The general solution of the given differential equation is: y = c_1 e^x + (1/x)∫xe^x dx.
What is genral solution?A general solution is a comprehensive approach that is applicable to a wide variety of situations and problems. It is usually used to solve complex problems that have multiple variables and factors. General solutions often involve a combination of strategies, techniques, and processes that can be adapted to fit a particular context. In some cases, general solutions may require a combination of both traditional and modern methods. The goal of a general solution is to provide an effective, efficient, and sustainable solution to an issue.
The largest interval over which the general solution is defined is (-∞, ∞). There are no transient terms in the general solution, so the answer is NONE.
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calculate the double integral. 3xy2 x2 + 1 da, r = {(x, y) | 0 ≤ x ≤ 3, −2 ≤ y ≤ 2} r
The double integral for [tex]3xy^2/x^2+1[/tex] is 8㏑(2).
[tex]3\int\limits^1_0 \int\limits^2_2 \frac{xy^2}{x^2 + 1} \, dy dx[/tex]
3* 1/2 (㏑(2) - ㏑(1) ) * 1/3 (8+8)
8㏑(2)
A multiple integral in mathematics is a definite integral of a function with multiple real variables, such as f(x, y), or f(x, y) (x, y, z). In the real-number plane, integrals of functions of two variables over an area are referred to as double integrals, and integrals of functions of three variables over a region in real-number three-dimensional space are referred to as triple integrals.
The Cauchy formula for repeated integration can be used to calculate multiple integrals of a single-variable function.
The double integral of a positive function of two variables represents the volume of the region between the surface defined by the function (on the three-dimensional Cartesian plane where z = f(x, y)) and the plane that contains its domain, just as the definite integral of a positive function of one variable represents the area of the region between the graph of the function and the x-axis.
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for items 22-24, refer to the graph represents the santos family income and the corresponding monthly budget. the income is Php50,000.
The amount the family spend on items other than food and housing is PhP25000 over the time.
How to determine the amount spend?You should understand that budget involves the summary of income and expenditure of a person or individual over a period of time
If total expense is $50,000 and the spend 20% on food 30% on housing
Which make is 50% on both hosing and food leaving 50% on other expenses
Which makes half of the total budget
You have to work out 50% of 50000 to get
50/100* $50000 =PhP25000
This therefore means that the family spends PhP25,000 on items other than food and housing
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Complete question
The circle graph represents a family's monthly budget. If the total monthly budget is $50,000,
how much does the family spend on items other than food and housing?
some identical glasses are stacked on top of each other. a stack with eight glasses is 42 cm high. a stack with two glasses is 18 cm high. how high is a stack with six glasses?
the height of six glasses (24 / 6 = 4). Finally, we can multiply this by six to get the final answer, which is 30 cm.
30 cm
For two glasses, the height is 18 cm.
For eight glasses, the height is 42 cm.
Therefore, for six glasses, the height would be (42 - 18) / (8 - 2) * 6 = 30 cm.
To answer the question, we need to first determine the height of two glasses, which is 18 cm. Next, we need to find the height of eight glasses, which is 42 cm. Once we have these two values, we can calculate the height of six glasses. We can do this by finding the difference between the two heights (42 - 18 = 24), which will give us the height of six glasses (24 / 6 = 4). Finally, we can multiply this by six to get the final answer, which is 30 cm.
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in which month is the probability for an aircraft to experience crosswinds upon takeoff or landing greatest?
The probability for an aircraft to experience crosswinds upon takeoff or landing is generally greatest during the months of spring and fall, specifically in March, April, September and October.
During these months, the transition from winter to summer or summer to winter can lead to greater temperature and pressure differences between the air masses, which can create stronger winds. Additionally, these seasons are also associated with increased storm activity, which can also lead to stronger winds.
However, the probability of experiencing crosswinds upon takeoff or landing can also be affected by regional weather patterns and location, and it's always best to consult with local weather forecast and airport meteorological services before planning any flight.
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Use a suitable identity to get each of the following products.
(6x+ 5y)2
According to algebra, the square binomial (6 · x + 5 · y)² has the following equivalent expression: 36 · x² + 60 · x · y + 25 · y².
