The polar equation for the curve represented by the Cartesian equation V3x y = 3 is r = 3 / √(3cosθ + sinθ).
To convert the given Cartesian equation into polar form, we can use the relations x = rcosθ and y = rsinθ. Substituting these values into the equation V3x y = 3, we get V3(rcosθ)(rsinθ) = 3. Simplifying this expression, we have V3[tex]r^2[/tex]cosθsinθ = 3.
Next, we can square both sides of the equation to eliminate the radical: 3[tex]r^2[/tex]cosθsinθ = 9. Rearranging the terms, we have [tex]r^2[/tex]cosθsinθ = 3. Now, we can use the identity cosθsinθ = 1/2sin2θ to further simplify the equation: [tex]r^2[/tex](1/2sin2θ) = 3. Multiplying both sides by 2, we obtain[tex]r^2[/tex]sin2θ = 6.
Finally, we can rewrite the equation in terms of r and θ: [tex]r^2[/tex]= 6/sin2θ. Taking the square root of both sides, we have r = √(6/sin2θ). Simplifying further, we get r = √(6/(2sinθcosθ)). Since sinθ = r/[tex]\sqrt(r^2 + z^2)[/tex] and cosθ = z/[tex]\sqrt(r^2 + z^2)[/tex], we can substitute these values into the equation: r = √(6/(2(r/[tex]\sqrt(r^2 + z^2)[/tex])(z/[tex]\sqrt(r^2 + z^2)[/tex]))). Simplifying this expression, we finally arrive at r = 3 / √(3cosθ + sinθ), which is the polar equation for the given curve.
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The members of a drama club sold tickets to a school play.
Each student ticket (s) costs $5.
Each adult ticket (a) costs $7.
28 more student tickets were sold than adult tickets.
The total amount of ticket sales was $800.
Which equation can be used to determine the number of adult tickets sold:
a
5(a + 28) + 75 = 800
b
5(a + 28) + 7a = 800
5(S + 28) + 7 a = 800
d
5(5 + 28) + 75 = 800
Answer:
Step-by-step explanation:
28*5 115 sub 115 from 800 then divide 685 by 5 then add 7 into that number 28 times
jessica made $234 for 13 hours of work. At the same rate, how many hours would she have to work to make $162?
Answer: 9 hours
We would get:
1 hour of work = $18
162 divided by 18 = 9
So she would have to work 9 hours
Answer:
9 hours
Step-by-step explanation:
Step One: A rate is the same thing as ratio. This just means that there is a proportion. For example, for every 3 dogs, there are 4 cats. This would mean that for 6 dogs there are 8 cats, and so on.
Step Two: Okay, because these numbers are larger, it is easiest to scale it back to one. The proportion or rate given is $234/13 hours. We would divide by 13 to get it to 1: $18/1 hour. The proportion is usually a decimal, but these numbers happen to divide nicely.
Step Three: Now, we can do 162/18 to see what the scale is, or how much times larger it is: 162/18=9.
Step Four: Lastly, just do 1 times 9, which tells it is 9 hours. To check the work, make sure 9 is less than the original proportion; it should take less time to make less money. 9 is less than 13, so this is the answer!
Perform the indicated operation. 5/17 x 3/8
Answer:
15/
x
136
Step-by-step explanation:
im pretty sure
Answer:
0.11
Step-by-step explanation:
The desirable answer would be 0.11029411∞, and it would go on forever. Therefore, by rounding the designated number above, thou shall get 0.11.
I hope this is of good use.
Jay is decorating a cake for a friend's birthday. They want to put gumdrops around the edge of the cake which has a 12 in diameter. Each gumdrop has a diameter of 1.25 in. To the nearest gumdrop, how many will they need?
Answer:
The nearest gumdrop required will be 30.
Step-by-step explanation:
We will find the circumference of the cake which has 12 inches diameter
Radius = diameter / 2 = 12 / 2 = 6 inches
C = 2 x 3.14 x radius
C = 2 x 3.14 x 6 = 37.68 inches
The gum drop dia = 1.25 inches
The total gum drops required to cover 37.68 inches = 37.68 / 1.25 = 30.144
The nearest gumdrop required will be 30.
help plz ? Mark brainliest?
