Answer:
5
Step-by-step explanation:
23 x + 977 y = 2023
977 x + 23 y = 2977
add the 2 together
1000x+1000y =5000
so x+y =5
x=5-y
plug this into first equation
23(5-y) +977y =2023
solve for y =2
so x=3
x² -y² =(x+y)*(x-y) =5*1 =5
Write each monomial in standard form and name its coefficient.
Answer:
The standard form is [tex]\boxed{3n^4m^2}[/tex] .
The coefficient is [tex]\boxed{3}[/tex]
Step-by-step explanation:
What is Standard Form of Polynomial?
The standard form of a polynomial is a way of writing a polynomial such that the term with the highest power of the variables comes first followed by the other terms in decreasing order of the power of the variable
We are given the expression
[tex]\dfrac{2}{3}m^2n \cdot 4.5 n^3\\\\[/tex]
and we have to convert to standard form
First multiply the constants together to get the coefficient:
[tex]\dfrac{2}{3} \cdot 4.5 = \dfrac{2 \cdot 4.5}{3} = \dfrac{9}{3} = 3[/tex]
There is only one m term which is m²
Multiply the two n terms to get [tex]n \cdot n^3 = n^(1 + 3} = n^4[/tex]
Therefore in standard form we get ( in decreasing order of exponents)
[tex]3n^4m^2[/tex]
The coefficient is 3
3. Put the following numbers in order from least to greatest: 0.8, 1/10, 3/100, 0.91
4. Put the following numbers in order from least to greatest: 0.9, 0.35, 11/100, 7/10, 0.6, 0.21
5. Put the following numbers in order from least to greatest: 36/100, 0.2, 1/10, 8/100, 0.5, 0.44
If you can answer all the questions thats awesome but i mainly need help with number 5.
3) Ascending order of numbers are, 3/100 , 1/10, 0.8, 0.91.
4) Ascending order of numbers are, 11/100, 0.21, 0.35, 0.6, 7/10, 0.9
5) Ascending order of numbers are, 8/100, 1/10, 0.2, 36/100, 0.44, 0.5
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
3) Numbers are,
⇒ 0.8, 1/10, 3/100, 0.91
It can be written as;
⇒ 0.8, 0.1, 0.03, 0.91
Hence, Ascending order of numbers are,
⇒ 0.03, 0.1, 0.8, 0.91
⇒ 3/100 , 1/10, 0.8, 0.91
4) Numbers are,
⇒ 0.9, 0.35, 11/100, 7/10, 0.6, 0.21
It can be written as;
⇒ 0.9, 0.35, 0.11, 0.7, 0.6, 0.21
Hence, Ascending order of numbers are,
⇒ 0.11, 0.21, 0.35, 0.6, 0.7, 0.9
⇒ 11/100, 0.21, 0.35, 0.6, 7/10, 0.9
5) Numbers are;
⇒ 36/100, 0.2, 1/10, 8/100, 0.5, 0.44
It can be written as;
⇒ 0.36, 0.2, 0.1, 0.08, 0.5, 0.44
Hence, Ascending order of numbers are,
⇒ 0.08, 0.1, 0.2, 0.36, 0.44, 0.5
⇒ 8/100, 1/10, 0.2, 36/100, 0.44, 0.5
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tina has scheduled a dinner with friends in 4.5 hours. what is the probability that her simulation study will be done by then?
The approximate distribution (give distribution name and parameters) of the total length will be = 450 minutes
The estimated distribution of the total length of Tina's simulation study is a triangular distribution with a base worth of 2 minutes, a greatest worth of 4 minutes, and a mode (most reasonable worth) of (2+4)/2 = 3 minutes.
Since the simulation time is generally consistently distributed somewhere in the range of 2 and 4 minutes, the total simulation time will be the sum of 150 free random variables each with a triangular distribution.
Hence, the total simulation time will also have a triangular distribution with a base worth of 2 minutes x 150 = 300 minutes, a greatest worth of 4 minutes x 150 = 600 minutes, and a method of (300+600)/2 = 450 minutes.
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The complete question is:
Tina is running a simulation study on her laptop. The duration of each simulation is roughly uniformly distributed between 2 and 4 minutes. She needs to run 150 simulations and she runs all her simulations back-to-back. - What is the approximate distribution (give distribution name and parameters) of the total length of Tina's simulation study? Explain your answer
A baby giraffe is 6 ft tall at birth. After one month, its height is 6 1/2 ft. After two months, its height is 7 ft. After three months, its height is 7 1/2 ft. Sketch a linear function that models the giraffe’s height. Months since birth should be on the x-axis.
The linear function that models the giraffe's height after x months is given as follows:
y = 6 + 0.5x.
The graph is given by the image presented at the end of the answer.
How to model the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the y-intercept, representing the value of y when x = 0.The parameters for this problem are given as follows:
b = 6, which is the height at birth.m = 0.5, as the height increases by 0.5 each month.Hence the function is defined as follows:
y = 0.5x + 6.
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a 250 gallon tank initially contains 100 gallons of a solution that holds 40 lbs of a chemical. a solution containing 3 5 lb/gal of the chemical runs into the tank at the rate of 5 gal/min and the mixture runs out at the rate of 7 gal/min. determine the time when the concentration of the chemical in the tank is 0.8 lb/gal.what
The time when the concentration of the chemical in the tank is 0.8 lb/gal is 36.31 minutes.
Let C be the concentration of the chemical in the tank and V be the volume of the tank.
Initially, V = 100 gal and C = 40 lb/100 gal = 0.4 lb/gal.
Let t be the time in minutes.
The rate of change of C is given by:
dC/dt = (5*3.5 lb/gal - 7*C)/V
Solving the differential equation, we get:
C = 0.4 + 0.6e^(-7t/100)
Setting C = 0.8 lb/gal, we get:
0.8 = 0.4 + 0.6e^(-7t/100)
=> 0.6e^(-7t/100) = 0.4
=> e^(-7t/100) = 0.67
=> -7t/100 = ln 0.67
=> t = 100*ln0.67/-7
=> t = 36.31 minutes
Therefore, the time when the concentration of the chemical in the tank is 0.8 lb/gal is 36.31 minutes.
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two cards are drawn without replacement from a standard deck of playing cards. what is the probability that at least one of them is spades?
The probability of getting 1 spade card when we take two cards out randomly of a deck of cards is 1/4.
What is probability?By dividing the entire number of possible outcomes by the total number of possible events, the probability is determined.
Probability and odds are two distinct ideas.
To calculate chances, divide the likelihood of an event by the likelihood that it won't occur.
Mathematicians investigate probability, which may be broken down into four primary categories: axiomatic, classical, empirical, and subjective.
So, we know that:
There are 13 spades in the deck of 52 cards.
Then use the probability formula which is as follows:
P(E) = Favourable events/Total events
P(E) = 13/52
P(E) = 1/4
Therefore, the probability of getting 1 spade card when we take two cards out randomly of a deck of cards is 1/4.
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A number line going from negative 5 to positive 5. From positive 2 to positive 5 is positive 3.
David added 2 and –3 using the number line tool. Which of the following errors did he make?
He started at 2 instead of zero.
He moved right 2 units for positive 2.
He moved right 3 units for negative 3.
He started at zero instead of 2.
The correct statement is :David started at 0 instead of 2
What is a number line in math?A number line is a horizontal line that has equally spread number increments. The numbers included on the line will determine how the number on the line can be answered. The question that goes with the number determines how it will be used, for example, plotting a point.
Given here: In a number line the interval (-5,5) is marked and 2 to 5 is 3
The right steps are
Add 3 to 2 to obtain the required number as there are 3 spaces between 2 and 5
Thus 2+3=5 which is the required answer
but David addes 2-3=-1 which is incorrect.
Hence, David started at 0 instead of 2
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Audrey is planning to drive from City X to City Y. The scale drawing below shows the distance between the two cities with a scale of ¼ inch = 24 miles.
City X
City Y
3 in
The actual distance between the two cities is 288 miles.
What is the actual distance?A scale drawing is a smaller version of a larger image / city. The scale drawing is reduced by a constant ratio. This means that the scale drawing of the two cities would be smaller than the actual cities.
The scale is used to keep the proportion of the dimensions between the scale drawing and the original diagram similar. This means that the scale drawing of the two cities would be smaller than the actual cities.
