Suppose that a particle has been shot into the air in such a way that the rate at which its height is changing is v= 320- 32t, in feet per second, and suppose that is is 1600 feet high when t=10 seconds. Write the equation that describes the height of the particle at any time in t.

Q: Find an equation of the line tangent to the graph of f(x) = - 2x at (2,- 16).

A:

Q: A5 feet 6 inches tall man is walking away from a lamppost at a rate of 2 ft/sec. If the lamppost is…

A: We have, A 5 feet 6 inches (5.5 feet) tall man is walking away from the lamppost of height 12 feet…

Q: Solve the first and second derivative and eliminate the arbitrary constant.  1. y = C1x + C2e-x +…

A: To eliminate the arbitrary constants.

Q: A 5-foot-tall person is walking towards a 7-foot-tall lamppost at a uniform rate of 2 feet per…

A:

Q: A spotlight on the ground shines on a wall 12 m away. If a man 2 m tall walks from the spotlight…

A:

Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx+2

A: Find the equation of line

Q: Find an equation of the line tangent to the graph of f(x) when x = 2: f(x) = Vx +2

A:

Q: Find an equation for the line tangent to the graph of 7x f(x) = x + 7 at the point (3, 2.1). y =

A: Given curve is Differentiating with respect to x, we get

Q: 3

A:

Q: A 6-foot-tall woman walks at 7 ft/s toward a street light that is 30 ft above the ground. What is…

A: Let L be the length of the woman's shadow  x be woman's distance from the street light dLdt=rate of…

Q: 1.) y = (3x² – 1 ) (4x +7 )

A:

Q: Suppose that the acceleration of a vehicle at time t (in s) is given by a(t) = 2t+ 1 (mph/s).If the…

A:

Q: If x + y represents a motorboat’s average velocity with the current, in miles per hour, its distance…

A: We can say Average Velocity=Average DisplacementTotal time=dt so according to the question…

Q: Find an equation for the line tangent to the graph of  f(x)= 2xex at the point (3,f(3)). y=?

A:

Q: Two people start biking from the same point. One heads east at 13 mph, the other south at 17 mph.…

A: Given, two bikers start at same point. One heading east at 13mph and other heading south at 17 mph.

Q: solve for the first and second derivative of the function:

A: Given function is: f(x)=log2 cos x + ln π We need to find the first and second derivative of the…

Q: Find an equation of the line tangent to the graph of ƒ(x) = (2x - 1) (x + 4) at (1, 5).

A: To findEquation of the line tangent to the graph y=(2x-1)(x+4)  at (1,5)⇒y=2x2+7x-4.

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A: Here we use the application of derivative

Q: Find the derivative of the function y = 63x−4

A: We have to find derivative of y=63x-4. Taking log on both sides of given function,…

Q: The volume of a cube is increasing at 24 cubic inches per minute. What is the rate of change of its…

A: volume of cube = side3 V= volume  x= side dVdt=24 in3/minutedxdt=? at x=2

Q: Find the equation of the line tangent to y = x2 - 1 going through x = 1

A:

Q: N or 8x 5 y 3= . 4x 2

A: Given function is y=8x+54x-2 To find derivative of the given function. Solution: Quotient rule of…

Q: 3. =メー1 x+1 デー

A:

Q: Find the slope and equation of the line tangent to f (x) = x2 +9 at the point (1, 10).

A:

Q: At what rate is the distance between Jack and Jill changing if Jack is 3 miles from the bakery and…

A: Given:         To determine:

Q: A spotlight on the ground is shining on a wall 24m away. If a woman 2m tall walks from the spotlight…

A:

Q: What is the equation of the tangent line to y=(−5x−8)e^−x at x=0? Write the equation of the tangent…

A:

Q: Find a formula for the derivative of the function 2x2 – 3

A:

Q: Find the second derivative of the function. y = (8x + 5)3

A: Given: y=8x+53 The power rule for derivatives is expressed as ddxxn=nxn-1…

Q: A $1500 washing machine in a laundromat is depreciated for tax purposes at a rate of $125 per yeaar/…

A: It is given that a $1,500 washing machine in a laundromat is depreciated for tax purpose at a rate…

Q: Find the equation of the line tangent to the graph f(x) = – at the point (4,1).

A: Given:            fx=4x To find the slope of the tangent line, find the value of the derivative of…

Q: Write the equation of the line tangent to f (x): x2 – 3x + 5 at the x

A: To find an equation of the tangent line of f(x)  at the point x=0

Q: One car leaves a given point and travels north at 30 mph. Another car leaves1 hour later, and…

A:

Q: What is the velocity (in ft/s) of a sandbag 3.0 s after it is released from a hot-air balloon that…

A: According to Questions  Initial velocity (u)=0 ft/s  time=t=3s

Q: The time required to empty a tank varies inversely as the rate of pumping. If a pump can empty a…

A: Where k is constant of variation.

Q: Determine the equation of the line tangent to the graph of y when x = 9. 2 + VI

A:

Q: After a ball bounces off from the top of a hill, its velocity at t seconds is v(t)=45-30t feet per…

A: Given velocityv(t) = 45 - 30t

Q: What is the equation of the line that crosses the y-axis at 2 and h. a unit rate of ?

A: We have to find the equation of the required line. The required line crosses the y axis at 2, that…

Q: Find the equation of the curve whose tangent line has a slope of f'(x)=5x-6/7 if the point ​(minus…

A: Given that And it is passing through (-1,-9).

Q: The pressure exerted by a certain liquid at a given point varies directly as the depth of the point…

A:

Q: From a point 56 feet above the ground, a stone is thrown vertically downward and hits the ground at…

A:

Q: One car leaves a given point and travels north at 30 mph. Another car leaves 1 hour later, and…

A: Assuming that car are travelling along the y-axis and x-axis respectively.The position of cars is…

Q: Find the equation of the line tangent of f(x) = 3x - e-5x when x = 0.

A: f'x=3-e-5x-5=3+5e-5x We know that the slope of the tangent at x=a is f'(a). So the slope of the…

Q: Find the first and second derivative if y=4-2x-x-3

A:

Q: What is the equation of the tangent line to the curve y=−5x^2+4x+7 at x=-1? Write the answer in…

A:

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.