La solución de la ecuación diferencial dy / dx = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] es la ecuación y = - 3 · ㏑ |x³ - 4 · x + 4| + C.
¿Cómo resolver una ecuación diferencial con variables separables?
En este problema tenemos el caso de una ecuación diferencial ordinaria con variables separables, esto es, que las variables x, y pueden ser apartadas a cada lado de la identidad. A continuación, se presenta el procedimiento de la solución de la ecuación diferencial.
Primero, se escribe la ecuación diferencial y se separan las variables:
dy = [(12 - 9 · x²) / √(x³ - 4 · x + 4)] dx
Segundo, se simplifica la expresión y se aplica la integral a ambos lados:
∫ dy = - 3 ∫ [(3 · x² - 4) / √(x³ - 4 · x + 4)] dx
Tercero, emplear la fórmula de sustitución algebraica u = x³ - 4 · x + 4:
du = 3 · x² - 4 dx
∫ dy = - 3 ∫ [du / u]
Cuarto, integral la expresión resultante:
y = - 3 · ㏑ |u| + C, donde C es la constante de integración.
Quinto, reversar la fórmula de sustitución algebraica:
y = - 3 · ㏑ |x³ - 4 · x + 4| + C
ObservaciónNo existen problemas verificados en español, de modo que se añade una pregunta en inglés.
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Find the unit rate: 3 1/4 miles in 11/2 hours
Answer:
6/10 of a mile in one hour
Step-by-step explanation:
3.25 ÷ 5.5 = 0.59 or approx 0.6 miles
Consider the equation q = 4+0. 8p.
What value of p would make the equation true when
9 = 60?
The value of p that would make the equation true when q = 9 is p = 6.25.
To determine the value of p that would make the equation q = 4 + 0.8p true when q = 9, we can substitute the given values into the equation and solve for p.
Given:
q = 9
Substituting q = 9 into the equation q = 4 + 0.8p, we have:
9 = 4 + 0.8p
Next, we can isolate the term with p by subtracting 4 from both sides of the equation:
9 - 4 = 0.8p
Simplifying the equation:
5 = 0.8p
To solve for p, we divide both sides of the equation by 0.8:
5/0.8 = p
p = 6.25
Therefore, the value of p that would make the equation true when q = 9 is p = 6.25.
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Please help thank you
Answer: D (4,1)
Step-by-step explanation:
2x + 3(x-3) = 11
2x + 3x - 9 = 11
5x = 11 + 9
x = 20/5 = 4
y = x-3
= 4-3 = 1
Andrew is home one winter day studying for an exam. It is lunchtime and he is hungry. Instead of making a sandwich from roast beef in the fridge, he drives to taco bell and spends $5 for 2 tacos, a burrito, and a dr. Pepper. He reasons that he can make $10 per hour cutting lawns so he really saves $5 by going to taco bell rather than preparing his own meal. What's wrong with andrews argument?.
Answer:
He cannot save $5 when he is buying something instead of making it himself.
Step-by-step explanation:
He makes $10 from lawn mowing and spends $5 on Taco Bell. He has $5 left.
If he made is lunch, He would have had $10 dollars.
Andrew's argument is flawed because he is not considering all of the costs and benefits associated with his decision to go to Taco Bell instead of preparing his own meal.
What is the argument?An argument is a collection of claims, the premises of which are provided in support of another statement, the conclusion.
There are a few problems with Andrew's argument.
First, he is assuming that the only cost of preparing his own meal is the price of the ingredients. However, there are also opportunity costs associated with preparing his own meal, such as the time he spends making it and the opportunity to do something else during that time (such as study for his exam).
Second, Andrew is assuming that he would have spent the same amount of money on ingredients as he did on his meal at Taco Bell. However, it is possible that the ingredients he would have used to make his own meal would have cost less than $5, in which case he would not have saved as much money as he thinks.
Finally, Andrew is assuming that he would have spent the same amount of time preparing his own meal as he did going to Taco Bell. However, it is possible that it would have taken him longer to prepare his own meal, in which case the opportunity cost of his time would have been even higher.
Overall, Andrew's argument is flawed because he does not evaluate all of the expenses and advantages of his decision to eat at Taco Bell instead of cooking his own dinner.
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Please show clear solutions to these additional questions involving gas laws. A complete solution shows
all steps, including necessary unit conversions. Final answers must be rounded to correct significant
figures.
1. If placing a balloon of gas into a freezer at –80.0 °C causes its volume to change to 76.4 % its
initial volume, then what was the balloon’s initial temperature in °C?
2. Suppose instead of volume, we built a thermometer that measures temperature by pressure
changes. A sample of gas is placed into a rigid glass vial along with a pressure sensor. At room
temperature (25.0 °C), the pressure of the gas is 1.01 atm. The gas thermometer is then placed
into a bath of hot oil. The pressure of the apparatus changes to 1.38 atm. What is the temperature
of the oil in °C?
1. The balloon's initial temperature was ____ °C.
2. The temperature of the oil is ____ °C.
1. To find the balloon's initial temperature, we can use the combined gas law, which states that the initial pressure times the initial volume divided by the initial temperature is equal to the final pressure times the final volume divided by the final temperature. Given that the volume changes to 76.4% of its initial volume and the final temperature is -80.0 °C, we can solve for the initial temperature. First, we convert the volume change to a decimal by dividing 76.4% by 100, giving us 0.764. Plugging in the values into the combined gas law equation, we can rearrange it to solve for the initial temperature.
2. To determine the temperature of the oil, we can use the ideal gas law, which states that the pressure times the volume divided by the temperature is equal to the gas constant times the number of moles. Since the volume remains constant and we are given the initial and final pressures, we can solve for the temperature. By plugging in the values into the ideal gas law equation and solving for the temperature, we can find the temperature of the oil in °C.
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Plz help I needs its
Can you pleprovide me with the three examples of
chance/random causes of variation and three examples of assignable
causes of variation ?
Chance/random causes: Raw material variation, machine errors, environmental factors. Assignable causes: Equipment malfunction, operator errors, process parameter changes.
Chance/random causes of variation are inherent in any process and are typically beyond the control of individuals or organizations. These sources of variation arise from natural variability in the system and cannot be eliminated completely.
For example, in manufacturing, variations in raw materials such as moisture content, density, or chemical composition can impact product quality. Random machine errors, influenced by electrical noise or mechanical wear, can also introduce variation. Unpredictable environmental factors like temperature or humidity can further contribute to chance causes.
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Anyone know this one ?
Does anyone know how to do this please help it’s harder than it looks I have to use an image because it’s hard to put in words
Answer:
i dont think ther is a ancer for that
Step-by-step explanation:
-To do this you shuld use your brain base off of memory. If that dosn't
work contact a parent, teacher, or a trusted adult to help with this work.
1. Pedro is a good student.
a.
b.
Answer:
your answer is (A)
Step-by-step explanation:
in the affirmative
plz mark me as brainlist
y/4-x/5=6 x/15+y/12=0 solve the system of equations
Upon answering the query As a result, the following is the system of equations' solution: x = -150, y = 120.
What is equation?An equation in math is an expression that connects two claims and uses the equals symbol (=) to denote equivalence. An equation in algebra is a mathematical statement that establishes the equivalence of two mathematical expressions. For instance, in the equation 3x + 5 = 14, the equal sign places a space between each of the variables 3x + 5 and 14. The relationship between the two sentences that are written on each side of a letter may be understood using a mathematical formula. The sign and only one variable are frequently the same. as in, 2x - 4 equals 2, for instance.
To solve
\(Y/4 - x/5 = 6 ........ (1)\\x/15 + y/12 = 0 ....... (2)\\\)
After using the substitution approach to find the value for one of the variables, we can use that value to find the value for the other variable.
We can solve for x in terms of y using equation (2):
\(x = - (5/4) y ........ (3)\)
Equation (1) may now be changed to an equation in terms of y by substituting equation (3) for equation (1):
\(y/4 - (-5/4)y/5 = 6\\5y - 4y = 120\\y = 120\\x = - (5/4) (120) = -150\\\)
As a result, the following is the system of equations' solution:
x = -150, y = 120.
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Does this graph show a function? Explain how you know
Use logarithmic differentiation to find the derivative of the function y=x^2x
The derivative of the function y = x^2x using logarithmic differentiation is dy/dx = x^2x(2 + 2ln(x)).
To find the derivative of the function y = x^2x using logarithmic differentiation, we follow these steps:
Take the natural logarithm of both sides of the equation:ln(y) = ln(x^2x)Apply the logarithmic property to simplify the equation:ln(y) = (2x)ln(x)Differentiate both sides of the equation implicitly:(1/y) * dy/dx = (2x)(1/x) + ln(x)(d/dx)(2x)Simplify the equation:(1/y) * dy/dx = 2 + 2ln(x)Multiply both sides of the equation by y:dy/dx = y(2 + 2ln(x))Substitute the original function back into the equation:dy/dx = x^2x(2 + 2ln(x))Learn more:About logarithmic differentiation here:
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To find the derivative of the function y = x^(2x) using logarithmic differentiation, we take the natural logarithm of both sides, apply logarithmic properties, and then differentiate implicitly.
Start by taking the natural logarithm of both sides of the equation:
ln(y) = ln(x^(2x))
Apply the power rule of logarithms to simplify the expression:
ln(y) = 2x * ln(x)
Now, differentiate both sides of the equation implicitly with respect to x:
(1/y) * dy/dx = 2 * ln(x) + 2x * (1/x)
Simplify the expression:
(1/y) * dy/dx = 2 * ln(x) + 2
Multiply both sides by y to isolate dy/dx:
dy/dx = y * (2 * ln(x) + 2)
Substitute the original value of y = x^(2x) back into the equation:
dy/dx = x^(2x) * (2 * ln(x) + 2)
The derivative of the function y = x^(2x) using logarithmic differentiation is dy/dx = x^(2x) * (2 * ln(x) + 2). Logarithmic differentiation is a useful technique for differentiating functions that involve exponentials or complicated algebraic expressions, as it allows us to simplify the calculation by taking the logarithm of both sides and then differentiating implicitly.
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mr.torres is 6 1/4 feet tall. Mr. torres is 5 1/2 feet tall. How much shorter is Mrs. torres than her husband PLEASE HURRY!
Answer: 3/4
Step-by-step explanation: 6 1/4 - 5 1/2
Answer: The answer is 1 2/8
Step-by-step explanation:
5 1/2 X 4/4 = 4/8 So the answer is 1 and 2/8
6 1/4 X 2/2 = 2/8
6 4/8
-
5 2/8
___
1 2/8Fritz can build a bookcase in 8 hours and Holly can build the same bookcase in 10 hours. After working together for 3 hours, Fritz leaves how long will it take holly to finish the bookcase by herself?
Holy will take 13/5 or 2.6 hours to finish the bookcase.
What is relation between time and work?The relation between time and work is
Work Done = Time Taken × Rate of Work ·
or, Rate of Work = 1 / Time Taken ·
or, Time Taken = 1 / Rate of Work ·
Now it is given that,
Time taken by Fritz to build a bookcase = 8 hours
So, Bookcase build by Fritz in 1 hour = 1/8
Similarly,
Time taken by Holly to build a bookcase = 10 hours
So, Bookcase build by Holly in 1 hour = 1/10
So, bookcase build in 3 hours
Fritz = 3/8
Holly = 3/10
Total bookcase build in 3 hours = 3/8 + 3/10 = 27/40
So. remaining work = 1 - 27/40 = 13/40
Thus, Time taken by Fritz to complete the bookcase = 8 * (13/40) hours
= 13/5 or 2.6 hours
Thus, Holy will take 13/5 or 2.6 hours to finish the bookcase.
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Solve the equation
6x – 4 - 2x = 20
A- X = -3
B- X = 3
C- X= - 6
D - = 6
PleSe help
Answer:
answer is 6
Step-by-step explanation:
6x-4-2x=20
4x-4=20
4(x-1)=20
x-1=5
X=6
Answer:
\(6x - 4 - 2x = 20 \\ collecting \: like \: terms \: \\ 6x - 2x - 4 = 20 \\ 2x - 4 = 20 \\ 4x = 20 + 4 \\ 4x = 24 \\ x = \frac{24}{4} \\ x = 6\)
Step-by-step explanation:
so answer is
\(x = 6\)
Clarissa made 5 identical sundaes using 4 pints of ice cream. How much ice cream did Clarissa use for each sundae?
The number of pints of ice cream used for each sundae is 0.8 pints.
What is a unit rate?It is the quantity of an amount of something at a rate of one of another quantity.
