224. Suppose that a particle moves along a straight line with velocity defined by v(t) =t-3t-18, where 0st s6 (in meters per second). Find the displacement at time t and the total distance traveled up to t= 6.

Q: The line y = 3x + k is tangent to the curve y = x when k is equal to

A: Given,        The line y=3x+k is tangent to the curve y=x3

Q: 3 Find the slope of the tangent line to x/y +yVx = 10 at (1,8).

A: given: x3y + y3x= 10differentiate given equation with respect to xx3 ddxy + y ddx x3+ y3ddxx+ x ddx…

Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

A:

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 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: Suppose that a particle moves along a straight line with velocity defined by v(t) =2t2 -t - 3, where…

A:

Q: 2 Find the line tangent to the curve r3 +y3 at the point 4 (-3/3, –1).

A:

Q: 3. What is the slope of the tangent line to y = 4* at x = 0?

A:

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: 4. A. Use the tangent line to find a linear approximation to the function f (x) = Vx near x = 64.…

A:

Q: -1 Where on the curve y = (256+ x²)¯* does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: 2. Find the equation of the line tangent to x* – 3xy+ y³ = 1 when x = 0.

A:

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

A: Given : θ = 26.75°

Q: 5. Find the equation of the tangent line for: x = vt + 9, y= at (4,-)

A: The objective is to find the equation of the tangent line.

Q: If the instantaneous rate of change of fx) at (9, -6) is 2, write the equation of the line tangent…

A:

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 14 cm high and…

A: *given:- radius of the cylindrical can, R = 6/2 = 3 cm height of the cylindrical can, h = 14 cm

Q: 4) Find the slope of the tangent line to the curve 4 y = 3(х3 — 2х2 + 3х — 5) at the point (2,) Give…

A:

Q: A truck is 300 kilometers due east of a car and is traveling west at a constant speed of 30km/hr.…

A: (a) Let the initial position of the car be at the origin. Take the x-axis from west to east and the…

Q: Determine the slope of the line tangent to y = x+1 at x = 1 3x2

A: y = (x+1)/3x2 slope = dy/dx dy/dx = (3x2(1) - 6x(x+1))/9x4 slope at x=1 dy/dx = (3 - 6(2))/9 dy/dx =…

Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

A:

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

A:

Q: If f(x) describes the position of an object over time, what is the average velocity on the interval…

A:

Q: If the instantaneous rate of change of g(x) at (-1, -2) is 1/2, write the equation of the line…

A:

Q: If the instantaneous rate of change of g(x) at (−1, −3) is 1/2, write the equation of the line…

A: Slope of tangent line is ½. So the equation is of the form:

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

A: Now in triangle ABC, by using Pythagorean theorem, we get

Q: -1 Where on the curve y = (196 + x²)¯ does the tangent line have the greatest slope? NOTE: Enter the…

A:

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 30 cm high and…

A: Given a closed cylindrical can has height 30 cm and 6 cm is diameter. the metal in the top  and…

Q: If the instantaneous rate of change of f(x) at (4, −3) is 7, write the equation of the line tangent…

A: The objective is to find the equation of the tangent line to the graph of f(x) at x=4.

Q: 8. An express train reducing its velocity to 40 km./h. , has to apply the brakes for 50 sec. . If…

A: Given that  Velocity of express train =40km/hr  Breaks apply at 50sec Retardation =0.5m/sec^2 To…

Q: What is the value of the slope of the tangent line to the curve *y+y²=5 passing through the point…

A:

Q: Use differentials to estimate the amount of paint needed (in m^3) to apply a coat of paint 0.04 cm…

A: Given that     A hemispherical dome with diameter 56m. Here we have to use the differentials to…

Q: 8. What is the rate of change of the slope of the tangent line to the curve y =x – 3x2 +1 when x =…

A:

Q: What will be the rate of change of the surface of the sphere when the radius of the sphere is 5.00…

A: Given; Radius= 5cm And time rate of change in Radius is= π/2.

Q: Find the slope of the line tangent to the graph of x2+2xy2+3y=31 at th epoint (2, -3)

A: To determine the slope of the tangent at the point (2, -3).

Q: Suppose that water is pouring into a swimming pool in the shape of a right circular cylinder at a…

A: Given that radius =7 ft dVdt=9 cubic ft per minutefind dhdt Also V=πr2h

Q: b) Suppose a ball is thrown downward with a speed of 8 meters per second from a height of 75 meters.…

A: Given: Suppose a ball is thrown downward with a speed of 8 meters per second from a height of 75…

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

A:

Q: 4) Find an equation to the line tangent to y = 5 + |x – 2| at the coordinate (2, 5).

A:

Q: A baseball diamond is a square with with side 90 feet (between the bases). A batter hits the ball…

A: Roughly draw the situation first Where x= Distance covered by batter at time t D= Distance of the…

Q: D A child is rolling a spherical snowball with an outer 1) Tayer of ice so that the volume Of the…

A: As per bartleby answering guidelines we are supposed to answer only first question in case of…

Q: 5) Find the equation of the line tangent to 9x? + 4y³ = 76 at x = 2.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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: Suppose that a rocket is launched vertically and it is known that the exaust gases are emitted at a…

A: Given Constant Velocity u=19.5 m/sInitial mass mo=0.7kgGravity g=9.81 ms-2Time t=0.3 second,…

Q: If the instantaneous rate of change of f(x) at (6, −8) is 4, write the equation of the line tangent…

A:

Q: 4. If s t-5t2 + 5t - 3, the velocity is equal to 2 if t =,

A:

Q: What is the value of the slope of the tangent line to the x²+4xy + y=13 passing through the point…

A: Topic = Application of Derivative  As per guidelines, At a time only one question can be answered…

Q: Suppose the cost incurred in operating a cruise ship per hour is a+bv^33 dollars, where a and b are…

A: ANSWER :

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.

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!