The actual distance between the two cities = (3 x 24) ÷ 1/4
= 3 x 24 x 4 = 288 miles
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El sueldo de un trabajador de una empresa es de S/2000. A medio año recibe un incremento del 20 % y, al final del año, recibe otro incremento del 25 % por un bono de productividad.
Respuesta: $500
Explicación paso a paso:
S/2000 es el que no tiene por ciento entonces pones x sobre 2000 y haces 20/100 para el primero y 25/100 para el segundo
X
2000 20
100
100x=40,000/100x=$400 al final del año
tomas $400 y le agregas otro 25%
X
400 25
100
100x=10,000/100x=$100 se agrega a su salario
En total obtendrá $500
In the data set below, what is the mean absolute deviation?
2, 2, 1, 6, 6
If the answer is a decimal, round it to the nearest tenth.
answer
A) 2.1
B 2
c) 10.4
D 3.4
The mean absolute deviation is 3.4
Option D is the correct answer.
What is a mean?It is the average value of the set given.
It is calculated as:
Mean = Sum of all the values of the set given / Number of values in the set
We have,
2, 2, 1, 6, 6
Mean = (2 + 2 + 1 + 6 + 6) / 5 = 17/5 = 3.4
Thus,
The mean is 3.4
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. Metal spheres of radius 2 cm are packed into a rectangular box of internal dimensions 16 cm x 8 cm x 8 cm. When 16 spheres are packed the box is filled with a preservative liquid. Find the volume of this liquid. C
The volume of the preservative inside the box is 487.83 cm³.
What is the total volume of the box?The total volume of the box is calculated by using the following formula as shown below.
V = L x B x W
where;
L is the length of the boxB is the breadth of the boxW is the width of the boxV = 16 cm x 8 cm x 8 cm
V = 1,024 cm³
The total volume of the metal spheres inside the box is calculated as follows;
V = 16 x ( ⁴/₃πr³ )
where;
r is the radius of the sphereV = 16 x ( ⁴/₃π(2 cm)³ )
V = 536.17 cm³
The volume of the preservative inside the box = 1,024 cm³ - 536.17 cm³
= 487.83 cm³
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Can someone help with this
Based on the word problem "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." Eric's fraction is 12/30.
What are the parts of a fraction?Generally speaking, a fraction comprises two (2) main parts and these include the following:
NumeratorDenominatorNext, we would translate the word problem "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." into an algebraic expression as follows;
n/(n + 18) = 2/5
By cross-multiplying, we have:
5n = 2(n + 18)
5n = 2n + 36
5n - 2n = 36
3n = 36
n = 36/3
n = 12.
Now, we can determine the fraction as follows;
n/(n + 18) = 12/(12 + 18)
n/(n + 18) = 12/30.
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Complete Question:
Eric has a riddle: "I am thinking of a fraction that is equivalent to 2/5 and the numerator is 18 less than the denominator." what is his fraction?
a map has a scale of 1 inch: 15 miles. if two cities are 3.4 inches apart on the map, how far are they actually apart? show your work!
A map is scale at one inch to fifteen miles. On a map, if two cities are 3.4 inches apart, They are actually apart 15.
A scale is a collection of values, such as levels or numbers, that are applied to a particular system of measurement or comparison. Scale is the ratio that establishes the relationship between the model and the actual figure. The real figures in smaller units are shown by it on maps. As an illustration, a scale of 1:5 means that 1 on the map is equivalent to the size of 5 in the real world. A framework or application can manage heavier loads if it scales properly.
Based on the given conditions, formulate:: 3.4*15/1
3.4 in x 15mi/1in = 51 mi
Calculate the product or quotient: 51
They are actually apart 15
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The ratio of the circumference of circle A to the circumference of circle B is 3:1. What is the ratio of the area of circle A to the area of circle B? Be sure to show your work! (Remember, your answer should be a RATIO!)
