Solve the first order linear differential equation dy/ dx +3y=2x+8 y(0)=0 y(x)=
Answers
The general solution to the first-order linear differential equation dy/dx + 3y = 2x + 8 is y(x) = x^2 + 8x.
To obtain the general solution, we start by rearranging the equation to the standard form of a linear first-order differential equation:
dy/dx + 3y = 2x + 8
The integrating factor μ(x) is given by
μ(x) = e^(∫3 dx) = e^(3x).
We multiply both sides of the equation by μ(x) to make the left-hand side exact:
e^(3x)dy/dx + 3e^(3x)y = 2xe^(3x) + 8e^(3x)
Applying the product rule, we can rewrite the left-hand side as d(ye^(3x))/dx = 2xe^(3x) + 8e^(3x)
Integrating both sides with respect to x, we have
∫d(ye^(3x))/dx dx = ∫(2xe^(3x) + 8e^(3x)) dx
Simplifying, we get ye^(3x) = ∫(2xe^(3x) + 8e^(3x)) dx
Integrating and applying the constant of integration, we have
ye^(3x) = x^2e^(3x) + 8xe^(3x) + C.
Dividing both sides by e^(3x), we obtain
y(x) = x^2 + 8x + Ce^(-3x).
Since y(0) = 0, we can substitute this initial condition into the equation to find the specific value of C:
0 = 0 + 0 + Ce^(-3*0).
Solving for C, we have C = 0.
Therefore, the particular solution satisfying the initial condition is y(x) = x^2 + 8x.
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Related Questions
HELP ME PLS PLS PLS The maximum number of oranges in a box of volume one cubic foot can be modeled by the inequality |x − 17| ≤ 5, depending on the size of the oranges. Solve the inequality to find the greatest and least numbers of oranges that could be in a box. Complete the explanation of how you found your answer.
The box can contain a minimum of ___ oranges and a maximum of ____ oranges. The inequality needs to be split into ____ and ____ before solving. The solutions to each of these inequalities can be combined to make ___ ≤ x ≤ ___
Answers
Answer:
The first two blanks are 12 and 22 and the last two blanks are 12 and 22
Step-by-step explanation:
right triangle abc is shown. triangle a b c is shown. angle a c b is a right angle and angle c b a is 50 degrees. the length of a c is 3 meters, the length of c b is a, and the length of hypotenuse a b is c. which equation can be used to solve for c? sin(50o)
Answers
The equation that can be used to solve for c in the given right triangle is the sine function: c = (3 meters) / sin(50°).
In the given right triangle ABC, we are given that angle ACB is a right angle (90°) and angle CBA is 50°. We also know the length of side AC, which is 3 meters. The length of side CB is denoted by "a," and the length of the hypotenuse AB is denoted by "c." To solve for c, we can use the trigonometric function sine (sin). In a right triangle, the sine of an acute angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. In this case, we can use the sine of angle CBA (50°) to find the ratio between side CB (a) and the hypotenuse AB (c).
The equation c = (3 meters) / sin(50°) represents this relationship. By dividing the length of side AC (3 meters) by the sine of angle CBA (50°), we can find the length of the hypotenuse AB (c) in meters. Using the given equation, we can calculate the value of c by evaluating the sine of 50° (approximately 0.766) and dividing 3 meters by this value. The resulting value will give us the length of the hypotenuse AB, completing the solution for the right triangle.
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all real numbers less than 69
Answers
Answer:
68
Step-by-step explanation:
68 numbers from 1 to less than 69
PLEASE LED ME THE ANSWER
ILL GIVE YOU 20 POINTS
Answers
Answer:
DEC+DEF=180
DEC=180-116
DEC=64°
in triangle DCE
angle D+angle C+angle E=180
7y+6+4y+64=180
11y+70=180
11y=180-70
11y=110
y=110/11
y=10°
angle C=4y
=4(10)
=40°
Please answer this in two minutes
Answers
Answer:
∠ G ≈ 38.9°
Step-by-step explanation:
Using the cosine ratio in the right triangle
cos G = \(\frac{adjacent}{hypotenuse}\) = \(\frac{GH}{GI}\) = \(\frac{7}{9}\) , thus
∠ G = \(cos^{-1}\) (\(\frac{7}{9}\) ) ≈ 38.9° ( to the nearest tenth )
Step by step below
Complete the sentence about Pattern G and Pattern H. Use the table
to help. Can you help me ?