Answer:
-1(3x^2) +4x-7
Step-by-step explanation:
grouping
why do i have depression
Answer:
are u ok tho
Step-by-step explanation:
Let P be the vector space of polynomials of degree at most 2. Select each subset of P that is a subspace. Explain your reasons. (No credit for an answer alone.) (a) {p(x) = P₂|p(2)=0} (b) {p(z) € P₂ | x-p'(x) + p(x) = 0} (c) {p(z) E P₂|p(0) = P(1)} d) {ar2 + (a +1)x+b|a, b ER}
Let P be the vector space of polynomials of degree at most.
(a) is a subspace of P.
(b) is not a subspace of P.
(c) is a subspace of P.
(d) is a subspace of P.
(a) {p(x) = P₂|p(2)=0}
This subset consists of polynomials in P₂ that evaluate to 0 at x = 2. To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is in this subset since it evaluates to 0 at x = 2.
Let p₁(x) and p₂(x) be two polynomials in this subset. If p₁(2) = 0 and p₂(2) = 0, then (p₁ + p₂)(2) = p₁(2) + p₂(2) = 0 + 0 = 0. Hence, the subset is closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. If p(2) = 0, then (cp)(2) = c(p(2)) = c(0) = 0. Hence, the subset is closed under scalar multiplication.
Therefore, (a) is a subspace of P.
(b) {p(z) € P₂ | x-p'(x) + p(x) = 0}
This subset consists of polynomials in P₂ that satisfy the equation x - p'(x) + p(x) = 0. To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is not in this subset since it does not satisfy the equation x - p'(x) + p(x) = 0.
If p₁(x) and p₂(x) are two polynomials in this subset, (p₁ + p₂)(x) = p₁(x) + p₂(x) satisfies the equation x - (p₁ + p₂)'(x) + (p₁ + p₂)(x) = 0. However, we need to check if it satisfies the equation x - (p₁ + p₂)'(x) + (p₁ + p₂)(x) = 0 for all x, not just at certain points. This condition may not hold, so the subset is not closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. If we consider cp(x), the equation x - (cp)'(x) + cp(x) = 0 may not hold for all x, depending on the value of c. Therefore, the subset is not closed under scalar multiplication.
Therefore, (b) is not a subspace of P.
(c) {p(z) E P₂|p(0) = p(1)}
This subset consists of polynomials in P₂ that satisfy the equation p(0) = p(1). To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is in this subset since it satisfies the equation p(0) = p(1) (both sides are 0).
If p₁(x) and p₂(x) are two polynomials in this subset, (p₁ + p₂)(x) = p₁(x) + p₂(x) satisfies the equation (p₁ + p₂)(0) = p₁(0) + p₂(0) and (p₁ + p₂)(1) = p₁(1) + p₂(1). Since p₁(0) = p₁(1) and p₂(0) = p₂(1), it follows that (p₁ + p₂)(0) = (p₁ + p₂)(1). Hence, the subset is closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. If we consider cp(x), the equation (cp)(0) = (cp)(1) holds since p(0) = p(1). Hence, the subset is closed under scalar multiplication.
Therefore, (c) is a subspace of P.
(d) {ar² + (a + 1)x + b | a, b ∈ R}
This subset consists of all polynomials of the form ar² + (a + 1)x + b, where a and b are real numbers. To check if it is a subspace, we need to verify the three conditions:
The zero polynomial is in this subset since it can be written as 0r² + (0 + 1)x + 0 = x.
If p₁(x) and p₂(x) are two polynomials in this subset, their sum p₁(x) + p₂(x) is of the form ar² + (a + 1)x + b, where a and b are real numbers. Hence, the subset is closed under vector addition.
Let p(x) be a polynomial in this subset, and c be a scalar. Then cp(x) is of the form car² + (ca + c)x + cb, where a, b, and c are real numbers. Hence, the subset is closed under scalar multiplication.
Therefore, (d) is a subspace of P.
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number 3 please help me
Answer:
D. {1}Explanation:
given f(x) = 3x - 1
for f(x) = 2
3x - 1 = 2
3x = 2 + 1
3x = 3
x = 3/3
x = 1
Which of the following is equal to the expression listed below?
