02 + 0.1 = 0.62 kilometers

So the obstacle course is 0.62 kilometers long.

Step-by-step explanation:

ANYONE GOOD AT MATH PLEASE HELP! SHOW YOUR WORK TOO PLEASE I BEG OF U

Answers

12-39/681-*02(7,0)8.902)4 I got this by adding subtracting and dividing
Other Questions
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