A particle moves according to a law of motion: s(t) = t2 - 8t + 12, where t > 0; tis measured in seconds, and s is measured in feet. Find the total distance traveled during the first 6 seconds. Express your answer as a decimal if necessary. Be sure to include proper units!

Q: What is the daredevil’s acceleration at t = 3 seconds?

A:

Q: A body moves along a horizontal line in accordance to s t + 9t2 + 24t. Find the total distance…

A: Given query is to find the distance traveled by the body

Q: Given that s is proportional to t and the fact that s = 264 when t = 66, determine the value of s…

A:

Q: If a rock is thrown upward on the planet Mars with a velocity of 10m/s, its height (in meters) after…

A: This is application of derivative problem

Q: The rate at which ice is melting in a pond is given by R (t) = V1+ 2', where Ris measured in cubic…

A: We use substitution method to solve integration to find out amount of ice melting in first 5 minutes

Q: The displacement (in meters) of a particle moving in a straight line is given by = 9t3 + 4t – 18, |…

A: Given,         The displacement in meters of a particle moving in a straight line is given by…

Q: t and capable of creatir econds and a is in ft/s2 = motion at 32 f/2. N

A: 2. The acceleration of the rocket is, anet=10t-32 Calculate the velocity of the rocket from the…

Q: The velocity of a moving object is v(t)=2t +/t in meters per second. What is its displacement, in…

A:

Q: Solve the differential equetion (x²y²Jdy=2xydx -

A: Consider the provided D.E,

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: Suppose that 4 J of work is needed to stretch a spring from its natural length of 32 cm to a length…

A:

Q: An object is dropped from a 64-foot tower and reaches the ground in 2 seconds. What would the…

A:

Q: An object is thrown straight up with a velocity, in ft/s, given by v(t)=−32t+47v(t)=−32t+47, where…

A:

Q: A projectile is released with an initial (vertical) velocity of 110 m/s. Use the formula…

A: The velocity of particle at any time t is When the particle reach its maximum height , its velocity…

Q: dy

A: Given below the detailed solution

Q: With time t in seconds, the velocity of a bicycle, in feet per second, is given by At) = 4t. How far…

A:

Q: How much work (in J) is required to move a box that weighs 12 kg upward by 55 cm? Use the fact that…

A:

Q: If z = 3x2 + y² and (x, y) changes from (1, 3) to (1.05, 2.9), compare the values of Az and dz.…

A: Given, (x,y) changes from (1,3) to (1.05, 2.9) f(x,y) = z = 3x² +y²

Q: An object is thrown downward, with an initial speed of 16 ft/s, from the top of a building 320 ft…

A:

Q: The width of a rectangle is increasing at a rate of 2cm/sec, while the length increases at 3cm/sec.…

A:

Q: Suppose car A is heading south at 85 km/h and car B is heading east at 90 km/h. Both are headed for…

A: Consider

Q: In the given question as follows, assume the accleration of the object is a(t)= 32 feet per second…

A:

Q: If the velocity of a moving object is v(t)=t-2/t^2 in meters per second, then what is its…

A: We have to find displacement

Q: The forward motion of a SpaceX Dragon, t seconds after touchdown, is described by s(t) = 198t – ti,…

A: Velocity and acceleration

Q: What is the approximate value of V16 - V10?

A: The approximate value of 16 -10  is  =4 x 4 - 10=4-10 9 is 3 and 16 is 4 so value of 10 is slightly…

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 ball is free falling from height of 200 mifind 1-the time of the ball wheureach to the ground. 2-…

A: Part(a): Given, Height=200 mg=9.8 m/s2u=0 Velocity for free falling body Let, the time be t and…

Q: The velocity of a sky driver t seconds after jumping is given by v(t)=80(1−e-0.02t), measured in…

A:

Q: A 2.63-kg steel ball is dropped from a plane to an ocean. If the velocity of the ball just before…

A:

Q: An object is thrown straight up with a velocity, in ft/s, given by v(t)=−32t+47v(t)=−32t+47, where…

A:

Q: Solve the given question below using integration by substitution.

A:

Q: The velocity, v m/s of a ball thrown directly up in the air is given by ? = 20 − 10?, where t is the…

A: Soln :-         V = 20-10t            The time (t) when V is between 5 and 15 m/s.…

Q: If the velocity of a moving object is v (t)=t- 2 in meters per second, then what is its…

A:

Q: Using appropriate substitution 1 dx V9x² – 36x + 37 Is equal to

A:

Q: The position (in meters) of a particle moving along a straight line is given by s ( t ) = 4 t2 -10 t…

A:

Q: If a ball is thrown vertically upward from the roof of 4848 foot building with a velocity of 6464…

A: s(t) = 48 + 64t - 16t2Hence, s’(t) = 64 – 32ts”(t) = - 32When s is maximum, s’(t) = 0; hence 64 –…

Q: What is the position at time t of a car that is accelerating at a rate of 5 meters per second…

A: To determine the position of the car from the given data. (note that s =20 when t=2, not as given)

Q: Suppose that a particle moves along a straight line with velocity v(t) = 14 – 2t, where 0 <t < 3 (in…

A:

Q: An impulse of -9 N*sec is applied during 3 seconds to a 2Kg mass, the acceleration is:

A:

Q: A Ferrari's position at time t is given by s(t) = t3-9t2 + 24t 4) At what time is the acceleration…

A: Given the equation of position of Ferrari's s(t)=t3−9t2+24t    ....(1)

Q: The tempature at any point on a cordinate plane is T=3x2+4y2+5. What is the rate of change from the…

A: Note: We know that, We need to find the rate of change from the origin, considering it's the same…

Q: In 30 minutes, a thousand eight hundred tank of water empties from the bottom.The amount of water…

A: Proceed as shown below

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: What is the velocity at time t for a car that begins accelerating at a rate of 4 feet per second…

A: Given query is to find the velocity.

Q: The displacement, 8 in feet, of a particle moving in a straight line is given by 8 = 5t2 6t + 14,…

A:

Q: (a) Find the velocity of the particle at time t. s'(t) = (b) When is the velocity 0? (Use n as the…

A: Follow the procedure given below.

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: We need to choose correct option.

Q: The diameter of a steel ball is measured to be 16 cm, with a maximum error of 0.3 cm. Estimate the…

A: The relation between the radius, r, and the diameter, l, can be defined by the equation: r=l2. It is…

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.