18 + 12
OA. 6(3+2)
OB. (6 x 3)(6 x 2)
OC. 6+ (3 x 2)
OD. (6 + 3)(6 + 2)
Answer:
OA
Step-by-step explanation:
18+12=30
6×3=18
6×2=12
18+12=30
hope this helps
Answer:
Which of the following is equal to the expression listed below?
18 + 12
OA. 6(3+2)
OB. (6 x 3)(6 x 2)
OC. 6+ (3 x 2)
OD. (6 + 3)(6 + 2)
Step-by-step explanation:
the answer is (B)
Un terreno cuadrado tiene una superficie de 900 metros cuadrados. ¿Cuántos metros lineales de alambre se necesitan para cercarlo?
Respuesta:
120 metros
Explicación paso a paso:
Dado que:
Área del lote cuadrado = 900 m²
Área, A de cuadrado = s²
Donde, s = longitud del lado
s² = 900
Toma el cuadrado de ambos lados
s = raíz cuadrada (900)
s = 30
Se requiere metro lineal de alambre para cercar, el lote será el perímetro del lote cuadrado;
El perímetro del lote cuadrado = 4s
Por eso,
Perímetro del lote cuadrado = 4 * 30
Perímetro del lote cuadrado = 120 m
Write the equation of a circle whose diameter is 12 and whose center is at (-6,-3)?
Answer:
(x +6)² +(y +3)² = 36
Step-by-step explanation:
The standard form equation of a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
__
We have a circle with diameter 12, so its radius is 6. The center is given as (h, k) = (-6, -3), so the equation can be written ...
(x -(-6))² +(y -(-3))² = 6²
Simplifying this a suitable amount, we have the equation ...
(x +6)² +(y +3)² = 36
Which of the following is true? O (LS - ES) >= 0 O (LF-LS) > (EF - ES) Slack = (LF-LS)
The answer option that is true include the following: D. Slack = (LF-LS).
What is project management?Project management is a strategic process that involves the design, planning, developing, leading and execution of a project plan or activities, especially by using a set of skills, knowledge, tools, techniques and experience to achieve the set goals and objectives of creating a unique product or service.
Under project management, the slack of a project can be calculated by taking the difference between the activity's latest start and earliest start time.
In this context, the slack of a project is the difference between its latest finishing time (LF) and earliest finishing time (LS):
Slack = (LF - LS)
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What is the surface area of the prism below?
A
216 ft2
B
312 ft2
C
432 ft2
D
10,800 ft2
i F 49x ²b = (7x +1/2)(7x-1/2)
then Find the value b.
Answer:
0
Step-by-step explanation:
Apply Only the Outside and Inside Method of the Foil Method.
[tex]7 \times - \frac{1}{2} = - 3.5x[/tex]
[tex] \frac{1}{2} \times 7x = 3.5x[/tex]
Add them together
[tex] - 3.5x + 3.5x = 0[/tex]
So our b value is 0.
A _____ is a ratio comparing quantities measured in different units.
• A unit rate is a rate that compares a quantity to exactly one ______ of another quantity.
• Unit rates can be used to make rate _____ consisting of equivalent ratios (fractions).
• A _____ table can be used to solve a problem. Find a missing value in a ratio table by:
• using a pattern of ____ each time.
• multiplying.
• writing an ____ ratio.
A unit rate is a ratio comparing quantities measured in different units. Unit rates are most useful in finding an equivalent ratio, proportion, and also a missing value in a ratio table.
A ratio table can be used to solve a problem. Find a missing value in a ratio table by using a pattern of multiplying each time or by writing an equivalent ratio. Unit rates can be used to make rate statements consisting of equivalent ratios (fractions). The missing value refers to one value in the ratio that is not provided and has to be found by calculation or by estimation.A ratio is a comparison of two or more values that can be written in different forms, including fraction form, ratio form, and percentage form. A unit rate is a type of ratio that compares a quantity to exactly one unit of another quantity.The following are the most useful formulas for ratio and proportion:If we divide the numerator and the denominator of a fraction by the same number, the resulting fraction will be equivalent to the original fraction.If the same number is multiplied to both the numerator and denominator of a fraction, the resulting fraction will be equivalent to the original fraction. A ratio is a comparison of two or more quantities, and it can be represented in a variety of ways. A unit rate is a ratio that compares a quantity to one unit of another quantity. Unit rates can be used to create equivalent ratios that are similar to one another. In a ratio table, a missing value can be found by using a pattern of multiplying or by writing an equivalent ratio.