The ratio of the area of circle A to the area of circle B is 9:1
What is ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, the ratio of the circumference of circle A to the circumference of circle B is 3:1. What is the ratio of the area of circle A to the area of circle B
The circumference of circle = 2π × radius
We have,
Circumference(A) / Circumference(B) = 3 / 1
Let the radius of A be R and that of B be r,
2πR / 2πr = 3/1
R/r = 3
R = 3r
Now, the area of a circle = π × radius²
Area(A) = πR²
= π(3r)² = 9πr²
Area(B) = πr²
Ratio of the area of circle A to Circle B = 9πr² / πr²
= 9/1
Hence, the ratio of the area of circle A to the area of circle B is 9:1
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Una piedra cayó al mar desde la cima de un acantilado. En el aire tuvo una velocidad promedio de 16 m/s. En el agua tuvo una velocidad promedio de 3 m/s antes de tocar el fondo del mar. La distancia total desde la cima del acantilado hasta el fondo del mar es 127 metros, y la caída completa de la piedra duró 12 segundos. ¿Cuánto tiempo cayó la piedra a través del aire y cuánto tiempo a través del agua?
Resolviendo un sistema de ecuaciones, veremos que que la piedra estuvo 7 segundos en el aire y 5 en el agua.
¿Cuánto tiempo cayó la piedra a través del aire y cuánto tiempo a través del agua?Sabemos que:
En el aire tuvo una velocidad promedio de 16 m/s. En el agua tuvo una velocidad promedio de 3 m/s antes de tocar el fondo del mar.
Definamos las variables:
x = tiempo que la piedra estuvo en el aire.
y = tiempo que la piedra estuvo en el agua.
Sabemos que el trayecto completo duro 12 segundos, entonces podemos escribir:
x + y = 12
Y la caida total fueron 127 metros, entonces:
x*16 + y*3 = 127
Entonces tenemos un pequeño sistema de ecuaciones:
x + y = 12
x*16 + y*3 = 127
En la primera podemos aislar x:
x = 12 - y
Reemplazar eso en la otra ecuacion:
(12 - y)*16 + y*3 = 127
192 - 13y = 127
192 - 127 = 13y
65 = 13y
65/13 = y
5 = y
Entonces la piedra esta 5 segundos en el agua y los otros 7 segundos en el aire.
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In a 14-sided polygon, what is the sum of
a) the interior angles?
b) the exterior angles?
Give your answers in degrees (°).
The Sum of interior angles is, 2160°.
The sum of the exterior angles of a 14-sided polygon is 360°
What is interior angle?Angles inside a polygon are referred to as interior angles. A triangle, for instance, has three internal angles. Interior angles are sometimes defined as "angles confined in the interior area of two parallel lines when they are crossed by a transversal."
Given:
A polygon with 14 sides.
The Sum of interior angles = (n - 2) × 180°
= 12 x 180
= 2160°
The sum of the exterior angles of a 14-sided polygon is 360°
Therefore, all the required values are given above.
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in a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the true population proportion of water specimens that contain detectable levels of lead is between
In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the levels of lead is between (0.4958, 0.7422).
p is 26/42=0.6190
rootp(1-p)/n=root0.6190(1-0.6190)/42=0.0749
satisfies that above this and under the standard normal density there is an area of 0.05. In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead. the 90% confidence interval for the true population proportion of water specimens that contain detectable levels of lead is between (0.4958, 0.7422).
Density is the number of things—which could be people, animals, plants, or objects—in a certain area. To calculate density, you divide the number of objects by the measurement of the area. The population density of a country is the number of people in that country divided by the area in square kilometers or miles.
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HELP pls will mark brainliest
Answer:
y = 20x +22
Step-by-step explanation:
What is the value of 8 in this number?
17,896,043,922
A. 8 billion
B. 800 million
C. 800 thousand
The value of 8 in the number is 800million
What is place value?Place value in Maths describes the position or place of a digit in a number. Each digit has a place in a number. When we represent the number in general form, the position of each digit will be expanded. Those positions start from a unit place or we also call it one's position.
For example the place place value of 4 in 400 is 4 hundred. Place value starts with unit, tens hundreds, thousands, ten thousands, hundred thousands , million, ten million, 100million e.t.c
The place value of 8 in the number is 8 hundred million. This means 800,000.
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The price of an item has been reduced by 80%. The original price was $70. What is the price of the item now?
IT'S TIMEEEEEEEDDDDDDDDD
The new price of the item after a deduction of 80% from the original price is $14
What is the price of the item now?Percentage discount = 80%
Original price of the item = $70
New price of the item= Original price of the item - (Percentage discount × Original price of the item)
= 70 - (80% × 70)
= 70 - (0.8 × 70)
= 70 - 56
= $14
In conclusion, the item now cost $14 after deducting discount.
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Let sine of theta equals the quantity 2 times radical 2 end quantity over 5 and pi over 2 is less than theta is less than pi period
Part A: Determine the exact value of cos 2θ.
Part B: Determine the exact value of sine of the quantity theta over 2 end quantity period
Answer:
[tex]\textsf{A)} \quad \cos 2 \theta=\dfrac{9}{25}[/tex]
[tex]\textsf{B)} \quad \sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]
Step-by-step explanation:
Given:
[tex]\sin \theta=\dfrac{2\sqrt{2}}{5},\quad \dfrac{\pi}{2} < \theta < \pi[/tex]
[tex]\hrulefill[/tex]
Part ATo determine the exact value of cos 2θ, we can use the Cosine Double-Angle formula:
[tex]\large\boxed{\cos^2\theta = 1 - 2 \sin^2 \theta}[/tex]
Substitute the given value of sin θ into the formula:
[tex]\begin{aligned}\cos 2 \theta&=1-2\left(\dfrac{2\sqrt{2}}{5}\right)^2\\\\\cos 2 \theta&=1-2\left(\dfrac{8}{25}\right)\\\\\cos 2 \theta&=\dfrac{25}{25}-\dfrac{16}{25}\\\\\cos 2 \theta&=\dfrac{9}{25}\end{aligned}[/tex]
[tex]\hrulefill[/tex]
Part BTo determine the exact value of sin (θ/2), we can use the half-angle formula for sine:
[tex]\large\boxed{\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\cos \theta}{2}}}[/tex]
First, find the value of cos θ by substituting the given value of sin θ into the trigonometric identity sin²θ + cos²θ = 1:
[tex]\begin{aligned}\left(\dfrac{2\sqrt{2}}{5}\right)^2+\cos^2\theta&=1\\\\\dfrac{8}{25}+\cos^2\theta&=1\\\\\cos^2\theta&=1-\dfrac{8}{25}\\\\\cos^2\theta&=\dfrac{17}{25}\\\\\cos\theta&=\pm \sqrt{\dfrac{17}{25}}\\\\\cos\theta&=\pm \dfrac{\sqrt{17}}{5}\end{aligned}[/tex]
As cos θ is negative on the interval π/2 < θ < π, we take the negative square root. Therefore:
[tex]\cos\theta&=-\dfrac{\sqrt{17}}{5}[/tex]
Now, substitute the found value of cos θ into the half-angle formula:
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{1-\left(-\dfrac{\sqrt{17}}{5}\right)}{2}}[/tex]
Therefore:
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5}{5}+\dfrac{\sqrt{17}}{5}}{2}}[/tex]
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{\dfrac{5+\sqrt{17}}{5}}{2}}[/tex]
[tex]\sin\left(\dfrac{\theta}{2}\right) = \pm \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]
As sin θ is positive on the interval π/2 < θ < π, we take the positive square root. Therefore:
[tex]\sin\left(\dfrac{\theta}{2}\right) = \sqrt{\dfrac{5+\sqrt{17}}{10}}[/tex]
tricia wants to install a decorative wall paper border around the top of the wall in her master bedroom. the room measures 14ft by 17ft. how many feet of the border will will she need?
tricia wants to install a decorative wall paper border around the top of the wall in her master bedroom. the room measures 14ft by 17ft. then perimeter 62 feet of the border will will she need
For the installation of a decorative wall paper Tricia will need 70 ft of the border to decorate the wall of her master bedroom.
The measures of the room is 17 ft by 14 ft.
So, the length of the room (l) = 17 ft
The width of the room(w) = 14 t
As we know that, perimeter of rectangle is 2(l×w).
We will get perimeter of he room = 2l × 2w
= 2(17) × 2(14)
= 62 ft.
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horses are to race over a certain english meadow for a distance of 4.0 furlongs. what is the race distance in (a) rods and (b) chains? (1 furlong
1 furlong, a unit used in horse racing, is equal to 40 rods and 10 chains, both units used in surveying and equal to 201.168 meters (660 feet).
