In a typical equation of the linear model, V( Y) must be: OA. 0. OB. V(u).
Q: Find the general solution of thedifferential equation. (2+x)y'=3y
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Q: Find the general solution for the equation: dy=(x^2+x)y^3dx
A: Given: dy=x2+xy3dx
Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
A: Given equation, y3+9x2=b Used formulas:…
Q: The first-order DE is a linear equation if it has the following form: A a;(v) +a,(1y)x= g(x)"* dx dx…
A: A first order linear differential equation is an equation in which the highest derivative of the…
Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
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Q: Calculate the gradient and y-intercept for the following linear equations. a) y - 2x = -4 b) 2y =-…
A: As there are multiple sub parts, a),b),c) are solved here.
Q: In a linear relationship, as the X scores increase, the Y scores change a. in only one direction.…
A: So the correct option is Option a. in only one direction
Q: Find the order and degree of each DE, and state whether it is linear or nonlinear and why? a. y'+xy2…
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Q: Rewrite the given linear equation into the standard form of the equation of the line. 2x = 5y + 4
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Q: Give the substitution that converts the given nonlinear equation into a linear equation then find…
A: The objective is to find the substitution that convert the given nonlinear equation into linear…
Q: f ? = 0, then the two variables under consideration are linearly ________.
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Q: L (x, y) = 12 :45 10
A: The given contour diagram is:
Q: Give the substitution that converts the given nonlinear equation into a linear equation then find…
A: We need to find solution of differential equation.
Q: Identify the linear equation. O y=x2.4 Oy = Oy=+3 %3D O y= bd +5
A: Option (3) is correct.
Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
A: I have stated the used formulas in the solution
Q: rewrite the following second order linear equation into of two equations. y'' + 5y' - 6y = 0
A: Given y''+5y'-6y=0
Q: (D² + D – 1)²y = 0 ,when x= y = 0 , y' = y'"'' = 1 , y" = -1 %3| %3|
A: Ghfd
Q: xy''-(4+x)y'+3y=0, find the first four terms in each of the two linearly independent solutions about…
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Q: - Calculate the gradient and y-intercept for the following linear equations. a) y-2x = -4 c) -4y +…
A: Slope-intercept form: The slope-intercept form of a line is given by y = mx + c, where m is slope…
Q: If these two y's, y1=e^tcos(t) and y2(t)=e^tsin(t) are both solutions to y''+j(t)y'+k(t)y=0, how do…
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Q: Find the general solution of the fifth order linear equation: y(6) – 6y(3)+9./ 0
A: First form the auxiliary equation and solve it for roots than write the solution with its help.
Q: Show that a linear equation dy a(x)- + b(x)y = c(x) d.x %3D is exact if a' (x) = b(x).
A: Given linear differential equation axdydx+bxy=cx.....1 We have to show that the given differential…
Q: Rewrite the given linear equation into the standard form of the equation of the line. = 2y - 3
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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
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Q: Consider the following linear equations :
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Q: Use reduction of order to find a second linearly independent solution: x²j – xy + y = 0, Yı = x Then…
A: We have given a second order homogeneous linear differential equation equation with variable…
Q: y" + 2lf + 2y = 0, y(0) = 1, f(0) = 1 he solution as a linear combination of y, and y2-
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Q: What is the equilibrium solution of the equation y '(t) = 2y - 4? Is itstable or unstable?
A: The equation given is y't=2y-4. To find the equilibrium solution of the equation y't=2y-4.…
Q: Replace the Cartesian equation with equivalentpolar equations. xy = 2
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Q: Determine whether the equation is linear in the variables x and y.e−2x + 5y = 8
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Q: 2.x. 1. 2x -y²= 10 1 2. 2 y=1 3. e y=s | 4.5inTTX -y = 0 5. x -y=-1
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Q: Find the general solution of the fifth order linear equation: y(5) – 6y(3) + 9 .y' = 0
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Q: Ralph has been keeping track of how much his plant has been growing in centimeter each week and…
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Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
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Q: Find a general linear equation Ax+By+C=0 of the straight line that passes through: a. (-2,-2) and…
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Q: Find the general solution of the fourth order linear equation y(4) + 4y" + 4y = 0.
A: Given problem is :
Q: The equation below is said to be A. Linear in x O B. Linear in y C. Linear in both x and y O D.…
A: We will find out the required value.
Q: 設+xy=X, y(の)=-6
A: see 2nd step for this question's solution.
Q: dy 4. dx = 1- xy + y²
A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…
Q: Which of the following equations represents the line perpendicular to y = 2 – 4x that passes through…
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Q: Consider the following system of equations in R²→R? y + 2xỉ + x3 - yıY2 = 15 2y + xỉ + x + YıY2 = 38…
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Q: Find the solution to the first order linear equation, x- + y = xe*. dx dy • Y = ex _ e*¸ C В. у 3…
A: The given linear differential equation is xdydx+y=xex We have to solve equation
Q: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
A: Solve for the value of constant(C) by obtaining the orthogonal trajectory of the given equation…
Q: Which of the following are first-order linear equations? y +x?y = 1 xy +y = e (b) y' +xy2 = 1 (d) xy…
A: To identify the first-order linear equations.
Q: Myron records the number of chirps per minute (x) that crickets make at different temperatures. (y)…
A: Topic - equation of straight line
Q: y varies jointly as x and z can be modeled by the equation
A: Fill in the blanks: y varies jointly as x and z can be modeled by the equation ...............
Q: Identify the graph of the linear equation 4x + 2y + z = 8 in three dimensional space?
A: See the details solution in below
Q: y varies jointly as x and z can be modeled by the equation________ .
A: y varies jointly as x and z can be modeled by the equation
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- The phone company, Splint, has a monthly cellular plan where the customer pays a flat monthly fee and then a cost of money per minute used on the phone. If the customer uses 330 minutes, the monthly cost is $106.50. If the customer uses 570 minutes, the monthly cost is $166.50. a. Find a linear model of the form y=mx+b, where x is the number of monthly minutes used, and y is the total monthly cost of the Splint plan.y= b. Using the equation from part a., find the total monthly cost if 823 minutes are used.If 823 minutes are used, the total cost will be___________dollars.The table lists the distances (in megaparsecs; 1 megaparsec = 3.085 × 10^24cm, and 1 megaparsec = 3.26 million light-years) and velocities (in kilometers per second) of four galaxies moving rapidly away from Earth. (a) Does there appear to be a relationship or trend for the data? (b) Find a linear equation in the form y =max that models these data using the points (520,40000) and (0,0). (c)The galaxy Hydra has a velocity of 60000 km per second. How far away to the nearest megaparsec, is the galaxy according to the model in part (b)? (d) The value of m is the Hubble Constant. The Hubble Constant can be used to estimate the age of the universe A (in years) using the formula A = 9.5 x 10^11/m. Approximate A using the value of m. Round to the nearest hundredth of a billion years. (e) Astronomers currently place the value of the Hubble Constant between 50 and 100. What is the range for the age of universe A?The graph of the linear equation r=y passes through the point: O (4, 4) O (4,0) O(0,-4) O (4,-4) O (0,4)
- 2. Delilah wants to join a gym, so she shops around to find the one with the lowest overall price (she is not sure how long she will be a member). She finds the Harbor Square Athletic Club is running a special, and only charges a $55 initiation fee plus $86 a month to be a member. The local YMCA charges $120 to join and has a monthly fee of $54. Find the equations for the linear models for the costs of the Harbor Square Athletic Club and the YMCA. Use C = cost ($) and m = months. a. Athletic Club: YMCA: b. Use algebra to determine when she will have spent a total of $500 at Harbor Square: after ______ months. show work c. Use algebra to determine when the two gyms would cost the same: after____ months. show workIn 1990, the profit of the Gamma company was $11,900,848. Each year after 1990, profits fell by $48,263 on average. Construct a linear model for this scenario and use it to solve for the profits in the year 2020. Round your answer to a whole dollar.Consider the example of injection moulding of a rubber component as shown in Figure Q3(b). The process engineer would like to optimise the strength of the component by optimising the following factors: temperature = 190°C and 210°C, pressure = 50 MPa and 100 MPa, and speed of injection = 10 mm/s and 50 mm/s. What type of mathematical model that the engineer can develop if the relationship is linear and no interactions are significant? Write down the general equation that relates the strength of the component with the process factors.
- A zoologist studied the running speeds of animals in terms of the animals' body lengths. The results of the study are shown in the table below. (A graphing calculator is recommended.) Body length (in centimeters), x 1 9 15 16 24 25 60 Running speed (in meters per second), y 1 2.5 7.5 5 7.4 7.6 20 (a) Use the points (9, 2.5) and (60, 20) to find a linear model that will predict the running speed of an animal with a body length of x centimeters. (Round your coefficients to three decimal places.) y = (b) Use your linear model to estimate the expected running speed of an animal whose body length is 13 centimeters. Round to the nearest tenth of a meter per second. m/secA zoologist studied the running speeds of animals in terms of the animals' body lengths. The results of the study are shown in the table below. (A graphing calculator is recommended.) Body length (in centimeters), x 1 9 15 16 24 25 60 Running speed (in meters per second), y 1 2.5 7.5 5 7.4 7.6 20 (a) Use the points (9, 2.5) and (60, 20) to find a linear model that will predict the running speed of an animal with a body length of x centimeters. (Round your coefficients to three decimal places.)Questions 11-17. The environment club has saved 200 pounds of cans and promises to collect 20 pounds of cans each week and will use the profits to buy additional recycling bins. Create a linear model for their collection program. How many pounds of cans will the club have by week 12?
- f ? = 0, then the two variables under consideration are linearly ________.Two linearly independent solutions of the equation y" + y' -6y=0 are: Select one: a. e^-t , e^6t b. e^-31,e^2t c. e^-6t , e^t d. e^-21 , e^3tThe city is considering a raise taxi rate. Currently taxi companies charges a 3.50$ flat fee and 0.80$ per mile. Using y=mx+B what is the linear model for the taxi chargess? Y=
