GoWnuffsaid

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance, d that she traveled during these three seconds.

t(s) 0 0.5 1.0 1.5 2.0 2.5 3.0

v(ft/s) 0 6.7 11.2 15.5 18.1 19.8 20.2

d (lower estimate)

d (upper estimate)

A drug response curve describes the level of medication in the bloodstream after a drug is administered. A surge function, given below, is often used to model the response curve, reflecting an initial surge in the drug level and then a more gradual decline. If, for a particular drug, A = 0.03, p = 6, k = 8, and t is measured in minutes, estimate the times, t corresponding to the inflection points. (Round the answers to three decimal places.)

S(t) = At p e-kt

t > 0

(smaller value)

(larger value)

When a foreign object lodged in the trachea (windpipe) forces a person to cough, the diaphragm thrusts upward causing an increase in pressure in the lungs. This is accompanied by a contraction of the trachea, making a narrower channel for the expelled air to flow through. For a given amount of air to escape in a fixed time, it must move faster through the narrower channel than the wider one. The greater the velocity of the airstream, the greater the force on the foreign object. X-rays show that the radius of the circular tube contracts to about two-thirds of its normal radius during a cough. According to a mathematical model of coughing, the velocity v of the airstream is related to the radius r of the trachea by the equation below, where k is a constant and s is the normal radius of the trachea. The restriction of r is due to the fact that the trachea wall stiffens under pressure and a contraction greater than 0.5s is prevented (otherwise the person would suffocate).

v(r) = k(s - r)r2

0.5s ≤ r ≤ s

(a) Determine the value of r in the interval [0.5s, s] at which v has an absolute maximum.

r =

(b) What is the absolute maximum value of v on the interval?

v =

Find the absolute maximum and absolute minimum values of f on the given interval. (Round all answers to one decimal place.)

f(t) = t sqrt(25 - t^2)

[-1, 5]

Consider the following function.

y=1/(x+2)

(a) Find the differential dy.

(b) Evaluate dy for x = 0 and dx = -0.1.

Compute Δy and dy for x = 1 and dx = Δx = 1. (Round the answers to three decimal places.)

y = √x

dy =

Δy =

Find the derivative. Simplify if possible.

g(x) = cosh(ln(x))

g'(x) =

h(x) = ln(cosh(2x))

h'(x) =

Compute Δy and dy for x = 1 and dx = Δx = 1. (Round the answers to three decimal places.)

y = √x

dy =

Δy =

thanks

At noon, ship A is 70 km west of ship B. Ship A is sailing south at 25 km/h and ship B is sailing north at 35 km/h. How fast is the distance between the ships changing at 4:00 PM?

Gravel is being dumped from a conveyor belt at a rate of 10 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 14 ft high? Give your answer correct to three decimal places.

a person is walking along a straight path at a speed of 4 m/sec. a searchlight located on the ground y=25ft from the path is kept focused on the walker. at what rate is the searchlight rotatating when the walker is 30 feet from the point on the path closest to the searchlight?

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When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round the answers to one decimal place.)

(a) When will its temperature be 12°C?

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If a snowball melts so that its surface area decreases at a rate of 1 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm. (Give your answer correct to 4 decimal places.)

thank you in advance need it by saturday night

Brain weight B as a function of body weight W in fish has been modeled by the power function B = 0.007W2/3, where B and W are measured in grams. A model for body weight as a function of body length L (measured in centimeters) is W = 0.12L2.53. If, over 10 million years, the average length of a certain species of fish evolved from 16 cm to 24 cm at a constant rate, how fast was this species' brain growing when the average length was 18 cm?

thanks is advance need by saturday night

Boyle's Law states that when a sample of gas is compressed at a constant temperature, the pressure P and volume V satisfy the equation PV = C, where C is a constant. Suppose that at a certain instant the volume is 100 cm3, the pressure is 200 kPa, and the pressure is increasing at a rate of 20 kPa/min. At what rate is the volume decreasing at this instant?

A street light is mounted at the top of a 15 foot tall pole. A man 6 ft tall walks away from the pole with a speed of 7 ft/s along a straight path. How fast is the tip of his shadow moving when he is 40 ft from the pole?