A furlong is a unit of length used primarily in horse racing. It is equal to 201.168 meters (660 feet). A rod is a unit of length used in surveying and is equal to 5.5 yards (16.5 feet). A chain is also a unit of length used in surveying and is equal to 66 feet.
To calculate 1 furlong in rods, we multiply 1 furlong by the conversion factor of 40 rods per furlong:
1 furlong x 40 rods/furlong
= 40 rods
To calculate 1 furlong in chains, we multiply 1 furlong by the conversion factor of 10 chains per furlong:
1 furlong x 10 chains/furlong
= 10 chains
To convert from furlongs to rods, we multiply the number of furlongs by the conversion factor of 40 rods per furlong:
4.0 furlongs x 40 rods/furlong = 160 rods
And to convert from furlongs to chains, we multiply the number of furlongs by the conversion factor of 10 chains per furlong:
4.0 furlongs x 10 chains/furlong = 40 chains
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6 less than twice a number x is 36 what is x
The value of x is 21.
The question above can be written:
2x-6=36, then simplified the equation
2x=36+6
2x=42
x= 21
Definition of Mathematical ModelsMathematical models are used to simplify problems so that they are easy to understand. Therefore, a mathematical model is a model that represents a problem with a system that reflects relationships between symbols or mathematical relationships.
A mathematical model is a form of human interpretation in translating or formulating existing problems into mathematical forms, so that these problems can be solved using mathematics.
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HELP ASAP
Estimate the solution(s) to the system of equations graphed below. Choose all that apply:
{xy=10
y−x=−3}
Options:
a. (5, 2)
b. (-5, -2)
c.(-2, -5)
d.(0, -3)
Answer:
a and c
Step-by-step explanation:
The lines on the graph cross over those two points. Hope this helps.
Find the arc length of the partial circle
The arc length of the partial circle is, 28.26 units.
What is Circle?The circle is a closed two dimensional figure , in which the set of all points is equidistance from the center.
We have to given that;
Radius of semicircle = 9 units
Now, We know that;
Arc length of semicircle = (2πr) × 180°/360°
Here, Radius of semicircle = 9 units
Hence, We get;
Arc length of semicircle = (2πr) × 180°/360°
Arc length of semicircle = (2 × 3.14 × 9) × 180°/360°
Arc length of semicircle = 28.26 units.
Thus, The arc length of the partial circle is, 28.26 units.
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which of the following statements is true? group of answer choices the version of the sample variance where you divide by n is biased. all of these choices are true. the sample mean is consistent. the sample mean is relatively more efficient than the sample median.
The correct answer is option 1. The version of the sample variance where you divide by n is biased.
This is because dividing by n will produce a biased downward population variance estimate. We must divide by n-1 rather than n to correct this bias. Mathematically, this can be expressed as:
Population Variance = s2 = ∑ (x - μ)2 / n Sample Variance = s2 = ∑ (x - x(bar))2 / (n-1)
In other words, we must subtract 1 from the sample size in the denominator when calculating the sample variance. This is due to the fact that the sample variance and the sample mean are both unbiased estimators of the population variance, respectively.
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Complete Question:
which of the following statements is true?
group of answer choices
the version of the sample variance where you divide by n is biased.all of these choices are true.the sample mean is consistent. the sample mean is relatively more efficient than the sample median.2/5 y − 0.2y − 6 + (−2).
Answer:
(−3.6)y − 4
Step-by-step explanation:
2/5 y − 0.2y − 6 + (−2)
= (2/5 y − 0.2y) − (6 + (−2))
= (2/5 y − 0.2y) − 4
= (2/5 y − 4) − 0.2y
= (2/5 y − 0.2y) − 4
= (2/5 − 0.2)y − 4
= (−3.6)y − 4
Find the general solution of the following differential equation. Primes denote derivatives with respect to x. 3x^2y' +6xy = 15y^3 The general solution is ___
The general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].
The general solution of the following differential equation is [tex]$\quad 3 x^2 y^{\prime}+6 x y=15 y^3$[/tex].
