The solution to the separable differential equation y' = 3yx^2, in implicit form, is log |y| = x^3 + c, where c represents the constant of integration.
To solve the separable differential equation y' = 3yx^2, we start by separating the variables. We can rewrite the equation as y'/y = 3x^2. Then, we integrate both sides with respect to their respective variables.
Integrating y'/y with respect to y gives us the natural logarithm of the absolute value of y: log |y|. Integrating 3x^2 with respect to x gives us x^3.
After integrating, we introduce the constant of integration, denoted by c. This constant allows for the possibility of multiple solutions to the differential equation.
Therefore, the solution to the differential equation in implicit form is log |y| = x^3 + c, where c represents the constant of integration. This equation describes a family of curves that satisfy the original differential equation. Each choice of c corresponds to a different curve in the family.
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What do a rectangle and a rhombus have in common? Select all that apply.
Their angle measures add to 360°.
They have four right angles.
They have four congruent sides.
The opposite sides are parallel.
The opposite sides are parallel.
Their angle measures add to 360°
write an equation, waths the equation for thise graph.
Answer:
y = -2x + 3
Step-by-step explanation:
If you do rise/run, you recognize that the slope of the line is -6/3, which = -2. You can also see that the y-intercept of the line is at 3.
The equation of a line is represented by y=mx+b, with m being the slope and b being the y-intercept value.
Just plug in -2 as m and 3 as b in y=mx + b, and you will get your answer.
2. Find the area of a circle with a diameter of 10
feet.
Step-by-step explanation:
d=2r
πr^2
10/2=r
5=r
5^2π
25π=78.5398
Hope that helps :)
1) Evaluate the following expressions.show your work
a) 7(m - 8) for m = -4
Answer:
-84
Step-by-step explanation:
Since m=-4, we can plug -4 into the expression and use PEMDAS
7(m - 8)
7((-4)-8)
7(-12)
-84
How many permutations of S9, have cycle strucrure 3^3?
There is only 1 permutation in S9 with a cycle structure of [tex]3^3[/tex].
To find the number of permutations of S9 with a cycle structure of [tex]3^3[/tex], we can use the concept of cycle index.
In a permutation with a cycle structure of[tex]3^3[/tex], we have three cycles of length 3. The cycle index of S9 with respect to cycles of length 3 can be determined using the Polya enumeration theorem.
The cycle index of S9 with respect to cycles of length 3 is given by:
[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3[/tex]
Expanding this expression, we get:
[tex]Z(S9, t1, t2, t3) = (t1^3 + t3^3)^3\\\= (t1^9 + 3t1^6t3^3 + 3t1^3t3^6 + t3^9)[/tex]
To count the number of permutations with the desired cycle structure, we need to find the coefficient of the term [tex]t1^9t3^9[/tex].
From the expanded form, we see that the coefficient [tex]t1^9t3^9[/tex] is 1.
Therefore, there is only one permutation in S9 with a cycle structure of [tex]3^3[/tex]
In summary, there is 1 permutation of S9 that has a cycle structure of [tex]3^3[/tex].
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Select all the figures that are shaded to represent 60% of the whole. Whoever answers correctly and first will be marked as brainliest!!!!
Answer:
the first one
Step-by-step explanation:
Choose the compound inequality that can be used to solve the original inequality |3x – 5| > 10.
Step-by-step explanation:
Nsjssjsjsjshsnmsksjnsnsns
James has a bank account with $500 that collects 3% interest annually. How much will be in James account after 24 months if no transaction are made?
Answer:
$360
Step-by-step explanation:
Find 3% of 500 = 15
Multiply 15 by 24 = 360
The price of fuel may increase due to demand and decrease due to overproduction. Marco is studying the change in the price of two types of fuel. A and B. over time.
The price in dollars of fuel A after x months is represented by the function below.
10 = 2.961.04)
Part A: is the price of the increasing or decreasing and by what percentage per month? Justify your answer. (5 points)
Part 8: The table below shows the price 9m) in dollars of fuels afer m months
64
m (number of months) 1
3
sim) (price in dollars) 3.04 3.22 3.41 3.61
Which ope of fuel recorded a greater percentage change in pace over the previous month? Justity your answer. (5 points)
Answer:
A. Increasing by 4%.
Step-by-step explanation:
Answer:
A) The price of product A is increasing by 3% per year.
(B) The product A recorded a greater percentage change in price over the previous year.