How to find an equivalent expression for a square binomial
According to algebra, we find the case a square binomial, whose equivalent form is shown below by following rule:
(a + b)² = a² + 2 · a · b + b²
Where a, b are real coefficients.
If we know that a = 6 · x and b = 5 · y, then the equivalent form of the square binomial is:
First, write the entire expression:
(6 · x + 5 · y)²
Second, use power properties:
(6 · x)² + 2 · (6 · x) · (5 · y) + (5 · y)²
Third, perform associative and commutative properties:
6² · x² + (2 · 6 · 5) · (x · y) + 5² · y²
Fourth, multiply similar terms:
36 · x² + 60 · x · y + 25 · y²
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I need help with this question
decrease the number 35 by 0.6 of it
Answer:
14
Step-by-step explanation:
1) "the number 35" means 35
2) "decrease 35 by 0.6 of it" means -(0.6)*(35)
Put them together:
35 - (0.6)*(35)
35 - 21
= 14
Divide $3300 into three parts with the ratio of 1:3:7
PLEASE ANSWER QUICKLy!!!!!!
Answer:
Step-by-step explanation:
So you add 1+3+7 which gives you 11
And the you divide 3300 by 11 which gives you 300 and from that you do:
1 x 300= 300
3 x 300= 900
7 x 300= 2100
And there you have it in the ratio of 1:3:7
300:900:2100
And to simplify it you find a number which you can divide them all from in this case is 100 and so:
300÷100=3
900÷100=9
2100÷100=21
3:9:21
Hope that helped.
Detroit, Michigan, like a number of large cities, is losing population every year. Below is a table showing the population of Detroit each decade.
Year 1960 1970 1980 1990 2000
Population (millions) 1.67 1.51 1.20 1.03 0.95
a. Find an equation for the regression line.
b. Find the correlation coefficient and explain the meaning of its sign.
c. Estimate the population of Detroit in 2008
please show all work
The equation for regression line is ŷ = -0.0192X + 39.288,
The correlation coefficient is -0.9817,
The population of Detroit in 2008 is 0.73 millions.
What is a regression line?A line that, using the bivariate data gathered, summarises the linear relationship (or linear trend) between the two variables in a linear regression study.
An estimate of the line that depicts the actual, but the unidentified, linear relationship between the two variables is called a regression line. When the value of the explanatory variable is known, the regression line's equation is used to predict (or estimate) the value of the response variable.
Given table showing the population of Detroit each decade.
year 1960 1970 1980 1990 2000
Population (millions) 1.67 1.51 1.20 1.03 0.95
A. equation for regression line,
X - Mx Y - My (X - Mx)² (X - Mx)² (X - Mx)(Y - My)
-20 -20 400 0.158 -7.96
-10 -10 100 0.057 -2.38
0 0 0 0.005 0
10 10 100 0.059 -2.42
20 20 400 0.104 -6.44
Sum: 1000.00 Sum: 0.382 Sum: -19.200
Sum of X = 9900
Sum of Y = 6.36 millions
Mean X = 1980
Mean Y = 1.272
Sum of squares (SSX) = 1000
Sum of products (SP) = -19.2
Regression Equation = ŷ = bX + a
b = SP/SSX = -19.2/1000 = -0.0192
a = MY - bMX = 1.27 - (-0.02*1980) = 39.288
ŷ = -0.0192X + 39.288
B. correlation coefficient,
X Values
∑ = 9900
Mean = 1980
∑(X - Mx)² = SSx = 1000
Y Values
∑ = 6.36
Mean = 1.272
∑(Y - My)² = SSy = 0.382
X and Y Combined
N = 5
∑(X - Mx)(Y - My) = -19.2
r Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))
r = -19.2 /√((1000)(0.382)) = -0.9817
Meta Numerics
r = -0.9817
The value of R is -0.9817.
High X variable scores correlate negatively with low Y variable scores because of this strong negative connection (and vice versa).
C. population in 2008
y = -0.0192X + 39.288
substitute x = 2008
y = -0.0192(2008) + 39.288
y = 0.7344
population in 2008 is 0.73 millons.