In 2 hours, a man can walk for 6 miles
In 1 hour, a man will walk for 3 miles.
We have,
4 pints of icecream = 5 sundaes
Divide both sides by 5.
4/5 pints of icecream = 1 sundaes
0.8 pints of icecream = 1 sundaes
Thus,
0.8 pints of ice cream is used for each sundae.
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Determine all values of h and k for which the system has no solution.5x + 9y = h-4x + ky = -9k= ?h does not equal ?
When solving a system of equations, the values of h and k must be chosen in order to make the equation have no solution. The equation 5x + 9y = h and -4x + ky = -9 can have no solution if h does not equal the value of k.
This means that for any value of h that does not equal the value of k, the system of equations will have no solution.
For example, if h=2 and k=3, the system of equations will have no solution because 5x + 9y does not equal 3. Similarly, if h=3 and k=2 the system of equations will have no solution because -4x + 2y does not equal -9. Therefore, for any value of h and k in which h does not equal k, the system of equations will have no solution.
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Find the minimum or maximum of the function below.
f(x) = 6x² - 2
А. minimum of-2
B. maximum of -2
C. minimum of 8
D. maximum of 6
PLEASE ANSWER QUICK ILL HIVE BRAINLYEST
Answer:
A) minimum of -2Answer:
A. minimum at x = -2.
Step-by-step explanation:
Finding the derivative:
f'(x) = 12x.
12x = 0 for a maxim/ minimum.
x = 0.
As the second derivative (12) is positive, we have a minimum value when x = 0.
So the function has a minimum value where f(x) = 6(0)^2 -2 = -2.
A window is 12 feet above the ground. A ladder is placed on the ground to reach the window. If the bottom of the ladder is placed 5 feet away from the ladder building, what is the length of the ladder
Answer:
Therefore, the length of the ladder is 13 feet.
Step-by-step explanation:
This is a classic example of a right triangle problem in geometry. The ladder serves as the hypotenuse of the triangle, while the distance from the building to the ladder and the height of the window serve as the other two sides. Using the Pythagorean theorem, we can solve for the length of the ladder:
ladder^2 = distance^2 + height^2 ladder^2 = 5^2 + 12^2 ladder^2 = 169 ladder = √169 ladder = 13
Therefore, the length of the ladder is 13 feet.
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The Marted out of 10.00 He question Your answer is correct The point with cylindrical coordinates [p. p. 21-12-√3.6 has spherical coordinates [r. 0.p] [sqrt(48), pi/13, pi/6] NOTE: In the text and the lecture notes cylindrical coordinates are denoted by [r..z). So, in this question (p.) are polar coordinates in the the xy-plane. In the text and the lecture notes spherical coordinates are denoted by le, 8, 1, where is the radius, the distance from the origin to the point P, the angle is the angle between positive x-axis and the projection of anto xy-plane, and is the angle between positive - axis anda. Thus, in your answer use for r. 0 for p and for 0. Your last answer was interpreted as follows: [V answer is partially correct. The value of r is correct. The value of is incorrect. The value of op is incorrect. Please try again. You have 2 attempts remaining.
The shape with a series of parallel cross sections that are congruent circles is a cylinder.
The cross-section that results from cutting a cylinder parallel to its base is a circle that is congruent to all other parallel cross-sections. This is true for any plane that is perpendicular to the cylinder's base. The only shape that has parallel cross-sections that are congruent circles is a cylinder, for this reason.
Two parallel, congruent circular bases that lay on the same plane make up the three-dimensional shape of a cylinder. A curved rectangle connecting the bases makes up the cylinder's lateral surface. Congruent circles are produced when a cylinder is cut in half parallel to its base.
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In a group of dogs and their owners, there are exactly 20 heads and 64 legs. How many dogs are in the group
Answer:
If we assume that everyone in the group is an owner, we would have
\(20*2=40\) legs.
\(64-40=24\) legs
Therefore, we need 24 more legs.
These 24 additional legs can be made from the difference of legs between the owners and dogs.
In this case, dogs have \(4-2=2\) more legs than an owner.
24 ÷ 2 = 12.
There are 12 dogs in the group.
7. The rectangle below is dilated by a scale factor of
3.6 to create a new rectangle. Which of the following
could be the dimensions of the new rectangle?