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The missing value in a ratio table can be found by using a pattern of multiplying each time, multiplying, and writing an equivalent ratio.
A ratio is a comparison of two quantities measured in the same units.
A unit rate is a rate that compares a quantity to exactly one unit of another quantity.
They can be used to make rate conversions consisting of equivalent ratios (fractions).
A ratio table can be used to solve a problem.
The missing value in a ratio table can be found by using a pattern of multiplying each time, multiplying, and writing an equivalent ratio.
So, A ratio is a ratio comparing quantities measured in different units.
A unit rate is a rate that compares a quantity to exactly one unit of another quantity.
Unit rates can be used to make rate conversions consisting of equivalent ratios (fractions).
A ratio table can be used to solve a problem.
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In a correlated t test, if the independent variable has no effect, the sample diff ores are a random sample from a population where the mean difference score (μ d) equals______
a. 0 b. 1 c. N d. cannot be determined
The correct answer i.e. mean difference is (a) 0.
What is the mean difference?
The mean difference is a statistical measure that represents the average difference between pairs of values in a dataset. It is calculated by taking the sum of all the differences and dividing it by the total number of pairs.
To calculate the mean difference, follow these steps:
Identify the pairs of values in your dataset for which you want to calculate the difference.
Calculate the difference between each pair of values.
Sum up all the differences.
Divide the sum by the total number of pairs.
In a correlated t-test, the null hypothesis assumes that the mean difference between paired observations is zero, indicating no effect of the independent variable. Therefore, if the independent variable has no effect, the sample difference scores are expected to be a random sample from a population where the mean difference score, denoted as μd, equals 0.
Hence, the correct answer is (a) 0.
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Matt tried to evaluate 49 x 24 using partial products. His work is shown below
Answer:
step 5
Step-by-step explanation:
What value does the 2 represent in the number 0.826
Answer:
.02
Step-by-step explanation:
Find the next two terms in
the sequence 11, 7, 3,-1,
Answer:
The next term will be -5.
Step-by-step explanation:
This is actually an AP with a = 11 and common difference d = -4.
Therefore next term will be -1 - 4 = -5
Answer:
Step-by-step explanation:
The numbers in this sequence come by subtracting 4 so
11, 7, 3, - 1, - 5, - 9, - 13
Given this higher ODE, use the reduction of HODE via systems of ODE and find the general nonhomogeneous solution y" – 2y' – y + 2 = 0
The general nonhomogeneous solution for the given higher-order differential equation, y" – 2y' – y + 2 = 0, can be found by reducing it to a system of first-order differential equations (HODE) and solving the resulting system.
To reduce the higher-order differential equation to a system of first-order differential equations, we introduce two new variables, u and v. We let u = y' and v = y''. By taking the derivatives of these new variables, we have u' = y'' and v' = y'''.
Substituting these expressions into the original equation, we obtain the following system of first-order differential equations:
u' = v
v' = 2u + v - 2
Now, we can solve this system using standard techniques. The characteristic equation associated with this system is r^2 - r - 2 = 0, which factors as (r - 2)(r + 1) = 0. Hence, the eigenvalues of the system are λ₁ = 2 and λ₂ = -1.
For λ₁ = 2, we find the corresponding eigenvector to be [1, 0]. For λ₂ = -1, the eigenvector is [1, -2].
The general solution of the homogeneous system is given by:
u(t) = c₁e^(2t) + c₂e^(-t)
v(t) = c₁e^(2t) + (-2c₁ + c₂)e^(-t)
To find the particular solution, we assume a solution in the form of u_p = At and v_p = Bt + C. Substituting this into the system, we obtain A = -3 and C = -1.