H
0
0
8
2
16
24
6
the
Each term in Pattern Gis
corresponding term in Pattern H.
of
2 times
4 times
111 of
+
11
Complete
Answers
Answer:
It would be 4 times
Step-by-step explanation:
How does the minimum or maximum value of a parabola relate to the vertex of the same parabola?
Answers
Answer:
The graph of a quadratic function is a U-shaped curve called a parabola. ... If the parabola opens up, the vertex represents the lowest point on the graph, or the minimum value of the quadratic function. If the parabola opens down, the vertex represents the highest point on the graph, or the maximum value.
Step-by-step explanation:
please mark me brainlist
The relationship between the vertex and the minimum or maximum value of the parabola is given below.
What is a parabola?A plane curve produced by a moving point such that its separation from a fixed point equals that of a fixed line is a parabola.
Let the vertex be any parabola is (x, y).
When the graph of the parabola opens up,
then the y-value of the vertex is the minimum value.
And when the graph of the parabola opens down,
then the y-value of the vertex is the maximum value.
Therefore, the explanation is given above.
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I don't know what im doing I need help!
Answers
Answer:
(D) 336 ft²
Step-by-step explanation:
The lateral surface area of the right rectangular prism = 2( l + w )h = Ph
L.S.A. = 2(14 + 7)8 = 336 ft²
D 336 ft²
Drag each tile to the correct box.
Answers
Answer:
The order is 4) → 5) → 6) → 7) → 2) → 1) → 3)
Please find diagram with the arrangements
Step-by-step explanation:
The horizontal width of an hyperbola
For
1) \(\dfrac{(y - 11)^2}{7^2} -\dfrac{(x - 2)^2}{6^2} = 1\)
h = 2, k = 11
The widths are;
Horizontal (h - a, k) to (h + a, k) which is (2 - 7, 11) to (2 + 7, 11) = 14 units wide
(h, k - b) to (h, k + b) which is (2, 11 -6) to (2, 11 + 6) = 12 units wide
2)
\(\dfrac{(y - 1)^2}{5^2} -\dfrac{(x - 7)^2}{12^2} = 1\)
h = 7, k = 1
(h - a, k) to (h + a, k) which is (7 - 5, 1) to (7 + 5, 1) = Horizontal width 10 units wide
(h, k - b) to (h, k + b) which is (7, 1 -12) to (7, 1 + 12) = 24 units wide
3) \(\dfrac{(x - 6)^2}{6^2} -\dfrac{(y + 1)^2}{3^2} = 1\)
h = 6, k = -1
a = 8, b = 3
The widths are;
(6 - 8, -1) to (6 + 8, -1) Horizontal width = 16
(6, -1 - 3) to 6, -1 + 3) width = 6
4) \(\dfrac{(x - 4)^2}{2^2} -\dfrac{(y + 2)^2}{5^2} = 1\)
h = 4, k = -2, a = 2, b = 5
(4 - 2, (-2)) to (4 + 2, (-2)) Horizontal width = 4
(4, -2 - 5) to (4, -2 + 5) width = 10
5) \(\dfrac{(y + 5)^2}{2^2} -\dfrac{(x + 4)^2}{3^2} = 1\)
h = -4, k = -5, a = 2, b = 3
(-4 - 2, (-5)) to (-4 + 2, (-5)) Horizontal width = 4
(-4, -5 - 3) to (4, -5 + 3) width = 6
6) \(\dfrac{(y + 1)^2}{2^2} -\dfrac{(x - 1)^2}{9^2} = 1\)
h = 1, k = -1, a = 2, b = 9
(1 - 2, (-1)) to (1 + 2, (-1)) Horizontal width = 4
(1, -1 - 9) to (1, -1 + 9) width = 18
7) \(\dfrac{(x + 7)^2}{4^2} -\dfrac{(y - 9)^2}{9^2} = 1\)
h = -7, k = 9, a = 4, b = 9
(-7 - 4, 9) to (-7 + 4, 9) Horizontal width = 8
(-7, 9 -9) to (-7, 9 + 9) width = 18
Reduce 9/153 to simplest terms.
Answers
Answer:
1/17
Step-by-step explanation:
Answer:
1/17
Step-by-step explanation:
Please mark brainliest!!! Have a awesome dayyy^_^ :33
ANSWER ASAP AND PLEASE BE CORRECT FOR BRAINLIST PLEASE HURRY IT'S DUUE IN 4 MORE HOURS AND I WILL FAIL PLEASE HELP ME !
Question 12
A recent conference had 750 people in attendance. In one exhibit room of 70 people, there were 18 teachers and 52 principals. What prediction can you make about the number of principals in attendance at the conference?
There were about 193 principals in attendance.
There were about 260 principals in attendance.
There were about 557 principals in attendance.
There were about 680 principals in attendance.
Question 13
A college cafeteria is looking for a new dessert to offer its 4,000 students. The table shows the preference of 225 students.
Ice Cream Candy Cake Pie Cookies
81 9 72 36 27
Which statement is the best prediction about the number of cookies the college will need?
The college will have about 480 students who prefer cookies.
The college will have about 640 students who prefer cookies.
The college will have about 1,280 students who prefer cookies.
The college will have about 1,440 students who prefer cookies.
Question 14
A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Basketball Baseball Soccer Tennis
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Question 15
The line plots represent data collected on the travel times to school from two groups of 15 students.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 4, 6, 14, and 28. There are two dots above 10, 12, 18, and 22. There are three dots above 16. The graph is titled Bus 47 Travel Times.
A horizontal line starting at 0, with tick marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9, 18, 20, and 22. There are two dots above 6, 10, 12, 14, and 16. The graph is titled Bus 18 Travel Times.
Compare the data and use the correct measure of center to determine which bus typically has the faster travel time. Round your answer to the nearest whole number, if necessary, and explain your answer.
Bus 18, with a median of 13
Bus 47, with a median of 16
Bus 18, with a mean of 13
Bus 47, with a mean of 16
Answers
12) There were about 557 principals in attendance. 13) Option A: The college will have about 480 students who prefer cookies. 14) Option C: bar graph, title favorite sport and the x axis labeled sport and the y axis.
What is proportion?The relationship between two quantities that are measured on the same scale and in the same units is known as a percentage. The relative size or magnitude of one thing in comparison to another is represented by proportions, which are frequently stated as ratios, fractions, or percentages. For instance, if there are 8 girls and 12 boys in a class, the girl-to-boy ratio is 8:12, or 2:3, which indicates that there are 3 guys for every 2 girls. Statistics, geometry, and physics are just a few of the mathematical and scientific disciplines that use proportions. Proportions are frequently used in statistics to describe the distribution of a population or a sample.
12) For the number of principals in conference we set up a proportionality with total people as follows:
We know that, 52 principals out of 70 people thus:
52/70 = x/750
Now,
x = (52/70) * 750
x = 557.14
Hence, we can predict that there were about 557 principals in attendance at the conference.
13) Given that, out of 225 students 27 prefer cookies thus,
27/225 = 0.12
That is 12% students like cookies.
Now, for the total number of students we have:
0.12 * 4000 = 480
Thus, option A: The college will have about 480 students who prefer cookies.
14) For the collected data the best representation is option C: bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44.
15) For the given description of the line plot the median is:
For Bus 47 = 16
For Bus 18 = 13
The faster bus is Bus 47, with a median of 16.
