A population of bacteria is growing. The population, P million, after time t minutes is given by P = 3 x 2'. a Find the average rate of change of population between times 1 = b Find an estimate for the instantaneous rate of change of population with respect to 2 and t = 4. time at t = 2.

Q: The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rates of…

A:

Q: A spherical balloon is deflating and its radius r is decreasing at the rate of 5 mm per minute.…

A:

Q: The length of a rectangle is given by 2t + 5 and its height is Vt, where t is time in seconds and…

A: In the given question the length and height of the rectangle are given:   The area of the rectangle…

Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always three…

A:

Q: A rectangular box has its height increasing at a rate of 1m/s while its volume is decreasing at a…

A: We have to find the  rate of change of length.

Q: The length of a rectangle is given by 4t - 3 and its height is 2t, where t is time in seconds and…

A: Given the rectangle whose length and height are given L=4t−3H=2t3

Q: 2): The side of a cube decreases at a rate of 6 m/sec. Find the rate at which the surface area of…

A:

Q: The edge of an expanding cube is changing at the rate of 2.3 cm/s at the instant its edge is 18.3 cm…

A:

Q: When a vertical beam of light passes through a transparent medium, the rate at which its intensity I…

A:

Q: Find the average rate of change for the following on the given interval. Then find the instantaneous…

A: The average rate of change of f(x) in the interval x =1 to x =4 is a measure of the slope of the…

Q: A tank is initially filled with 1000 gal. of salt solution containing 500 H of salt. Fresh water…

A: Let At the amount of salt at the time t Then the rate of change of the amount of salt dAdt=0lbL.10…

Q: The radius of a spherical balloon is decreasing at a rate of 2 - in/sec. Which of the following is…

A: As we know that the expression for the volume of the sphere: v=43πr3 Where; ''r'' is the radius of…

Q: Consider a pool shaped like the bottom half of a sphere, that is being filled. The radius of the…

A: The volume of hemisphere filled with liquid to height h = πrh2-π3h3

Q: Sand falls from an overhead bin and accumulates in a conical pile with a radius that is always two…

A: The radius is 2 times the height, the rate at which the height increases is 3 cm/s when the pile is…

Q: A spherical balloon is expanding. If the radius is increasing at the rate of 2 inches per minute, t…

A:

Q: An 8- meter ladder is leaning against a vertical wall. If a the ladder away from the person pulls…

A: Given  Length of the ladder = 8 meter The rate at which ladder is pulled away from the wall =0.7m/s…

Q: 1. If the radius of a spherical balloon is increasing at the rate of 3 cm/s, which of the following…

A: We are only allowed to solve one question at a time so we will answer only the first question.…

Q: The length of a rectangle is given by 6t + 5 and its height is √t, where t is time in seconds and…

A: Formula:  Area=length times height A(t)=t(6t+5)

Q: Assume that the radius r of a sphere is expanding at a rate of 70 cm/min. The volume of a sphere is…

A: Given Data: The rate of increase in radius is: drdt=70 cm/min The volume of the sphere is: V=43πr3…

Q: 2. Air is being pumped into a spherical balloon so that the volume increases at a constant rate of…

A: Given rate of change of volume dVdt = 7 ft3/s we need to find rate of change of radius drdt

Q: For the function y = 4x2: (a) Find the average rate of change of y with respect to a over the…

A:

Q: A 18 ft ladder leans against a wall. The bottom of the ladder is 5ft from the wall at time t=0 and…

A:

Q: A square with side x, is changing with time where x(t) =3t + 1. What is the formula for the rate of…

A:

Q: A designer develops a cylindrical box with a fixed height of 15 cm. Calculate the instantaneous rate…

A:

Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: This question can be solved using the concept of rate of change of physical quantities.

Q: The length of a rectangle is given by 4t−3 and its height is (2t)1/3, where t is time in seconds and…

A: Given, The length of the rectangle is 4t - 3 and it's height is (2t)13.

Q: A particle is moving along the curve y = x². As the particle passes through the point (1,e), its…

A: Given: A particle is moving along the curve y=x2. As the particle passes through the point (1, e),…

Q: The height h of a right circular cylinder is twice its radius r. Find the rate of the volume V of…

A: The volume of the right circular cylinder is given as: V=πr2h where 'r' is the radius of the cone…

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

A: The amount of mold at time 0 is m0. The amount of mold present after t hours is m. The rate of…

Q: The top of a ladder slides down a vertical wall at a rate of 1.5 m/s. At the moment when the bottom…

A:

Q: The radius of a right circular cylinder is increasing at the rate of 8 in/sec while the height is…

A: Given- drdt=8 in/sec and dhdt=-3 in/sec To Find- The rate of the volume changing when r= 7 in and…

Q: An old tire is deflating initially at a rate of v(t) = \E + 2 where v(t) is its volume in in' at any…

A: To find out the instantaneous volume at 1 hour.

Q: Suppose the area A of a particular rectangle increases at a rate of 2 cm^2/sec and the width w of…

A:

Q: Consider a rectangular metal box without a top lid which, because of being heated, is increasing in…

A:

Q: 2. The volume of a cube decreases at a rate of 10m/sec. Find the rate at which the side of the cube…

A: dVdt=10m3/min, side=2mFormula of volumeV= side3

Q: A 20 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and…

A: A 20 ft ladder leans against a wall. The bottom of the ladder is 3 ft from the wall at time t=0 and…

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 brine solution of salt flows at a constant rate of 3 L/min into a large tank that initially held…

A:

Q: 6. Air is being pumped into a spherical ball at a rate of 7 cm³/sec. What is the rate of change of…

A:

Q: The radius of a right circular cylinder is given by   square root t + 9 and its height is 1/9…

A: GivenThe radius of a right circular cylinder and height is given by

Q: A weather balloon is rising vertically at the rate of 10ft/s. An observer is standing on the ground…

A: Given: -

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: A balloon is rising vertically above a level, straight road at a constant rate of 4ft/sec. Just when…

A: See below the answer

Q: A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the…

A:

Q: A particle is moving along the curve y = x2 + 2 dx Find all values of xat which the rate of change…

A:

Q: A spherical balloon has been poked with a needle and air is seeping out at a rate of 2cm³ /hr. Find…

A: The volume of the spherical balloon is decreasing at the rate of 2 cm3/hr. We have to find the rate…

Q: 13. (a) Find the average rate of change of the area of a circle with respect to its radius r as r…

A: (a) The average rate of a function f between the points a and b is given by: The area of a circle…

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:-

Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.