need help A container with a square base (Fig Q3) of size 5 m x 5 m is filled with sand.The sand is uneven whereby the surface height, in metres, measured from thebottom of the container, is given by the function:h(x,y) = -0.01(x – 3)² +7Sm 2.5mFig Q3: domain of containerdetermine the total volume of sand. Answer in m³ to 3 decimal place accuracy.b)find the expression for the partial derivative -c)find the expression for the partial derivative -

In the given question, the concept of volume is applied. Volume The volume of Cuboid is given by…

Answered: he sand is uneven whereby the surface…

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter3: Polynomial And Rational Functions

Section3.1: Quadratic Functions And Models

Problem 56E: When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream...

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When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream After t minutes is given by C(t)=0.06t0.0002t2 where 0t240 and concentration is measured in mg/L .When is the maximum serum concentration reached, and what is that maximum concentration?
The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?
The radius r, in inches, of a spherical balloon isrelated to the volume, V, by r(V)=3V43 . Air is pumped into the balloon, so the volume after t seconds is given by V(t)=10+20t . a. Find the composite function r(V(t)) . b.Find the exact time when the radius reaches 10 inches.
Tsunami Waves and BreakwatersThis is a continuation of Exercise 16. Breakwaters affect wave height by reducing energy. See Figure 5.30. If a tsunami wave of height H in a channel of width W encounters a breakwater that narrows the channel to a width w, then the height h of the wave beyond the breakwater is given by h=HR0.5, where R is the width ratio R=w/W. a. Suppose a wave of height 8 feet in a channel of width 5000feet encounters a breakwater that narrows the channel to 3000feet. What is the height of the wave beyond the breakwater? b. If a channel width is cut in half by a breakwater, what is the effect on wave height? 16. Height of Tsunami WavesWhen waves generated by tsunamis approach shore, the height of the waves generally increases. Understanding the factors that contribute to this increase can aid in controlling potential damage to areas at risk. Greens law tells how water depth affects the height of a tsunami wave. If a tsunami wave has height H at an ocean depth D, and the wave travels to a location with water depth d, then the new height h of the wave is given by h=HR0.25, where R is the water depth ratio given by R=D/d. a. Calculate the height of a tsunami wave in water 25feet deep if its height is 3feet at its point of origin in water 15,000feet deep. b. If water depth decreases by half, the depth ratio R is doubled. How is the height of the tsunami wave affected?

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he sand is uneven whereby the surface height, in metres, measured fr ottom of the container, is given by the function: (x, y) = -0.01(2 – 3)² +7