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A and b are monomials where a = 125 and b = 27p12. what is the factored form of a – b? (5 – 3p4)(25 15p4 9p8) (25 – 3p4)(5 15p3 9p3) (25 – 3p4)(5 15p4 3p8) (5 – 3p4)(25 15p3 3p4)
Answers
The correct option is (A). The factored form of a-b is (5-3p⁴)(25+15p⁴+9p⁸).
Given that A and B are monomials where a = 125 and b = 27p¹².
Monomial expressions include only one non-zero term. Numbers, variables, or multiples of numbers and variables are all examples of monomials.
Firstly, substitute a=125 and b = 27p¹² into a-b, we get
a-b=125-27p¹² ......(1)
As we know, 125=(5)³, 27p¹²=(3p⁴)
So, equation (1) can be rewritten as
a-b=(5)³-(3p⁴)
Now, apply a³-b³=(a-b)(a²+ab+b²).
a³-b³=(5-3p⁴)(5²+5(3p⁴)+(3p⁴)²)
Further, Simplify using exponent rule with the same exponent (ab)ⁿ=aⁿbⁿ.
a³-b³=(5-3p⁴)(5²+5×3p⁴+3²×(p⁴)²)
Furthermore, calculate the power, we get
a³-b³=(5-3p⁴)(5²+5×3p⁴+9(p⁴)²)
Then, Simplify using exponent power rule (aˣ)ⁿ=aˣⁿ, we get
a³-b³=(5-3p⁴)(5²+5×3p⁴+9p⁸)
Now, multiply the monomials, we get
a³-b³=(5-3p⁴)(5²+15p⁴+9p⁸)
Further, calculate the power, we get
a³-b³=(5-3p⁴)(25+15p⁴+9p⁸)
Finally, reorder the expressions, we get
a³-b³=(5-3p⁴)(9p⁸+15p⁴+25)
Hence, the factored form of a-b where a and b monomials and a = 125 and b = 27p¹² is (5-3p⁴)(9p⁸+15p⁴+25).
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Answer:a
Step-by-step explanation:
i just did it
what is the scale of 40 cm and 15 mm
Answers
The scale of 40 cm and 15 mm will be 80 mm : 3 mm
What is Scale Drawing?A scale drawing is an enlargement of an object. An enlargement changes the size of an object by multiplying each of the lengths by a scale factor to make it larger or smaller. The scale of a drawing is usually stated as a ratio.
If we were to create a real size map of a house it would be a HUGE map. We wouldn't be able to grab it using our hands, and it wouldn't be useful either. The idea of a map is to have a diagrammatic representation of something.
scale of 40 cm and 15 mm
converting 40 cm to mm
40 x 10 mm = 400 mm
400 mm : 15 mm
Dividing through by 5
80 mm : 3 mm
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You may need to use the appropriate appendix table or technology to answer this question. The following results are for independent random samples taken from two populations. Sample 1 Sample 2 n1 = 20 n2 = 30 x1 = 22.8 x2 = 20.1 s1 = 2.2 s2 = 4.6 (a) What is the point estimate of the difference between the two population means? (Use x1 − x2. ) 2.7 (b) What is the degrees of freedom for the t distribution? (Round your answer down to the nearest integer.) (c) At 95% confidence, what is the margin of error? (Round your answer to one decimal place.) (d) What is the 95% confidence interval for the difference between the two population means? (Use x1 − x2. Round your answers to one decimal place.)
Answers
a). The difference between the two population means is estimated at a location to be 2.7.
b). 49 different possible outcomes make up the t distribution. The margin of error at 95% confidence is 1.7.
c). The range of the difference between the two population means' 95% confidence interval is (0.0, 5.4).
d). The (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
What is standard deviations?The variability or spread in a set of data is commonly measured by the standard deviation. The deviation between the values in the data set and the mean, or average, value, is measured. A low standard deviation, for instance, denotes a tendency for data values to be close to the mean, whereas a high standard deviation denotes a larger range of data values.
Using the equation \(x_1-x_2\), we can determine the point estimate of the difference between the two population means. In this instance, we calculate the point estimate as 2.7 by taking the mean of Sample
\(1(x_1=22.8)\) and deducting it from the mean of Sample \(2(x_2=20.1)\).