Therefore, the general nonhomogeneous solution to the given higher-order differential equation is:
y(t) = c₁e^(2t) + c₂e^(-t) - 3t - 1.
By reducing the given higher-order differential equation to a system of first-order differential equations and solving the resulting system, we found the general nonhomogeneous solution to be y(t) = c₁e^(2t) + c₂e^(-t) - 3t - 1.
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EASY POINTS!! INCLUDE A DISC!!
pls no bots i don't want any links :(
Step-by-step explanation:
[tex]180 - 35 - 65 = \\ = 145 - 65 = \\ = 80[/tex]
Answer:
i BELIVE it will be 50 I’m super sorry if I’m wrong lovly.
Step-by-step explanation:
Solve each equation mentally
10.
Consider the two properties that you would use to solve an equation like 3x + 5 = 26. Which of the following is true?
A. The standard method for solving an equation like 3x + 5 = 26 is to use the Multiplication Property of Equality and then the Division Property of Equality.
B. The standard method for solving an equation like 3x + 5 = 26 is to use the Division Property of Equality and then the Subtraction Property of Equality.
C. The standard method for solving an equation like 3x + 5 = 26 is to use the Subtraction Property of Equality and then the Division Property of Equality.
D. The standard method for solving an equation like 3x + 5 = 26 is to use the Subtraction Property of Equality and then the Addition Property of Equality.
Answer:
The standard method for solving an equation like 3x + 5 = 26 is to use the Subtraction Property of Equality and then the Division Property of Equality.
Step-by-step explanation:
To solve, you subtract both sides by 5 first. Then you divide both sides by 3 to isolate the x.
6. Select the coldest temperature from the list below. * O -11°F O 7°F O -4°F O 20°F
Answer:
-11 degrees Fahrenheit.
Step-by-step explanation:
the higher the negative number is, the colder it gets <D
help lol..............
Which table below does not represent a function?
Answer:
Option 2
Step-by-step explanation:
if an input produces more than one output, the table does not represent a function.
True or False
_____ The ANOVA Test uses the entire bell
_____ There are 2 types of hypotheses
_____ The null hypothesis may posit that there is no significant difference betwe
The given question can be answered as follows:
True or False:
The ANOVA Test uses the entire bell. - False_
____ There are 2 types of hypotheses. - True_
____ The null hypothesis may posit that there is no significant difference between - True
Explanation:
ANOVA (Analysis of Variance) is a statistical test used to determine whether two or more population means are equivalent. It does not use the entire bell, so the statement is false.There are two types of hypotheses: the null hypothesis and the alternative hypothesis. The statement is true.The null hypothesis is used to determine if there is a significant difference between two or more sets of data. It can posit that there is no significant difference between two or more sets of data. So, the statement is true.
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The ANOVA Test uses the entire bell is a false statement.
There are 2 types of hypotheses is a true statement.
The null hypothesis may posit that there is no significant difference between the groups is a true statement.
Hence, the correct answer is: False; True; True.
The given statements can be summarized as follows: Statement 1 is that the ANOVA Test uses the entire bell. It is false.
Statement 2 is that there are 2 types of hypotheses. It is True.
Statement 3 is that the null hypothesis may posit that there is no significant difference between the groups. It is True.
Hence, the correct answer is: False; True; True.
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An endocrinologist is interested in the effects of depression on the thyroid. It is believed that healthy subjects have a mean thyroxin (a hormone related to thyroid function) level of 7.0 micrograms/100 ml and a standard deviation of 1.6 micrograms/100 ml. The endocrinologist wants to assess whether the mean thyroxin level is different for those with depression. She samples 35 subjects with depression and obtains a sample mean of 7.82 micrograms/100 ml for thyroxin. What null and alternative hypotheses should she test
Answer:
H0: μ = 7.0
H1: μ > 7.0
Step-by-step explanation:
The null hypothesis will equal and take up the value of the population mean value ;
The population mean value, μ is 7.0
Null hypothesis ; H0: μ = 7.0
The alternative hypothesis will align with the claim ; which will take up and side with the value and direction of the sample mean ; 7.82 micrograms/100 ml
7.82 > 7.0 (sample mean is greater Than the population mean).
