To solve the given differential equation, variables need to be separated, followed by integration of both sides. Since the equation involves both exponential and inverse square terms, separation of variables and integration are key steps. A specific solution also requires substituting a given function of y into the found general solution to determine any integration constants.
Explanation:The question involves solving a differential equation 3e^(3x)dy/dx = -9x/y^2. First, we need to recognize this as a separable differential equation, which can be solved by isolating all terms involving y on one side and all terms involving x on the other side. After separation, we integrate both sides with respect to their respective variables.
Step 1: Separate the variables. We get dy/y^2 = -3x e^(-3x) dx.
Step 2: Integrate both sides. The integration of dy/y^2 with respect to y is -1/y, and the integration of -3x e^(-3x) with respect to x requires integration by parts or a table of integrals.
Step 3: Upon integration, we would find an implicit solution involving y and x, combined with an integration constant that needs to be determined based on initial conditions or additional information. Since specific initial conditions are not provided in the initial question, we'd include a constant C in our final expression.
For a specific solution when y(x) = cos(3x), additional steps are required to substitute this y expression into our general solution and solve for the constant.
what is 62.19 x 32.5
Gomez runs a small pottery firm. he hires one helper at $15,000 per year, pays annual rent of $6,500 for his shop, and spends $23,000 per year on materials. he has $40,000 of his own funds invested in equipment (pottery wheels, kilns, and so forth) that could earn him $6,000 per year if alternatively invested. he has been offered $20,500 per year to work as a potter for a competitor. he estimates his entrepreneurial talents are worth $5,000 per year (input cost for organizing resources). total annual revenue from pottery sales is $82,000. calculate the accounting profit and the economic profit for gomez's pottery firm.
The accounting profit for Gomez's pottery firm is $37,500, calculated by subtracting explicit costs from total revenue. The economic profit is $6,000, figured out by subtracting both explicit costs and implicit costs from total revenue.
Explanation:To calculate the accounting profit for Gomez's pottery firm, we subtract all explicit costs (money spent) from the total revenue. In this case, we subtract the salary of the helper ($15,000), the rent of the shop ($6,500), and the amount spent on materials ($23,000) from the total annual revenue from pottery sales ($82,000). Therefore, the accounting profit is $82,000 - $15,000 - $6,500 - $23,000 = $37,500.
On the other hand, to obtain the economic profit, we need to also subtract implicit costs, which are the opportunity costs of using the resources in one way rather than the next best alternative way. Gomez could have made $6,000 by investing his own $40,000 elsewhere, and he could have earned $20,500 by working for a competitor, so these are both implicit costs. Additionally, he estimates his entrepreneurial talents to be worth $5,000. Therefore, "the economic profit is $37,500 (accounting profit) - $6,000 (returns from alternative investment) - $20,500 (salary from competitor) - $5,000 (value of his entrepreneurial talents) = $6,000".
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Which function represents the graph of f(x)=|2x| after it is translated 5 units to the left?
g(x)=|2(x−5)|
g(x)=|2x+5|
g(x)=|2x−5|
g(x)=|2(x+5)|
Answer:
g(x) = |2(x+5)|
Step-by-step explanation:
To translate a function left 5 units, replace x with (x+5). In this function, that means
2x ⇒ 2(x+5) . . . . . matches the last choice
which of the following three dimensional objects has Rotational symmetry about a line A.a car. B.a set of rectangular stairs. C. a rolling pin. D.a stapler
Answer:
C. a rolling pin.Step-by-step explanation:
A rolling pin has a cylindric shape, which is a revolution surface. This means that the rolling pin is symmetric about a line or axis, therefore, it can be rotated around it.
A rolling pin has rotational symmetry about its longitudinal axis, making it the correct answer, while a car, a set of rectangular stairs, and a stapler do not demonstrate this symmetry.
Explanation:The question relates to the concept of rotational symmetry in three-dimensional objects, which is a part of the study of Physics, specifically dealing with rotational motion. The answer to which of the listed objects has rotational symmetry about a line is C. a rolling pin. A rolling pin has rotational symmetry because when it rotates about its longitudinal axis, its appearance is unchanged after a certain angle of rotation. In contrast, objects like a car, a set of rectangular stairs, and a stapler do not exhibit this symmetry because their appearance changes visibly when they are rotated about any line.
Allison practices her violin for at least 12 hours per week. She practices for three fourths of an hour each session. If Allison has already practiced 3 hours this week, how many more sessions remain for her to meet or exceed her weekly practice goal?