Step-by-step explanation:
(A)
The function representing the price, in dollars, of product A after x years is:
FA(x)=0.69*(1.03)x
The function FA(x)can be written as:
FA(x)=0.69*1+(0.03)x
The function FA(x) is similar to the exponential growth function, y=a(1+r)x .
Here r is the growth rate.
Thus, it can be said that the price of product A is increasing by 3% per year.
(B)
Consider the data of product B for the year 3 and 4.
The price of product B for year 3 and 4 are 10,303.01 and 10,406.04.
Compute the percent price change from year 3 to 4 as follows:
10406.04-10303.01/10303.01*100
which is 0.999%
~1%
The price of product B is increasing by 1% per year.
Thus, the product A recorded a greater percentage change in price over the previous year.
4th grade math lolll
Answer:
2/5x7
Step-by-step explanation:
The starting salary of a starting teacher is $40,000, which will increase by 2% each year.
Which of the following is the function that models the teacher salary scenario?
The answer choices are in the picture.
Answer:
The first choice is the correct one.
Step-by-step explanation:
The first choice is the correct one. It starts with the base salary and then is multiplied by (1 + 0.02)^t, which is the correct formula for compounding once per year.
hi i need help again
(I need help on number 9) ty
Answer:
You did not take the picture correctly, try taking it again
Step-by-step explanation:
I can’t seeeee
Which of the following equations? (picture included)
Answer:
B
Step-by-step explanation:
Find the surface area of the prism.
7 cm
13 cm
5 cm
12 cm
The surface area is
Answer:
please give more information
Step-by-step explanation:
A bakery produces five types of bagels, two of which are chocolate chip and cinnamon raisin.
(a) If there are at least 10 bagels of each type, how many different selections of 10 bagels are there?
(b) Suppose there are only 3 chocolate chip and 2 cinnamon raisin bagels, but at least 10 of the other three types. How many different selections of 10 bagels are there?
a) If there are at least 10 bagels of each type, we can calculate the number of different selections of 10 bagels by using the concept of combinations. Since there are 5 types of bagels and we need to select 10 bagels, the calculation can be done as follows:
[tex]\(\binom{10+5-1}{10} = \binom{14}{10}\)[/tex]
b) If there are 3 chocolate chip and 2 cinnamon raisin bagels, and at least 10 of the other three types, we can calculate the number of different selections of 10 bagels using the same concept of combinations. In this case, we have 3 types of bagels (excluding chocolate chip and cinnamon raisin) with at least 10 bagels each. So the calculation becomes:
[tex]\(\binom{10+3-1}{10} = \binom{12}{10}\)[/tex]
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This equation shows how the amount of time that a receptionist named Terrence spends on the phone is related to the number of phone calls he routes to employees.
t = p + 17
The variable p represents the number phone calls he routes, and the variable t represents the number of minutes he is on the phone. In all, how many phone calls does Terrence have to route to spend a total of 20 minutes on the phone?
phone calls
hmmm I dunno sorry ......
state four reasons why choice should be made in satisfaction human wants
select the correct answer. which expression is equivalent to x 3x2−2x−3÷x2 2x−3x 1 if no denominator equals zero? a. 1x2−2x−3 b. 1x2−4x 3 c. 1x2 2x−3 d. x 3x 1
The correct answer is option c. 1/(x² + 2x - 3). To determine which expression is equivalent to the given expression, let's simplify it step by step:
The given expression is (x³ - 2x - 3) ÷ (x² + 2x - 3).
Option a. 1/(x² - 2x - 3):
This option is not equivalent to the given expression because it represents the reciprocal of the quadratic denominator, which is different from the given expression.
Option b. 1/(x² - 4x + 3):
This option is not equivalent to the given expression because the signs of the quadratic terms are different. The given expression has a positive quadratic term, while this option has a negative quadratic term.
Option c. 1/(x² + 2x - 3):
This option is equivalent to the given expression because it represents the reciprocal of the quadratic denominator with the same signs for the quadratic terms.
Option d. x/(3x - 1):
This option is not equivalent to the given expression because it lacks the term x³ in the numerator.
Therefore, the correct answer is option c. 1/(x² + 2x - 3).
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I need help on the circled problem please
Answer:
There would be infinite solutions because the equations are exactly the same.
I hope this answered your question
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OWA OWA?PLEASE HELP ME!!!! I WILL MARK!!!
Answer:
6(x - 3 ) = 6x - 18
2(3x - 3) = 6x - 6
Step-by-step explanation:
A triangle has three angles that measure 15 degrees, 85 degrees and (4x - 20). What is the value of x?
y=Ax^2 + Bx + C is the solution of the DEQ: y'=87x. Determine A,B. A 'C' is the constant of integration.
The exact value of A in the general solution is 87/2 and B is 0
How to determine the value of A and B in the general solutionFrom the question, we have the following parameters that can be used in our computation:
y = Ax² + Bx + C
The differential equation is given as
y' = 87x
When y = Ax² + Bx + C is differentiated, we have
y' = 2Ax + B
So, we have
87x = 2Ax + B
By comparing both sides of the equation, we have
2Ax = 87x
B = 0
So, we have
2A = 87
B = 0
Divide both sides of 2A = 87 by 2
A = 87/2
B = 0
Hence, the value of A in the general solution is 87/2 and B is 0
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Can someone help me find and answer an equation to the following math question : Natalie earns 5% commission on all electronics she sells.On Monday she sold a television for $1130 and a DR that cost $325. What was the total she earned in commission?
Answer:
She will make a total commission of $1130+$325=$1445
Then 5% of $1445= $1445×5%=$72,75
A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps. 7. What is the radius? 8. What is the circumference? 9. What is the area?
Answer:
7. 13.25mm
8. 83.25 mm
9. 551.55 mm²
Step-by-step explanation:
The shape of a coin is circular.
A Susan B. Anthony dollar coin has a diameter of 26.5 millimeters. Round your final answers to the nearest hundredth. Show your steps.
7. What is the radius?
The formula for radius = Diameter/2
= 26.5 mm/2
= 13.25 mm
8. What is the circumference?
The formula for the circumference of a circle = 2πr
= 2× π × 13.25mm
= 83.25220532 mm
Approximately to the nearest hundredth = 83.25 mm
9. What is the area?
The formula for the area of a circle = πr²
= π × (13.25mm)²
= 551.54586025 mm²
Approximately to the nearest hundredth = 551.55 mm²
Find the Laplace transform of the following functions.(8 pts/each x 8 = 64 pts) a. a(t) = 28(t) + 3+ 4u(t) b. b(t) = 5 – 5e-2t(1 + 2t)
a. the Laplace transform of a(t) is (28/s^2) + (3/s) + (4/s). b. the Laplace transform of b(t) is 5/s - 10/(s + 2) - 10/(s^3 + 2s^2).
a. To find the Laplace transform of a(t) = 28t + 3 + 4u(t), where u(t) is the unit step function, we can apply the linearity property and the transform of elementary functions.
Applying the linearity property, we can split the transform into three parts:
L{28t} + L{3} + L{4u(t)}
Using the transform of t (L{t} = 1/s^2), we get:
28/s^2 + 3/s + 4/s
Simplifying, we can combine the terms:
(28/s^2) + (3/s) + (4/s)
Therefore, the Laplace transform of a(t) is:
(28/s^2) + (3/s) + (4/s).
b. To find the Laplace transform of b(t) = 5 - 5e^(-2t)(1 + 2t), we can again apply the linearity property and the transform of elementary functions.
Applying the linearity property, we can split the transform into two parts:
L{5} - L{5e^(-2t)(1 + 2t)}
The transform of 5 is simply 5/s.
For the second part, we need to use the transform of e^(-at) and t.
The transform of e^(-at) is 1/(s + a), and the transform of t is 1/s^2.
Using these formulas, we get:
-5/(s + 2)(1 + 2/s^2)
Simplifying and combining terms, we have:
5/s - 10/(s + 2) - 10/(s^3 + 2s^2)
Therefore, the Laplace transform of b(t) is:
5/s - 10/(s + 2) - 10/(s^3 + 2s^2).
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NOLINKS ..................
Answer:
The answer is in the link
Step-by-step explanation:
quntyfcjb/crown!.com :))))
ms.Rivera went to dinner for new year's eve the meal and sodas cost a total of $138 the sales tax in new york state is about 8% and ms Rivera wanted to leave a 20% tip because the service was good. What was the total cost of the meal
Answer:
138 + 27.6 = 165.6
Step-by-step explanation:
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Expert Answer Please! If The Area Of A 60 Sector In A Circle Is 75.4,Find The Diameter Of The Circle.
Answer:
multiply 75.4 by 60 =4,524
The volume of this cylinder is 4,939.22 cubic millimeters. What is the height? Use a 3.14 and round your answer to the nearest hundredth.
Answer:
13 mm
Step-by-step explanation:
V = πr²h
4,939.22 mm³ = 3.14 × (11 mm)²h
4,939.22 mm³ = 3.14 × (11 mm)²h
h = 13 mm
Answer: 13 mm