With the use of the equation \(df=n_1+n_2-2\), it is possible to determine the degrees of freedom for the t distribution. In this instance, the degrees of freedom are 49 because \(n_1\) = 20 and \(n_2\) = 30.
We must apply the formula to determine the margin of error at 95% confidence \(ME=t*\sqrt[s]{n}\).
The sample standard deviation (s) is equal to the average of \(s_1\) and \(s_2\) (3.4), the t value with 95% confidence is 1.67, and n is equal to the
average of \(n_1\) and \(n_2\) (25). When these values are entered into the formula, we get \(ME=1.67*\sqrt[3.4]{25}=1.7\).
Finally, we apply the procedure to determine the 95% confidence interval for the difference between the two population means \(CI=x_1-x_2+/-ME\).
The confidence interval's bottom limit in this instance is \(x_1-x_2-ME2.7-1.7=0.0\) and the upper limit is \(x_1+x_2+ME=2.7+1.7=5.4\).
As a result, the (0.0, 5.4) represents the 95% confidence interval for the difference among the two population means.
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Please hurry I need it ASAP
Answers
BC^2 = AC^2 + AB^2 - 2 AC•AB • cos A.
BC = √(29² + 24² - 2•29•24 • cos 78) = 33.6 ft
Answer: BC = 33.6 ft
x/6=x/7-5
Please show work thank you so much!!
Answers
Step-by-step explanation:
hope u like it plz follow and give thanks
A professor must randomly select 4 students to participate in a mock debate.
There are 20 students in his class. In how many different ways can these
students be selected, if the order of selection does not matter?
Answers
Answer:
Step-by-step explanation:
We can use combinations
20 choose 4:
20!/(16!*4!)
= (20*19*18*17)/4!
= 4845
What does calculus early transcendentals cover?
Answers
Calculus Early Transcendentals is a branch of mathematics that deals with the study of rates of change and slopes of curves. It is a fundamental area of mathematics that is widely used in a variety of fields, including engineering, physics, economics, and science.
The core concept of Calculus Early Transcendentals is differentiation, which is the process of finding the derivative of a function. A derivative is essentially the rate of change of a function at a given point, and it is used to determine how the value of the function changes as its input changes.
In addition to differentiation, Calculus Early Transcendentals also covers integration, which is the process of finding the area under a curve. Integration is the inverse of differentiation and is used to find the total change in a function over a given interval.
Another important area covered in Calculus Early Transcendentals is optimization, which is the process of finding the maximum or minimum value of a function. This is a useful tool in many real-world applications, such as finding the minimum amount of time or energy required to perform a task.
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(4x2 - x - 7) + (2x3 + 6x2 - 11)
Adding polynomials
Answers
Answer:
2x3 + 10x2 - x - 18
Step-by-step explanation:
hope this helps! goodluck & enjoy the rest of ur day /or night.
Answer:
(4x2 - x - 7) + (2x3 + 6x2 - 11) Adding polynomials
Step-by-step explanation:
Equation 2.5x + 18 = 3.5x - 4
Answers
Answer:
x=22
Step-by-step explanation:
I'm guessing this after that you have to find x
So, in that case:
2.5x + 18 = 3.5x - 4
22=x
x=22
Double-check:
2.5(22)+18=3.5(22)-4
55+18=77-4
73=73
Hope this helped!
I NEED HELP PLEASE I GIVE 5 STARS !
Answers
Answer:
I'm pretty sure 8 is the correct answer
Step-by-step explanation:
(-1)^(3/7) x 128^(3/7)
-1 x 128^3/7
128^(3/7) = 8
= 8
is this right? someone please check?
Answers
Answer:
The answer looks correct.
Step-by-step explanation:
All the other option doesn't match the above question's statement.
