A particle moves along a straight line with a velocity v(t) =t*e meters per second after t seconds. How far will it travel during the first 11 seconds?

Q: A mold grows at a rate that is proportional to the amount present. Initially there is 6 oz of this…

A:

Q: (a) What is the cyclist's average speed, in mph, over the time interval [0, 1]? (b) What is the…

A: a) At t=0, distance=0 miles At t=1, distance= 12 miles So the average speed in the time interval…

Q: A balloon leaves the ground 30 m from an observer. If it rises at the rate of 2 m/s, how fast is it…

A:

Q: Suppose that a shallow earthquake occurs in which the P waves travel 8 km/sec and the S waves travel…

A:

Q: If a ball is thrown straight up in the air with an initial velocity of 95ft/s, it's height in feet…

A: Given that: A ball is thrown straight up in the air with an initial velocity of 95ft/s, it's height…

Q: 25. A 10-foot ladder is placed against a vertical wall. Suppose that the bottom of the ladder slides…

A: Given :-  dx/dt= 3feet/sec  Ladder height= 10feet  Find rate at which ladder is sliding down from…

Q: A bacteria population starts with 400 bacteria and grows ata rate of  r(t) = (450.268)…

A:

Q: A particle that moves along a straight line has velocity v(t) = t'e-2t meters per second after t…

A:

Q: A ​13-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

A: Given  Length of ladder = 13 foot  Rate of movement of ladder from wall = 4ft/second

Q: A 10-foot ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

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: 11. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A:

Q: Suppose that electricity isdraining from a capacitor at a rate that is proportional to the voltageV…

A: Given equation in the question is: Integrating both sides: We have, at t = t0, V  = V0 =>ln(V0)…

Q: A man 1.69m m tall i s walking on a horizontal street at 3.2 kph away from a vertical street light,…

A:

Q: A man of 2 mts tall is approaching a lamp post at the rate of 0.5m/sec.if the lamp post is situated…

A:

Q: A 200-liter tank initially full of water develops a leak at the bottom. Given that 10% of the water…

A:

Q: A man of height 1.7meters walks away from a 5-meter lamppost at a speed of 1.1 m/s. Find the rate at…

A: Given that a man of height 1.7m walks away from a 5 meters lamp post at a speed of 1.1 m/s. We need…

Q: A rocket lifts off the surface of Earth with a constant acceleration of 20 m/sec2. How fast will the…

A:

Q: | Suppose that electricity is draining from a capacitor at a rate proportional to the voltage V…

A: The given differential equation is dVdt=-140V, where V is the voltage and t is the time in seconds.…

Q: 7. The top of a ladder slides down a vertical wall at a rate of 0.15 m/s. At the moment when the…

A: Given data A ladder slides a vertical wall at rate of 0.15 m/s  find the length of ladder = ?

Q: A lighthouse is located on a small island 4km away from the nearest point P on a straight shoreline,…

A:

Q: 4. A basketball player is 7 feet tall walking away from a light that is 28 feet above the ground at…

A:

Q: Assume that a snowball melts so that its volume decreases at a rate proportional to its surface…

A: Let V denote the volume and A denote surface area. Rate of melting is proportional to its surface…

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Given,           Because of job outsourcing, a town predicts that its public school population will…

Q: After 2 days, 10g of radioactive chemical is present. Three days later, 5g is present. How much of…

A: Given:      After  2 days, 10g of radioactive chemical is present. Three days later5 g chemical is…

Q: A particle moves along a straight line with a velocity v(t) = t²e²t meters per second after t…

A: A particle moves along a straight line with a velocity v(t)=t2e2t meters per second after t seconds.

Q: A mold grows at a rate that is proportional to the amount present. Initially, there is 5 oz of this…

A:

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given,  A ladder slides down a vertical wall at a rate of 0.675 m/s  When the bottom of the ladder…

Q: c. A man 5 ft tall is walking along a straight line at a rate of 3 ft/sec towards a lamp post that…

A: Definition uses-       Similar triangles -        If two triangles are similar then their…

Q: The rate at which bacteria multiply is proportional to the instantaneous Number Present. If the…

A:

Q: As an orange grows, the rate of change of the radius r of the orange is inversely proportional to…

A: Given query is to find differential equation.

Q: The top of a ladder slides down a vertical wall at a rate of 0.25 m/s. At the moment when the bottom…

A: Given:

Q: A car traveling at 60 mi/h (88 ft/s) skids 176 ft after its brakes are suddenly applied. Under the…

A:

Q: A 20 foot ladder leans against a vertical wall. If the base of the ladder is pulled away from the…

A:

Q: 3. A flare is fired straight up from the ground with an initial velocity of 100 ft/s. How long will…

A: The position equation is given by: s=-16t2+v0t+s0 Where s is the final position, s0 is the initial…

Q: At what rate is the height of the water rising at the instant the tank is half full?

A: To find the rate at water rising

Q: Find the equation of the tangent line to the curve at point (0, ln 2).   y=ln(e^x+e^4x)

A: the equation of the given curve is: y=lnex+e4x we have to find the equation of the tangent line to…

Q: A 20-foot ladder is leaning against a vertical wall. Suppose the base of the ladder slides away from…

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: A balloon is 20m horizontally away from an observer. At an constant, the balloon rises vertically at…

A: Let the distance between ballons and observer is y and vertically distance from the ground is x m…

Q: The top ladder slides down a vertical wall at a rate of 0.15m/S. At what moment when the bottom of…

A: Given that the top ladder slides down a vertical wall at a rate of 0.15m/s. the bottom of the ladder…

Q: Water is drained from a pool at a rate of R(t) = 50e-0.08t gallons per hour. If the drain is left…

A: 625 gal. water drains from the pool.

Q: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when the…

A: Given: The top of a ladder slides down a vertical wall at a rate of 0.675 m/s. At the moment when…

Q: A ball is thrown straight down from the top of a 370-foot building with an initial velocity of -18…

A: Given

Q: Find an equation of the line tangent to f(x) = Va at (4, 2).

A: equation of tangent line

Q: A baseball thrown directly upward at 160 ft/sec has velocity v(t) = 160- 32t ft/sec at time t…

A:

Q: A stone weighing 1/2 lb is thrown upward from an initial height of 5 ft with an initial speed of 32…

A:

Q: A flag is raised vertically from a pole at a constant rate of 1 m/s. A point B on the ground is…

A: solution:- draw a right angle triangle:-