When the arbitrary constant of the general solution takes some unique value, then the solution becomes the particular solution of the equation.The differential equations which are represented in terms of (x,y) such as the x-terms and y-terms can be ordered to different sides of the equation (including delta terms). Thus, each variable after separation can be integrated easily to find the solution of the differential equation. The equations can be written as:
[tex]f(x) dx+g(y)dy=0[/tex], where f(x) and g(y) are either constants or functions of x and y respectively.solution: [tex]$\quad y^{\prime}=\frac{d y}{d x}$[/tex]
So rewritten question as
[tex]$$\begin{aligned}& 3 x^2 \frac{d y}{d x}+6 x y=15 y^3 \\& \frac{d y}{d x}+\frac{6 x y}{3 x^2}=\frac{15 y^3}{3 x^2} \\& \frac{d y}{d x}+\frac{2 y}{x}=\frac{5}{x^2} y^3\end{aligned}$$[/tex]
compare equation (1) with Bernoulli's Equation
[tex]$$\begin{aligned}& \frac{d y}{d x}+P(x) y=Q(x) y^n \\& P(x)=\frac{2}{x} \quad Q(x)=\frac{5}{x^2} \\& n=3\end{aligned}$$[/tex]
Substitute:
[tex]v & =y^{1-n} \\v & =y^{1-3} \\v & =y^{-2} \\y \quad y & =v^{(-1 / 2)}-(2) \\\frac{d y}{d x} & =-\frac{1}{2}\left(v^{-\frac{1}{2}-1}\right) \frac{d v}{d x}\end{aligned}$$[/tex]
[tex]\frac{d y}{d x}=-\frac{1}{2} v^{-3 / 2} \frac{d v}{d x}[/tex]
substitute value of y and [tex]$\frac{d y}{d x}$[/tex] from 4 (2) and (3) respectively in equation (1)
⇒[tex]& \frac{-1}{2} v^{-3 / 2} \frac{d v}{d x}+\frac{2}{x} \cdot v^{-1 / 2}=\frac{5}{x^2} \cdot v^{-3 / 2}[/tex]
⇒[tex]& \frac{d v}{d x}-\frac{4}{x} v=\frac{-10}{x^2} \\[/tex]
⇒ Integrating factor[tex]=e^{\int-4 / x d x} \\[/tex]
[tex]& =e^{-4 \ln x} \\& =e^{\ln x^{-4}} \\& =x^{-4} \\& =\frac{1}{x^4} \\[/tex]
⇒[tex]\frac{1}{x^4} v=\int \frac{1}{x^4} \times \frac{-10}{x^2} d x \\[/tex]
[tex]& =-10 \int x^{-6} d x \\[/tex]
[tex]& =+10 \frac{x^{-6+1}}{(-6+1)}+C=\frac{+10^2}{+8} x^{-5}+C \\&[/tex]
⇒[tex]\frac{1}{x^4} \cdot v & =\frac{2}{x^5}+c \\[/tex]
⇒[tex]v & =\left(\frac{2}{x^5}+c\right) x^4 \\[/tex]
⇒[tex]v & =\left(\frac{2}{x}+c x^4\right)[/tex]
Now replace v=y-2
⇒[tex]& y^{-2}=\frac{2}{x}+c x^4 \\[/tex]
⇒[tex]& y=\left[\frac{1}{\left(\frac{2}{x}+\left(x^4\right)\right.}\right]^{1 / 2} \\[/tex]
⇒[tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex]
Therefore, the general solution of the differential equation is [tex]& y=\sqrt{\frac{x}{2+c x^5}}[/tex].
For more such questions on Bernoulli's Equation
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HELP ASAP!!!! DUE IN 30 MINSS!!!!!!!!!
The diameter of a hat is 4.7 inches. What is the distance around the hat using π = 3.14? Round to the hundredths place.
1.50 inches
7.38 inches
17.34 inches
14.76 inches
Answer:
To find the distance around a hat, you need to find the circumference of a circle with a diameter of 4.7 inches.
The formula for the circumference of a circle is C = π * d, where d is the diameter.
Plugging in the values and using π = 3.14, we have:
C = 3.14 * 4.7 = 14.758
Rounding to the hundredths place, the circumference of the hat is 14.76 inches.
So, the answer is 14.76 inches.
Answer:it is correct the awnser is d 14.76
Step-by-step explanation:did the test