The last answer is the correct (in my opinion)
Answer:
Absolutely Correct
Step-by-step explanation:
Based on the definition of midpoint;
It is equidistant from both endpoints, and it is the centroid both of the segment and of the endpoints.
meaning the distance from the midpoint to one end is the same as the distance to the other end
What is the range of the function shown on the graph
Answers
Answer:
\(y \geq - 6\)
Step-by-step explanation:
the range is all the y values shown in the graph, so as you can see, the y values are all those greater than or equal to -6
help me pleaseee!!!
the correct answer will get brainly!!
This for algebra 1
Answers
B= 4
M is the slope
B is the y-intercept
how to determine if a binomial is a factor of a polynomial
Answers
A binomial is a factor of a polynomial has been determined by using the
polynomial division method.
To determine if a binomial is a factor of a polynomial, you can use the polynomial division method. The basic idea is to divide the polynomial by the binomial and check if the remainder is zero. If the remainder is zero, then the binomial is a factor of the polynomial. Here's the step-by-step process:
Write the polynomial and the binomial in standard form, with the terms arranged in descending order of their exponents.
Perform the long division of the polynomial by the binomial, similar to how you would divide numbers. Start by dividing the highest degree term of the polynomial by the highest degree term of the binomial.
Multiply the binomial by the quotient obtained from the division and subtract the result from the polynomial.
Repeat the division process with the new polynomial obtained from the subtraction step.
Continue dividing until you reach a point where the degree of the polynomial is lower than the degree of the binomial.
If the remainder is zero, then the binomial is a factor of the polynomial. If the remainder is non-zero, then the binomial is not a factor.
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What is joule per meter second?
Answers
Joule per meter second is the unit of measurement for momentum flux or power per unit area. It is commonly used in physics and engineering to quantify the rate of energy transfer or momentum flow per unit area.
Joule per meter second (J/m^2s) is not the correct unit for momentum flux or power per unit area. The correct unit for momentum flux is Newton per square meter (N/m^2), also known as Pascal (Pa), while the correct unit for power per unit area is watt per square meter (W/m^2). The joule per meter second (J/m^2s) is actually the unit for volumetric energy dissipation rate, which measures the rate at which energy is being dissipated within a fluid volume per unit volume. It is used in the study of fluid dynamics and turbulence.
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Given : BD is a perpendicular bisectsr AD = 40 - 2 BC = 8x + 10 AC = 10x - 20 BD = 12x + 5BAD=4x+3
Answers
Explanation
As BD is a perpendicular bisector
\(\begin{gathered} AD=DC\text{ and AC=2AD} \\ \text{replacing} \\ AC=2AD \\ 10x-20=2(40-2x) \\ 10x-20=80-4x \\ 10x+4x=80+20 \\ 14x=100 \\ x=\frac{100}{14} \end{gathered}\)\(\begin{gathered} \\ \end{gathered}\)
Find the velocity of the car at the end of a drag race. Round to the nearest whole number.
Answers
Answer:
183 miles per hour.
Explanation:
The estimated velocity(v) at the end of a drag race is modeled using the formula below:
\(v=234\sqrt[3]{\frac{p}{w}}\)Given:
• The horsepower, p = 1311
,• The weight (in pounds), w = 2744 pounds.
Substitute into the formula above:
\(\begin{gathered} v=234\sqrt[3]{\frac{1311}{2744}}=182.9 \\ v\approx183\text{ miles per hour} \end{gathered}\)The velocity is approximately 183 miles per hour.
3x - 2/5 = 1 - 4x + 5/10
Answers
I WILL MARK YOU AS BRAINLIEST IF YOU CAN ANSWER :)
Answers
Answer:
6 inches fell an hour
6x30 =180 so One hundred eighty inches in 30 mins
Step-by-step explanation:
Answer:
0.5 in per hour
16.2 in 30 hours
Step-by-step explanation:
If you want to find the amount of rain that falls in one hour, divide 13 by 24
13/24= 0.541 inches per hour
Then multiply this by 30
0.541 x 30 = 16.23
Since they want you to round to the nearest tenth, your answers would be:
0.5 in per hour
16.2 in 30 hours