Q: The tangent line to the graph of y=f(x)at the point (1,11) has the equation y=3x+8 (a) Find f′(1)…

A:

Q: One ship, Ship A, is approaching a port from the east, travleing west at 15 miles per hour, and is…

A:

Q: Suppose that a company can produce 12000 units when the number of hours of skilled labor y and…

A:

Q: In a simple electric circuit, Ohm's law states that V IR, where V is the voltage in volts, I is the…

A: From the given problem: dVdt=-0.01 volts per second ; dRdt=0.03 ohms per secondR=300 ohms ; I=0.04…

Q: Suppose x and y are functions of third variable t. In the equation x2+y2=45, what are the values of…

A: In the question it is given that x and y are the function of the variable t in the equation…

Q: A rectangle has width w inches and height h inches, where the width is twice the height. Both w and…

A: It is given that, a rectangle has width w inches and height h inches, where the width is twice the…

Q: A point on the graph of y = is moving along the curve in such a way that its x-coordinate is…

A: Given graph- y=1x Rate of increase of x-coordinate,dxdt= 6 units per second y-coordinate = 5 Then,…

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: We have, f is the focal length (constant) of a convex lens and an object is placed at a distance p…

Q: 4. The path of a baseball relative to the ground can be modelled by the function dlt) = – f² + 8t +…

A: derivative

Q: 2. If f(t) is the rate of change of some quantity, then what does f (t) dt represent?

A:

Q: Find the instantaneous rate of change of 7. y = (x + 1)*(x – 3) at a = 1.

A:

Q: A substance cools in moving air at a rate proportional to the difference between the temperature of…

A:

Q: A balloon is rising vertically over a point A on the ground at the rate of 15 ft/sec. A point B on…

A: Let the distance of the balloon from point B be denoted as p. The balloon, points A and B form a…

Q: In a simple physical apparatus, the distance x cm and y cm are connected by the relation 1.1 1…

A: Distance x cm and y cm are connected by the relation 1x+1y=19 ....(1) x is increasing at the rate of…

Q: A 5-foot-tall woman walks at 7 ft/s toward a street light that is 20 ft above the ground. What is…

A:

Q: What is the rate of change of y with respect to x for this function?

A:

Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: The rate of change of the volume V(t) of blood in the aorta at time t is given byV′(t) =…

A: Given data:The rate of change of the volume V(t) of blood in the aorta at time t is given by…

Q: The height h and radius r of the base of a straight circular cone are varying at constant rates of…

A: Topic:- application of derivatives

Q: 1 If a spherical drop of liquid evaporates at a rate proportional to its area, if initially its…

A: Let the surface area be A So rate of evaporates is dA/dt, According to the question, dVdtαAdVdt=-kA…

Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: Let I be the length of a diagonal of a rectangle whose sides have lengths a and y, and assume that a…

A:

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

A: Given,   x2+y2=45To find dydt, when dxdt=-2 and x=3

Q: Suppose a quantity described by the function y(t) = y0ekt, where t is measured in years, has a…

A: yt=y0ekt The quantity has a doubling time of 20 years. That is, yt=2y0 when t=20.

Q: Given the function f(x) = e-3x cos 3x, x = [0, 2π]. When is the rate of change of f(x) a maximum?

A: Here, the given function is: f(x)=e-3xcos(3x) Now, the rate of change is given by: f'(x)=e-3xddx(cos…

Q: Suppose that D = √x² + y² is the length of the diagonal of a rectangle whose sides have lengths x…

A: To find the formula for the rate of change of D with respect to x, differentiate D=x2+y2, using the…

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

A:

Q: What limit must be calculated to find the rate of change of a function g(t) at t = t0?

A: The rate of change of a function g(t) at t = t0 is given by g'(t0).

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: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

A: The number of hours of skilled labor is y and unskilled labor is x.

Q: At time t = 0, Car A passes through an intersection and goes east at a speed of 40 feet per second.…

A:

Q: If f is the focal length of a convex lens and an object is placed at a distance p from the lens,…

A:

Q: 1. Suppose that the volume V of a certain cone can be expressed as V =nh, where h is the height of…

A: For the solution of the problem follow the next steps.

Q: Suppose A is directly proportional to t. Explain what happens to t when A is increased by 5%.

A:

Q: If V(t) is the volume of water in a reservoir at time t (seconds), v(t) is the rate of change,  then…

A: Rate Change: Rate change is defined as the change in one quantity with respect to any other quantity…

Q: If x*y+2x+z°=1 find the rate at which z is changing with respect to x at the point (2/5,2/3,1/3)

A:

Q: Initially, 2 cars are parked side by side on a big field. Then, Car 1 starts to move directly to the…

A: Solution

Q: What is the rate of change of y with respect to x for 9x-11y+2=0

A: Given that 9x-11y+2=0 We need to find the rate of change of y with respect to x that is dy/dx.

Q: Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10 s later the…

A:

Q: If the rate of change in life expectancy I at birth for persons born in the United States can be…

A:

Q: Suppose a and y are related by a constant rate of change Ay and = 2, and y 4 when x = 3. Ax

A: Suppose x and y are related to the constant rate of change and ∆y∆x=2and y = 4 when x= 3

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: Given,1f=1p+1qwhere f is focal lenrth and an object is placed at a distance p from the lens and its…

Q: If f(x) = 5x2 − x3, what is the rate of change of f '(x) at (2, 12)?

A: To calculate the rate at which the given function changes at the given point

Q: The value of y varies at a constant rate of change of 1.7 with respect to x. If x varies from x=3 to…

A:

Q: Suppose that a factory worker starts to make face masks at t = 0 and his rate of change of…

A:

Q: What is the rate of change of y = In x at x = 1 O?

A: Given: y=lnx at x=1

Q: 7. If f (t) = -t2 + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A:

Q: If f is the (constant) focal length of a convex lens and an object is placed at a distance p from…

A: In the question, we were given the formula related to the length of the convex lens. Its equation is…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.