Hence the equation is ŷ = -0.0192X + 39.288,
the correlation coefficient is r = -0.9817
and population of Detroit in 2008 is 0.73 millions.
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a student added all her grades together and then divided by the total points possible to figure out her grade, as her instructor had said to do, and the result was 0.83. what percent of the possible points does she have?
The possible percentage of the marks the students will have is (D) 83%.
What is the percentage?A percentage, often known as percent, is a division by 100.
Percentage, which means "per 100," designates a portion of a total sum.
45 out of 100 is represented by 45%, for instance.
Finding the percentage of a whole in terms of 100 is what percentage calculation is.
Both manual calculation and the use of internet calculators are options.
So, we know that:
When we find the percentage, after division, we multiply the answer by 100 to get the answer in percentage.
Similarly,
0.83 * 100 = 83%
Therefore, the possible percentage of the marks the students will have is (D) 83%.
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Complete question:
A student added all her grades together and then divided by the total points possible to figure out her grade, as her instructor had said to do, and the result was 0.83. What percent of the possible points does she have?
a) 8.3%
b) 0.83%
c) Can't tell, but she has 83 total points.
d) 83%
If vec SD - vec SE - vec SG . and if m angle DSE=5x-4; m angle E5G=3x+4 and m angle DSG=72 find m angle DSE .
If vec SD, vec SE, and vec SG and if m angle DSE = 5x – 4, m angle E5G = 3x + 4, and m angle DSG = 72, m angle DSE = 90.
What are the angle called in math?Two straight lines or rays intersect at a same terminus to make an angle. The vertex of an angle is the point at which all points meet. Two rays (half-lines) combined into an angle have a single terminal. The latter is known as the vertex of the angle, while the rays are known as its sides, occasionally as its legs, and occasionally as its arms.
An angle is a figure created by two rays or lines that have the same termination in plane geometry. The Latin word "angulus," which meaning "corner," is where the term "angle" originates. The common terminal of the two rays—known as the vertex—is referred to as an angle's sides.
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Evaluate 4-0.25g+0.5h when g=10=5
Answer:
4
Step-by-step explanation:
First, substitute in g and h:
4-(0.25x10)+(0.5x5)
4-2.5+2.5
Then -2.5 and +2.5 cancel out, so you are left with:
4
John was 5 years old when his pet dog, Spot, was born.
Write an equation to show the relationship between John’s age (x) and his dog, Spot’s, age (y). (Do not include any spaces in your answer)
Answer:
Step-by-step explanation:
Answer:
5x = y
10x= 5y
20x= 15y
50x= 45y
60% of ms. howard's class ordered a hot lunch from the cafeteria. if 15 students ordered a hot lunch, how many students are in ms. howard's class?
Based on the number of 60% students, the total number of students in Ms. Howard's class are 25.
Let the total number of students be x. Based on the mentioned information, we can say that 60% of total number of students ordering a hot lunch are 15. Rewriting the mentioned information as equation -
60% × x = 15
60/100 × x = 15
x = 15 × 100/60
Performing multiplication on Right Hand Side of the equation
x = 1500/60
Cancelling zero and performing division on Right Hand Side of the equation
x = 25
Therefore, there are 25 students in the class.
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can someone help me with this please
The value of x is 16 cm.
What is the equilateral triangle?
An equilateral triangle is a type of triangle that has three sides of equal length and three equal angles of 60 degrees each. All equilateral triangles are also equiangular and isosceles triangles. The sides of an equilateral triangle are congruent, and it is symmetrical in all ways, meaning that it has rotational and line symmetry.
We have given,
Lengths of sides:
16 cm, 16cm, and x cm,
we have to find the value of x.
The given triangle is an equilateral triangle,
so, The length of all three sides of an equilateral triangle is equal.
16 cm = 16cm = x cm,
x = 16 cm
Hence, The value of x is 16 cm.
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how long would it take them to get to the point on the ferris wheel closest to the polar coordinate
It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.
1. The question is asking for an estimate of the time it would take for a person to get from the start of the ferris wheel to the point closest to the polar coordinate (6, 0).
2. To answer this question, we need to know the speed of the ferris wheel. Without this information, it is impossible to answer the question.
It would depend on the rate of the ferris wheel, so it is impossible to answer this question without knowing the wheel's speed.
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The person is around 2 meters tall and the street light is only 8 meters above the ground. The rate at which the person is walking is 4/3
Step-by-step explanation:
We find the answer by using the equation ds/dt which equals to 4/9.
s represents the length of the shadow while x represents distant of shadow from the street light.
Hence we get x/6 = s/2 so dx/dt putting the values we get 6ds/2dt and the answer is 4/3
By applying the first derivative of distance with respect to time, it can be concluded that the person is walking 4/3 meters per second.
Instantaneous velocity or rate is the first derivative of distance with respect to time. Mathematically it is written v = ds/dt, where v is the velocity, s is the distance and t is the time.
First, we make a simple drawing using the given information:
The walking person = 2 meters tall
The street light = 8 meters above the ground
The walking rate is constant
The person's shadow lengthening rate = 4/9 meter per second = dy/dt
We want to know the walking rate, dx/dt.
We determine the value of y:
8 / 2 = (x + y) / y
8y = 2x + 2y
6y = 2x
y = x / 3
Then we substitute the value of y into the equation:
dy/dx = d(x/3) / dx
= 1/3
Finally, we can get the rate dx/dt:
dx/dt = dy/dt * dx/dy
= 4/9 * 3
= 4/3
Thus, it can be concluded that the person is walking 4/3 meters per second.
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The distribution of prices for a certain car model is approximately normal with mean $21,800 and standarddeviation $400. A random sample of 4 cars of the model will be selected.What is the correct unit of measure for the mean of the sampling distribution of I?A DollarsB) ModelsCarsD) Samples
The correct unit of measure for the mean of the sampling distribution of I is A. Dollars.
The original distribution of prices for the car model is given in dollars, and the mean of the sampling distribution represents the average price of a random sample of 4 cars from that distribution. Hence, the correct unit of measure should be in dollars also.
In statistics, the mean is a measure of central tendency that represents the average value of a dataset. It is calculated by adding up all the values in a dataset and dividing by the number of observations. The formula for the mean of a dataset is:
mean = (sum of observations) / (number of observations)
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What is formula Work Class 9?
The formula for work is force multiplied by displacement.
Work done refers to the amount of energy used by a force to move an object. It is also a physical quantity. Its SI unit is Joule. Every time a force is applied to an object and it moves from one location to another, work has been done. The displacement is what needs to be taken into account and not the distance. Displacement is the smallest distance or straight line that connects the object's initial and final positions. Work is therefore equivalent to force times its displacement. Force is measured in newtons, and the displacement is measured in meters. Therefore, if a force of 1N is used to move a body by a displacement of 1m, then 1J of work has been completed.
[tex]W=F.S[/tex]
[tex]1J=1m.1N[/tex]
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what is the answer for this-order of operation?
Answer:
Step-by-step explanation:
always follow BODMAS or BIDMAS-
Do the multiplication, which is 15/3 and when simplifiyed becomes 5.
Then work out 6 divided by 3/2. In division for fractions, you always find the reciprocal of the 2nd number and multiply instead of divide, so its 6 x 2/3 which is 12/3, simplifiyed to be 4. 5+4=9. 9+10 is 19, and 19-4=15
PLEASE HELP MEEEEEEEE!!!!!!!!!
Answer:
70⁰ is the correct answer.
Are absolute value graphs even or odd?
An absolute value is defined as , | y | = | − y | for all y , we can thus say that their absolute value is even.
The definition of h in the equation is given as given next , | f (x) | = h (x). The logic when checking for an equation to be even or odd is defined as , if g (x) is an even function whereas f (x) is an odd function , then the value of g (f (x)) is even and f (g (x)) will also be even.
A function is known as an odd function is that ,
f(x) = f(−x) for all the value of x
A function is known as an even function is that ,
f(x) = f(−x) for all x
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What is the formula for finding absolute value?
Answer:
|x| = x if x >= 0, -x if x < 0
Step-by-step explanation:
1) coffee is draining from a conical filter into a cylindrical coffeepot at the rate of 10 3 in / min . a) how fast is the level in the pot rising when the coffee in the cone is 5 in. deep? b) how fast is the level in the cone falling then?
The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.
A cylinder is a three-dimensional solid in mathematics that maintains, at a given distance, two parallel bases connected by a curving surface.
For cylindrical pot,
Volume, V = πr²h
dV/dt = π(r²dh/dt+h * 2r dr/dt)
Since r is constant,
Therefore, dr/dt = 0
dV/dt = 100 = πr²dh/dt
100 = π * 225/4 *dh/dt (since r = 15/2 cm)
=> dh/dt = 400/ 225π = 16/9π cm/min.
Thus, The rate at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is 16/9π cm/min.
Correct question: Coffee is draining from a conical filter with height and diameter both 15 cm, into a cylindrical coffee pot with diameter 15 cm. The rate at which coffee drains from the filter into the pot is 100 cc/min. The rate in cm/min at which the level in the pot is rising at the instant when the coffee in the pot is 10 cm, is?
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how do you solve this?
Answer:
i have no clue big dawg you gonna have to cheat somewhere else
3. In the figure, DE and DF are midsegments of AABC. Find BC. (Example 3) 1 point
B
D
122°
E
8
А.
F
с
15
O A 8
B. 15
C. 16
O D. 30
The midsegments of AABC, hypotenuse BC is B. 15.
In a triangle, a midsegment is a line segment that connects the midpoints of two non-adjacent sides of the triangle. In this figure, DE and DF are the midsegments of AABC, which means that they connect the midpoints of the sides AB and AC, respectively. Since DE and DF are parallel, we know the triangle isosceles (both legs are congruent).
Since the angle at A is 122°, we know that the angle at B and C are 78° (180-122=58). Therefore, if we draw the altitude from B to AC, we have a 30-78-72 triangle. We have been given the length of the altitude, 8, and the angle of the base, 72. We can use the Sine Ratio to calculate the hypotenuse, BC.
sin(72) = opposite / hypotenuse = 8/BC
Solving for BC, we get 15
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I need help very fast
Find Least common multiple of
1-x^2 and (x-1)^3
Answer:
(x-1)^3.
Step-by-step explanation:
To find the least common multiple (LCM) of two polynomials, you can factor them and take the highest exponent of each variable that appears. In this case, the LCM is (x-1)^3 because it has the highest exponent of x that appears in both polynomials. It also contains all the other terms of both polynomials.
a) we roll 50 dice to find the distribution of the number of spots on the faces. b) howlikelyisitthatinagroupof120themajority may have type a blood, given that type a is found in 43% of the population? c) we deal 7 cards from a deck and get all hearts. how likely is that? d) we wish to predict the outcome of a vote on the school budget, and poll 500 of the 3000 likely voters to see how many favor the proposed budget. e) a company realizes that about 10% of its packages are not being sealed properly. in a case of 24, is it likely that more than 3 are unsealed?
We can use probability to find the answers to the questions - the final answers are given below.
The probability of an event occurring is defined by probability. There are many instances in real life where we may need to make predictions about how something will turn out. The outcome of an event may be known to us or unknown to us. When this happens, we say that there is a chance that the event will happen or not. In general, probability has many wonderful uses in games, in business to make forecasts based on likelihood, and in this emerging branch of artificial intelligence.
We will answer each part in detail.
Part (a)
No, there are more than 2 outcomes in this particular scenario.
Part (b)
Yes, there are two outcomes (Type A or not).
Part (c)
No, probability changes as the cards are dealt.
Part (d)
No, the trials are not independent.
Part (e)
Yes, two outcomes (more than 3 or not)
These are the final answers:
(a): No
(b): Yes
(c): Yes
(d): No
(e): Yes
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[tex]25 \div 2 [/tex]
How to solve this?
Answer:
25÷2=12.5
Step-by-step explanation:
you put the 25 inn the division box and the 2 on the outside and 12.5 is your answer
Answer: 12.5
How do you solve the given equation?[tex]\frac{25}{2} =12.5[/tex]
[tex]\frac{5^{2}}{2} = 12 \frac{1}{2} = 12.5[/tex]
Aubrey is older than Chase. Their ages are consecutive integers. Find Aubrey's age if the product of their ages is 56.