Hence, the alternative hypothesis, H1 will be ;
H1 : μ > 7.0
find the general solution of the indicated differential equation. If possible, find an explicit solution. 1. y =xy 2. xy =2y 3. y =e
x−y 4. y =(1+y 2)e x5. y =xy+y 6. y =ye x −2e x +y−2 7. y =x/(y+2) 8. y =xy/(x−1) 9. x 2 y =ylny−y 10. xy −y=2x 2y 11. y 3y =x+2y 12. y =(2xy+2x)/(x 2−1)
The equations you mentioned:
1. y = xy:
To solve this differential equation, we can separate the variables and integrate both sides.
dy/y = x dx
Integrating both sides gives:
ln|y| = (1/2)x² + C
Exponentiating both sides gives the general solution:
|y| = [tex]e^{((1/2)x^2 + C)[/tex]
Taking the positive and negative values of y, we get two branches of solutions:
y = [tex]Ae^{(1/2)x^2[/tex] and y = [tex]-Ae^{(1/2)x^2[/tex], where A is an arbitrary constant.
2. xy = 2y:
Rearranging the equation, we get:
xy - 2y = 0
Factoring out y, we have:
y(x - 2) = 0
This equation has two solutions:
y = 0 and x - 2 = 0, which leads to x = 2.
3. y = [tex]e^x[/tex] - y:
Rearranging the equation, we get:
y + y = [tex]e^x[/tex]
Combining like terms, we have:
2y = [tex]e^x[/tex]
Dividing both sides by 2, we get:
y = (1/2)[tex]e^x[/tex]
4. y = (1 + y²)[tex]e^x[/tex]:
Rearranging the equation, we get:
y - y² = [tex]e^x[/tex]
Factoring out y, we have:
y(1 - y) = [tex]e^x[/tex]
This equation has two solutions:
y = 0 and 1 - y = [tex]e^x[/tex], which leads to y = 1 - [tex]e^x[/tex].
5. y = xy + y:
Rearranging the equation, we get:
y - xy - y = 0
Combining like terms, we have:
-xy = 0
This equation has two solutions:
x = 0 and y = 0.
6. y = y[tex]e^x[/tex] - 2[tex]e^x[/tex] + y - 2:
Rearranging the equation, we get:
y[tex]e^x[/tex] - y = 2[tex]e^x[/tex]- 2
Factoring out y, we have:
y([tex]e^x[/tex] - 1) = 2([tex]e^x[/tex] - 1)
Dividing both sides by ([tex]e^x[/tex] - 1), we get:
y = 2
7. y = x/(y + 2):
Rearranging the equation, we get:
y(y + 2) = x
Expanding the equation, we have:
y² + 2y - x = 0
This equation doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.
8. y = xy/(x - 1):
Rearranging the equation, we get:
(x - 1)y = xy
Dividing both sides by y and rearranging, we have:
x - 1 = x/y
Solving for y, we get:
y = x/(x - 1)
9. x²y = ylny - y:
This is a nonlinear differential equation that doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.
10. xy - y = 2x²y:
Rearranging the equation, we get:
xy - 2x²y - y = 0
Factoring out y, we have:
y(x - 2x² - 1) = 0
This equation has two solutions:
y = 0 and x - 2x² - 1 = 0, which leads to x = (1 ± √3)/2.
11. y - 3y² = x + 2y:
Rearranging the equation, we get:
-3y² + y + 2y - x = 0
Combining like terms, we have:
-3y² + 3y - x = 0
This equation doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.
12. y = (2xy + 2x)/(x² - 1):
Rearranging the equation, we get:
y(x² - 1) = 2xy + 2x
Expanding the equation, we have:
x²y - y = 2xy + 2x
Combining like terms, we get:
x²y - 2xy - y - 2x = 0
This equation doesn't have a general solution in terms of elementary functions. It can be solved numerically or using approximation methods.
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I've got a problem and I need solving! Please find the answer.
Answer: x= 4y/7 - 1/7
7x/4+ 1/4
Step-by-step explanation:
Please help I really need it, I don’t know what to do
Answer:
i think it is b
Step-by-step explanation: