Suppose that x and y are functions of t and the rate of change of the distance x is double the rate of change of the distance y. Which of the following statements is definitely true? Select one: dy 2 dx dy dt y dt dx

Q: Which of the following is the derivative of y +3x ? Select one: dy a. da 3x 3 dy b. dz = 3x? dy C.…

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x 2−x−2=2y 2−2y

A: We have to find derivative of curve equation (implicitly).Curve equation is given by:

Q: dA The variablesr and A are related by A = r²t. The rate of change of the radius is 1. Find dt when…

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Q: Let z = Vx+ 3y. Then: The rate of change in z at (2, 1) as we change x but hold y fixed is The rate…

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Q: The distance of a particle from some fixed point is given by the following function. s(t) =r? + 3t-4…

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Q: (1) Where on the line r = ay does the function f(x, y) = (r - a)? + (y - 2)² attain its smallest…

A: We need to calculate minimum of f(x,y)=(x-a)2+(y-2)2.........(1) on the line x=ay...............(2)…

Q: 1. Find the average rate of change of the following functions over the given interval: (a) f(r) =…

A: Explained below

Q: For questions 10-12 consider: The volume of a frustum of a cone is given by the formula v=r2(x² + y?…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: dy =3, what is the value of dx Suppose x and y are functions of a third variable t. If Vx + Vy =5…

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Q: Given that x and y are functions of time, find the indicated rate of change dx/dt, when x = 2, y =…

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Q: Suppose that the rate of change of Q with respect to t is given by = kQ(M- Q), dt where 0 < Q < M…

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Q: Assuming that y is a function of x, differentiate x^9y^5 with respect to x. Use D for dy/dx in your…

A: by using chain and product rule of differentiationddx(x9y5)=9x9-1y5++5x9y5-1y'

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

A: First obtain the derivative of the given equation as follows.

Q: For a given table 6. 10 14 y 4 12 Find the value of at x = 2 using forward difference formula. dy dx…

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Q: Find dy/ dx, where y is defined as a function of x implicitly by the equation below. −6x 4+2y4 =11…

A: Consider the function that defines y  as a function of x implicitly by the equation

Q: b. A thermistor is being used to measure temperature. For a given resistance Rthe temperature is…

A: The temperature, T for a resistance R is given by, T=1T0+1βlnRR0−1

Q: Find the relative rate of change of the function f(t) = 7.4e-0.6t using %3D d In f(t). dt the…

A: Solution is given below:

Q: Let Y= x² +3 2 d. Find the average rate of Change of Y'o 79 over the following with respect to x…

A: Given query is to find the average rate of change and instantaneous rate of change for  y = x2+3

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dx dy x+4y +4y…

A: The given function,x2+4y2+4y=49; dxdt=2 when x=7 and y=-1

Q: Find dy for the given values of x and Ax. y = 3x-2x; x= -2; Ax= 0.5 What is the derivative of y? dy…

A: Given: y=3x3-2x

Q: Find the Average Rate of Change of the following function (That is, from t = 2 to t = 5.) over the…

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Q: Find dy for the given values of x and Ax. y = 3x+5; x = 1; Ax 0.24 What is the derivative of y = V3x…

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Q: Suppose a goose is swimming in the circle x = cos(t), y = sin(t) and that the water temperature is…

A: Given: Tx,y=x2ey-xy3, x=cost, y=sint for finding rate of change in temperature, first we find T in…

Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dx =1 whenx=6…

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Q: The acceleration function of a particle moving along a line is given by: a ( t ) = 2 t + 3 in m / s…

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Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 2 and dt dx…

A: Compute the value of y as follows.Substitute x = 2 in x3 + y3 = 16.

Q: Given that x and y are functions of time, find the indicated rate of change. dx Find when x = 4, y =…

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Q: A square with side x cm, is changing with time where x(t) = 4t – 2. What is the rate of change of…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Q.1 Suppose that w = x sin yz2 ; x = cost, y = t² , z = et Find the rate of change of w with respect…

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Q: The pressure in P = 10T/V     of a gas in a cylinder is given by   with T in kelvins (K) and V…

A: Given as : P=10TV By differentiating it with respect to t: dPdt=10VdTdt-TdVdtV2 ......1 1). If T is…

Q: The median weight of a boy whose age is between 0 and 36 months can be approximated by the function…

A: The given expression iswt=9.59+1.05t-0.0049t2+0.000224t3.

Q: b) The mass (in kg) of a product from a chemical reaction is denoted by 'y'. The dy rate at which…

A: b Separate the terms of both the variables Then let 1+y2=z2ydy=dzand 1+t2=u22tdt=2udu

Q: By direct calculation, estimate the value of df/dt for f(x) = 1/x^2 at x=4. Use an increment of…

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. −4x2 +3x+4=y2…

A: We have to find dy/dx of curve  (implicitly).Curve equation is given by:

Q: Given the following table, use your calculator to estimate dW/dt at t=0 using the average rate of…

A: Step 1:-  dWdt=W2-W1t2-t1 Here, t1=0⇒W1=350t2=4⇒W1=334

Q: Given that x and y are functions of time, find the indicated rate of change. dy when x 4 and dt dx…

A: First obtain the derivative of the given equation as follows.

Q: Suppose x and y are functions of third variable t. In the equation x+y=45, what are the values of t…

A: In this question we will use basic of calculus i.e concept of partial derivative. Solution of the…

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: A student has 3 hours to cram for an examination and during this time wishes to memorize a set of 60…

A: You must have an idea about solving differential equations. The initial and a purticular value is…

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x^2+y^6=1

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Q: Given the following function, determine the maximum rate of change of it at the point P(0,0, 1/2).…

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Q: If s(t) is the position on the x-axis of a particle at time t, then the quantitys(t + h)−s(t) / h…

A: If s(t) is the position on the x-axis of a particle at time t,

Q: (x) = 2x. Compute the following derivatives if y depends on r but z doesn't. dx known that d (a) dr…

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Q: Given that x and y are functions of time, find the indicated rate of change. dx dy Find when x = 4,…

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Q: Suppose h(t) = t² + 11t + 7. Find the instantaneous rate of change of h(t) with respect to t at t =…

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Q: Faraday's law characterizes the voltage drop across an inductor such as di V, = L dt where V voltage…

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Q: and hence determine the rate of change of y with respect to x for the following algebraic functions:…

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Q: dy dx Suppose x and y are functions of a third variable t. If Vx + Vy =5 and dt 3, what is the value…

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Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dx dy x² + 4y²…

A: Given :  x 2 + 4 y 2 + 6 y = 54  And dx / dt = 9  when x = 6 and y = - 3  Find :  dy / dt

Q: Which of the following is the derivative of y = Select one: dy a. da 3. dy b. 3. dy C. da 2. dy d.…

A: Option (b) is correct.