4 cm
B
C
A
D
A. 14.4 cm x 5.4 cm
B.5.4 cm x 7.2 cm
C.7.2 cm x 1.8 cm
D. 14.4 cm x 7.2 cm
Answer:
A
Step-by-step explanation:
you do 3.6 times both the cm or number and you get 14.4 cm and 5.4 cm
What is the solution to 12 = 3/4x
Answer:
3
Step-by-step explanation:
2
give an example of a polynomial f pxq with integer coefficients which factors (poly mod nq, but which has no roots, i.e., for which there are no integers x such that f pxq " 0 (poly mod n
An example of a +f(pxq) with integer coefficients that factors (poly mod nq), but has no roots is (x^2 + 1)(x^2 + 2). This polynomial satisfies the given conditions and demonstrates that it is possible to have a polynomial with integer coefficients that factors modulo n, but has no roots.
Let's consider the polynomial f(pxq) = (x^2 + 1)(x^2 + 2).
1. This polynomial has integer coefficients as both factors have integer coefficients.
2. Now, let's consider taking the modulo n, where n is any positive integer.
3. Since the modulo operation only affects the coefficients, we will still have a polynomial with integer coefficients after taking the modulo.
4. However, there are no integers x for which f(pxq) = 0 (poly mod n), as the factors x^2 + 1 and x^2 + 2 do not have any integer roots.
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Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar.
Complete the table of inputs and outputs for the given function.
g(x) = -4. – 19(1) = -41 - 1
WILL GIVE 50 POINTS PLEASE HELP ASAP
The complete inputs and outputs for the given function are
x g(x)
-2 7
0 -1
-2 13
-1 3
Determining the value of a functionFrom the question, we are to determine the value of the given boxes
The given function is,
g(x) = -4x -1
For the first box, we are to determine the value of x for which g(x) = 7
From the given function,
g(x) = -4x -1
Put g(x) = 7
Then,
7 = -4x - 1
7 + 1 = -4x
8 = -4x
∴ x = 8/ -4
x = -2
The value of x in the first box is -2
For the second box, we are to determine the value of g(x), for x = 0
g(0) = -4(0) -1
g(0) = 0 - 1
g(0) = -1
The value of g(x) in the second box is -1
For the third box, we are to determine the value of x for which g(x) = -13
-13 = -4(x) -1
-13 = -4x - 1
-13 + 1 = -4x
-12 = -4x
∴ x = -12/ -4
x = 3
The value of x in the third box is -2
For the fourth box, we are to determine the value of g(x), for x = -1
g(-1) = -4(-1) -1
g(-1) = 4 - 1
g(-1) = 3
The value of g(x) in the fourth box is 3
Hence, the complete inputs and outputs for the given function are
x g(x)
-2 7
0 -1
-2 13
-1 3
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PLEASE HELP!!! ILL GIVE BRAINLIEST
A map of a highway has a scale of 2 inches=33 miles. The length of the highway on the map is 6 inches. There are 11 rest stops equally spaced on the highway, including one at each end. You are making a new map with a scale of 1 inch=30 miles . How far apart are the rest stops on the new map?
How many inches apart are the rest stops?
Answer:
.305
Step-by-step explanation:
Step-by-step explanation:
2/33=6/x
x=99
since there are 11 rest stops and you are trying to find the space in the middle of the two rest stops.
99/11 rest stops
9 miles in between rest stops
9/y=30/1
9/30=y
3/10=y
.3 inches=y
Hope that helps :)
Que es un variable? (De matemáticas)
Answer:
\(\huge\boxed{Que \ es \ un \ variable \ ?\hookleftarrow}\)
✐ En matemáticas, una variable es un símbolo que funciona como marcador de posición para expresiones o cantidades que pueden variar o cambiar; se utiliza a menudo para representar el argumento de una función o un elemento arbitrario de un conjunto. Además de los números, las variables se utilizan comúnmente para representar vectores, matrices y funciones.
Consider the equation f (x) = (x + 1): – 3.
Which point does NOT lie on the graph of y=f-? (x)?
Answer:
-3
Step-by-step explanation:
x+1=3
kia practices the piano in 15 minute session.During a week,she practices for 345 minute.how many sessions did she practice during the week
Answer:
23 sessions
Step-by-step explanation:
345min (total) ÷ 15min (each session)
= 23 sessions