Suppose x and y are functions of third variable t. In the equation *+y=45, what are the values of the rate of change in y with dr respect to twhen dt 2 and x=3, at this instant?

Q: A point P is moving along the line whose equation is y=8x. How fast is the distance between P and…

A: Any point on line whose equation is y=8x is P(x,8x) Then , distance between point P and (3,0) is

Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

A:

Q: Estimate the instantaneous rate of change of y(x) 4 at the %3D x+ 1 point x = - 2

A:

Q: There is a constant outflow of a liquid into a inverted conical vessel 15 m deep and 7.5 m in…

A: Find the rate of change of volume of water in the cone, with respect to time:…

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: Find the instantaneous rate of change of y with respect to x at x=2 of the function y = 2x³ + 4 %3D

A: To Find: The instantaneous rate of change of the function y=2x3+4 at x=4. Given: The function is…

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

A:

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: If the population of bacteria in a certain region triples in 30 days. In how many days will be three…

A:

Q: Determine the percentage relative error (In 2 decimal places) when we compare the derivative of…

A:

Q: What is the rate of change of y = In x at x = 10?

A: Explanation: Given that,  y=lnx   Concept Used: To find the rate of change we will find the…

Q: How would i calculate the instantaneous rate of change given at the given point (3,10.1)?

A: Let's find.

Q: A point P is moving along the line whose equation is y =2x. How fast is the distance between P and…

A: The line is given by y=2x, differentiate w. r. t. t to get: dydt=2dxdt Let Px,y be a point on the…

Q: A spherical snowball is melting so that its diameter is decreasing at a rate of 0.4 cm/min. At what…

A:

Q: At what rate is the production of fish changing with respect to time 5 months from now?

A: Given Data: Production of pounds of fish per month is: QK=109K13 ......1 Total investment is:…

Q: A point P is moving along the line whose equation is y 2x. How fast is the distance between P and…

A:

Q: As the base of the ladder slides away from the house, the rate of change of the height of the ladder…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x? +…

A: Given is the function y=log(x2+1)2   .  It is needed to compute backward difference approximation…

Q: If

A: Explanation and solutions is given below....

Q: What are three methods that can be used to estimate the instantaneous rate of change in g(x) at x =…

A:

Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

A:

Q: At 12:00 p.m. a tank contains 150 g of salt dissolved in 8 L of water. Pure water begins flowing…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

A:

Q: A liquid solution is passing thru a conical filter 2 feet deep and 4/3 feet across the top, into a…

A: We have to find the rate at which the level of the solution in the cylinder rising.

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.4 cm/min.…

A:

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is…

A: The diameter of the snowball is decreasing at a rate of 0.1 cm/min. So, the decreasing rate of…

Q: 9. If the volume and radius of a sphere are functions of time,what is the relationship between the…

A:

Q: Suppose y = f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A:

Q: A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the…

A:

Q: Suppose y=f(x) is a curve that always lies above the x-axis and never has a horizontal tangent,…

A:

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.1 cm/min. At what is…

A:

Q: The length of the rectangle is decreasing at a rate of 5 cm per second, and its width is increasing…

A:

Q: The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height of the cylinder…

A: Given,         The radius of the base of a cylinder is increasing at a rate of 1 m/h and the height…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

A: Solution:

Q: Determine the instantaneous rate of change of the function πt³ √x sin (TE³ 2 f(x) = x3 1 + √t at…

A:

Q: If fex, yJ-o find dy /af partial derivative off dx

A:

Q: What is the instantaneous rate of change of y=y=−2x^2+2x at x=0 ?

A:

Q: here is a constant inflow of a liquid into a conical vessel 15 feet deep and 7.5 feet in diameter at…

A: The height of the conical vessel h = 15 feet.  Diameter of the lop d = 7.5 feet,  The radius of the…

Q: A point P is moving along the line whose equation is y = 2x. How fast is the distance between P and…

A: Firstly we find the distance between a random point on the line y = 2x, and then we differentiate…

Q: Let m(x) be the slope of the tangent line to the curve y = 2x° – 6x² + 3x at the point (x, y). Find…

A: We have to find instantaneous rate of change of m(x) at point (2,-2)

Q: A point moves along the curve y of 2 units per second. At what rate is x changing when = = 2x2 1 in…

A: According to the question, we have to find the rate of the x when x=-32, if the rate of change of y…

Q: A potter forms a piece of clay into a cylinder. As he rolls it, the length, L, of the cylinder…

A:

Q: A point P is moving along the curve whose equation is  y=4x. How fast is the distance between P and…

A:

Q: A hot air balloon is 120 ft. above the ground when a motorcycle (travleing in a straight line on a…

A: Given that, A hot air balloon is 120 ft. above the ground when a motorcycle (traveling in a straight…

Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

Q: 5) If the radius of a right circular cylinder is increasing at a rate of 1 inch per minute, and the…

A: The volume of cylinder is given by the formula V=πr2h. The given values are as follows: r=40 inches,…

Q: Assign variables and restate the following problem in terms of known and unknown derivatives (but do…

A:

Q: A radioactive material decays continuously at a rate proportional to the amount present. After 2…

A:

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

A:

Q: A rectangle has a length that is increasing at a rate of 16 mm per second with the width being held…

A: