y is directly proportional to x and inversely proportional to the square of z. If x = 4 and z = 3, then y = 16.

Q: Construct an equation of variation and find the constant of proportionality for the following…

A: It is given that, x is directly proportional to y and z.

Q: Use this order-three version of variation of parameters to find the general solution: y" + 2y" – y –…

A:

Q: The value y is proportional to the square of x and y = 12 when x = 2 %3D a) Find a formula for y in…

A: Use the concept of direct proportion and solve using simple calculation.

Q: It is easy to check that for any value of c, the function y = ce 2+e= is a solution of the equation…

A:

Q: From a lighthouse, ship A is at a distance of 6 √5 miles and on a bearing of 040° and ship B is at a…

A:

Q: Express the statement as an equation. (Use k as the constant of proportionality.) H is jointly…

A:

Q: If a 1600 foot bridge weighing 2100 tons supports 1400 tons, find the constant of proportionality k.…

A: Given:The weight a suspension bridge can support (B) = 2100 tonsBridge’s total length (l) = 1600…

Q: Find the mathematical model for the following statement. Remember to use k as the constant of…

A: We have to  find

Q: Given G = 6.66 x 10-8 C. G. S. unit, c = 3 x 10¹0 cm/sec. M = 1.99 x 1033 gm. Also if in the case of…

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Q: -y is inversely proportional to x and y = 14.3 when x = 0.6 %3D What is the value of constant of…

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Q: h is jointly proportional to q and v. It is found that q = 9 and v = 8 when h = 3. k =

A:

Q: he amount of juice in a grapefruit is directly proportional to the cube of its diameter. Let j…

A: To calculate the constant k and amount of juice in grapefruit with a 5-inch diameter.

Q: If z is directly proportional to the product of x and y and if z is 10 when x is 4 and y is 5, then…

A: To determine: The equation z=_____ Given information: If z is directly proportional to the product…

Q: The cost of filling up Jason's car is directly proportional to the number of gallons purchased. If…

A: We have, the cost of filling the car is directly proportional to number of gallons purchased. Thus,…

Q: Suppose that the manufacturer of a gas clothes dryer has found that, when the unit price is p…

A: The revenue R (in dollars) when the unit price is p dollars is given by R(p)=-4p2+4000p   (a) To…

Q: A student studies by the light of a desk lamp. The intensity of the light, I, in lumens is inversely…

A: To write that what happens with intensity when distance becomes double

Q: Suppose that z varies jointly with the cube of x and the square of y. Find the constant of…

A: Given z varies jointly with cube of x i.e x3 of y i.e y2

Q: The weight a suspension bridge can support, B, in tons, is directly proportional to the square root…

A: Given thatWeight of suspension bridge can support (B)= 1400 tonsWeight of bridge material (w)= 2100…

Q: The number of widgets that a manufacturing plant can produce varies jointly as the number of workers…

A: Wr have to find k and no of widgets.

Q: Given y is inversely proportional to the square of x and that x=3 when y= 6. then find 1 the value…

A:

Q: Construct an equation of variation and find the constant of proportionality for the following…

A: It is given that, x is directly proportional to square of y and inversely proportional to cube root…

Q: When exchanging US Dollars (USD) for Philippine Peso (PHP) the number of Philippine Pesos received…

A: As per our company guidelines we are supposed to answer only one question kindly post other question…

Q: Find the mathematical model for the following statement. Remember to use k as the constant of…

A: To write the mathematical model of the given condition

Q: It is easy to check that for any value of c, the function y = ce + e is a solution of the equation…

A: y=ce-2x+e-xSubstitute x=-4 and y=10 into the above equation.

Q: Express the statement as a formula that involves the given variables and a constant of…

A: Two or more variables are said to be directly proportional if a change in one variable results in a…

Q: 7. If y varies inversely as the square root of x, what is the constant of proportionality if y = 16…

A:

Q: Suppose that z varies jointly with the cube of x and the square of y. Find the constant of…

A:

Q: 10.* Solve max r-ay 22 + y? <1 x - y 2 0 for each a E R.

A:

Q: The time traveled, t is the inversely proportional to the rate, r, traveled, and the constant of…

A: Given that the time taken to travel is inversely proportional the rate. Let t denotes the time taken…

Q: The number of widgets that a manufacturing plant can produce varies jointly as the number of workers…

A:

Q: Suppose that y is inversely proportional to square of x. Find the constant of proportionality k if y…

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Q: IV. In each item, solve the constant of proportionality k, form the complete variation equation, and…

A: This question can be solved using the concept of constant of proportionality.

Q: The dosage for a certain type of chemotherapy drug depends on several parameters of the particular…

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Q: The surface area of a cube with length x is proportional to the square of its length. What is the…

A: We have to find the constant of proportionality for the given information.

Q: 2. Eliminate the arbitrary constant on the given equation: r Ae 60 + Ble 60

A: That is we have to eliminate constant A and B

Q: Construct an equation of variation and find the constant of proportionality for the following…

A: We have given, x is directly proportional to y &amp; zSo, we can write the equation as

Q: Use the given information to solve the problem. P is directly proportional to the square root of t.…

A:

Q: The number of views on a social media video, v, is jointly related to the number of followers, f,…

A: To rearrange the equation to isolate f ,  Given : V = kfd

Q: It can be shown that when the water level is h meters from the bottom of the tank, (see the figure),…

A:

Q: The value in dollars, v(x), of a certain car after x years is represented by the equation…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: () fo lve the IVe X = (, :)x, xc)= x(0) =

A:

Q: The value in dollars, o(x), of a certain car after x years is represented by the equation v(x) =…

A: vx=250000.86x take x=2 v2=250000.862 v(2)=250000.7396 v(2)=18490

Q: . Eliminate the arbitrary constant on the given equation: y = x + Cje + C2e¯2x

A:

Q: 4. Eliminate the arbitrary constant on the given equation: y = x + C1e2 + Cze-20 %3D

A: The given equation,y=x+C1e2x+C2e-2x

Q: y = Ae* + Bre

A:

Q: The number of widgets that a manufacturing plant can produce varies jointly with the number of…

A: The number of widgets that a manufacturing plant can produce varies jointly with the number of…

Q: If y varies directly with the square root of x and inversely with z, what is the constant of…

A: Given that, y varies directly with the square root of x and inversely with z. y α xz y=kxz…

Q: If y is directly proportional to x, and y=42 when x=7, find the constant of proportionality and…

A: Given that y is directly proportional to x or y ∝ x. So we Can write this in other form as:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.