Liliana takes 4 breaths per 10 seconds during yoga. At this rate, about how many breaths would Liliana Take in 2 minutes of yoga?
Write an equation of the line passing through (-5,5) and having slope -6. Guve the answer in slope-intercept form.
a pile of newspapers in the recycling bin was 12 1/4 inches high. each week the height of the pile increases by 4 5/8 inches. what is the height of the pile after 4 weeks
It takes a boat 2 hours to travel 22 miles downstream and 4 hours to travel 20 miles upstream. What is the speed of the boat in still water?
A group of friends are going to a cottage for the weekend. The scale used is 1 : 250,000. The distance measures 8.5cm on the map. What is the actual distance
which number line represents the solutions to |-2x|=4?
What is the simplified form of the following expression
To simplify the given expression, factor out the common factors from the denominator and rewrite the expression using the factored form.
Explanation:To simplify the given expression, we first need to simplify the denominator. This can be done by factoring out a common factor of 4 from each term:
(4a + 2)(2a - 3)
Next, we can rewrite the expression using the factored form:
1 / (4a + 2)(2a - 3)
This is the simplified form of the given expression.
The answer is c. [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex]
Separate the cube root: We can break down the cube root of a fraction into the cube root of the numerator divided by the cube root of the denominator:
[tex]\sqrt[3]{\frac{4 x}{5}} = \frac{\sqrt[3]{4 x}}{\sqrt[3]{5}}[/tex]
Simplify the cube root of 5: Since 5 is a perfect cube (5 = 1 * 5 * 5), its cube root is simply 5:
[tex]\frac{\sqrt[3]{4 x}}{\sqrt[3]{5}} = \frac{\sqrt[3]{4 x}}{5}[/tex]
Rationalize the denominator: To make the expression look more simplified, we can eliminate the cube root in the denominator. We do this by multiplying both the numerator and denominator by the cube root of 5:
[tex]\frac{\sqrt[3]{4 x}}{5} \times \frac{\sqrt[3]{5}}{\sqrt[3]{5}} = \frac{\sqrt[3]{4 x} \times \sqrt[3]{5}}{5 \times \sqrt[3]{5}}[/tex]
This simplifies to:
[tex]\frac{\sqrt[3]{20 x}}{5}[/tex]
Therefore, the simplified form of the expression is [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex].
Complete Question:
What is the simplified form of the following expression?
[tex]\sqrt[3]{\frac{4 x}{5}}[/tex]
a. [tex]$\frac{\sqrt[3]{4 x}}{5}$[/tex]
b. [tex]$\frac{\sqrt[3]{20 x}}{5}$[/tex]
c. [tex]$\frac{\sqrt[3]{100 x}}{5}$[/tex]
d. [tex]$\frac{\sqrt[3]{100 x}}{125}$[/tex]
On Anne's bicycle, the ratio of pedal turns to rear- wheel turns in second gear is 4 to 7. If her rear wheel turns 875 times per mile, how many times does she turn the pedal in one mile? HINT: Set up and solve as a proportion to find x.
Find the absolute value of the jacobian, ∣∣∂(x,y)∂(s,t)∣∣, for the change of variables given by x=s+5t,y=3s+8t
Anyone knows??? And like to help
Which line on the graph below has an undefined slope?
Answer:
R
Step-by-step explanation:
A vertical line has slope that is "undefined". Line R is the vertical line on your graph.
_____
The slope of a vertical line is "undefined" because of the way slope is defined. Slope is the vertical change divided by the horizontal change. When the line is vertical, there is no horizontal change, so the computation of slope involves division by zero. The result of division by zero is "undefined."
Answer:
C. R
Good Luck!
a rectangle has a side length 2x+9 and side width x. If the perimeter is 36 cm, what is the value of x?
How many feet of fencing is needed to fence in a 130 ft by 225 ft area?
Which is the most accurate way to estimate 23% of 70?
Which of the following numbers are divisible by 2? 74 , 296, 1110, 148, 370, 666, 9324, 111, 37, 555 , or 333?
Tiesha enjoys reading in her spare time. She reads 4 pages every 1/10 of an hour. The proportional relationship between the number of pages (p) and the number of hours (h) is represented by the equation ______. Write the equation in standard form with a constant of proportionality greater than 1.
The equation in standard form with a constant of proportionality greater than 1 is p=40h.
Given that, Tiesha enjoys reading in her spare time. She reads 4 pages every 1/10 of an hour.
What is the proportional relationship?Proportional relationships are relationships between two variables where their ratios are equivalent. Another way to think about them is that, in a proportional relationship, one variable is always a constant value time the other. That constant is known as the "constant of proportionality".
Now, p∝h
⇒p=kh-----(i)
So, 4∝1/10
⇒4=k/10
⇒k=40-----(ii)
Substitute equation (ii) in equation (i).
That is, p=40h
Therefore, the equation in standard form with a constant of proportionality greater than 1 is p=40h.
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Which equation represents a direct variation? y = 2x y = x + 4 y = x y =
If f(x)=8x and g(x)=2x+1, find(f•g)(x).
A) 16x+1
B) 10x+1
C) 16x+8
D) 16x^2+8x
Andrew has 10 more goldfish than todd.together they have 50 goldfish.how many goldfish each boy have?
Answer:
Andrew has 30 goldfish and Todd has 10 goldfish
Step-by-step explanation:
Lets call A the number of goldfish Andrew has and T the number of goldfish Todd has.
Andrew has 10 more goldfish than Todd:
A = T + 10
Together they have 50 goldfish:
A + T = 50
Lets replace A = (T + 10) in the las equation:
T + 10 + T = 50
Lets solve T in this equation:
2T + 10 -10 = 50 -10
2T /2 = 40 /2
T = 20
Todd has 20 goldfish
Now lets calculate A = T + 10 = 20 + 10 = 30
Andrew has 30 goldfish
There were 36,000 people at a ballgame in los angeles. the day's receipts from $12 reserved seats and $6 general-admission seats were $258,000 how many of each type of seat were sold?
14.4% of what is 10.44
Which of these story problem describes the sum 19 + (-12)? Check all that apply. Show your work to justify your answer.
Opening up the monthly cell phone bill can be alarming due to the uncertainty of the bill. suppose the amount of minutes used per month is distributed normally with a mean of 700 minutes and a standard deviation of 120 minutes. what is the probability that more than 940 minutes were used?
Answer:
the required probability = 0.25
Step-by-step explanation:
Mean = 700 minutes , Standard Deviation = 120 minutes
To find : the probability that more than 940 minutes were used.
Solution : First find the z-score for 940 minutes and then find the area under the curve to the right of associated standard deviations from the mean.
[tex]z-score=\frac{\mu_2-\mu_1}{\sigma}\\\\\mu_1=700,\mu_2=940,\sigma=120\\\\\implies z-score=\frac{940-700}{120}\\\\\implies z-score=2[/tex]
Now, calculate the area under the curve to the right of 2 standard deviations from the mean.
Take confidence level to be 95%.
The area to the right of 2 standard deviations is 0.5 that is half the area under the standard normal curve.
[tex]\implies Area < \frac{0.95}{2}\\\\\implies Area<0.475[/tex]
Now, to find the probability that more than 940 minutes were used = 0.5 - 0.475 = 0.25
Hence, the required probability = 0.25
Which is the graph of the function f(x) = x2 + 2x – 6? Mark this and return
The graph of the function f(x) = x² + 2x − 6 is an upward-opening parabola with the vertex at (-1, -7) and a y-intercept at (0, -6). There are no asymptotes for this quadratic function.
Explanation:To find the graph of the function f(x) = x² + 2x − 6, we need to look at the characteristics of this quadratic equation. This is a parabola that opens upward because the coefficient of x² is positive. We can find the vertex of this parabola by using the formula -b/2a for the x-coordinate of the vertex.
Here, a = 1 and b = 2. Applying the formula, we get the x-coordinate of the vertex as -b/2a = -2/(2×1) = -1. Now, we plug this value back into the function to get the y-coordinate of the vertex: f(-1) = (-1)² + 2(-1) − 6 = 1 - 2 - 6 = -7. Therefore, the vertex of the parabola is at (-1, -7). The parabola will intersect the y-axis when x = 0, which gives us the y-intercept f(0) = -6. No asymptotes are present in this quadratic function.
The graph of f(x) is symmetrical about the line x = -1 and has a y-intercept at (0, -6). The vertex at (-1, -7) is the lowest point on the graph since the parabola opens upwards. Thus, we are looking for a graph with these characteristics to represent the function f(x) = x² + 2x − 6.
Mr. and mrs. harris have six kids aged 5, 6, 8, 10, 16, and 19. the median age of the harris children is _____.
Answer:
The median age is 9 years old
Step-by-step explanation:
We can find the median by getting the average of the center number of the middle two numbers
8 and 10 are the two middle numbers in this scenario. 8 + 10 = 18
18/2 = 9