Problem #7: A large tank contains 50 litres of water in which 18 grams of salt is dissolved. Brine containing 15 grams of saltper litre is pumped into the tank at a rate of 7 litres per minute. The well mixed solution is pumped out of the tankat a rate of 2 litres per minute.Problem #7(a):(a) Find an expression for the amount of water in the tank after t minutes.(b) Let x(t) be the amount of salt in the tank after t minutes. Which of the following is a differential equation forx(t)?dxdx(A) = 105 - 2x() (B) = 14 - 2x), (C)dt50+ 5t50+ 7t(E) ± = 14 - ½ x(1) (F) ± = 14 -=7-Problem #7(b):Enter your answer as asymbolic function of t, as inthese examplesSelect ✓7x(t)50+ 5t= 7-x(t) (D)2x(1)50%), (H)50+ (G) = 7 -7x(t)7t= 105 - x(t)= 105 -7x(t)50+ 5t

NOTE: Refresh your page if you can't see any equations. . x=amount of salt at time t…

Answered: Problem #7: A large tank contains 50…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Similar questions

Suppose a person's utility function for items x and y is u = ln(x) + ln(y), and he currently has $200 in his pocket, and the price of x is $10 per item and the price of y is $20 per item, find the combination that maximises his utility.
5. As a plane lands, its height above ground level (in feet) is given by h(t) = 35000 − 1000t where t isthe amount of time which has passes since the plane began its descent (in minutes). How longdoes it take the plane to land (reach ground level) after beginning its descent?
A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at timet (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt-and-water solution being poured into the tank alternately gets faster and slower. a) Show how the following differential equation describe the salt concentration s in the solution at any time t. Show full solution ds 0.2(1 + cos 2t)? dt
A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the solution is being poured into the tank is through a device the controls the rate at which it is being poured. The controller ensures the solution is being poured at time t (minutes) with the expression (1 + cos(2t)) in liters per minute. It follows that the amount of salt for every liter of the solution being poured at time t (minutes) is described by the expression 0.2(1 + cos(2t)) in kilograms. This implies the rate the salt- and-water solution being poured into the tank alternately gets faster and slower. Determine which of the following differential equation describing the salt concentration S in the solution at any time t. O A. dS dt OB. dS dt OC. dS dt O D. dS dt = 0.2(1 + cos 21) ² = = = -0.2(1 + cos 21) ² 0.2 (1 + cos 21) ² 0.2 2 (1 + cos 21) ²
5) The population of a town is represented by the formula P(t) = A(1.2)'where A is the current population and t is time. Determine, to the nearest tenth of a year, how long it would take the #6 population to reach 3000 people if the current population is 1250.
number 2
(a) Suppose we create a model of the height of a shrub (Y) based on the amount of bacteria in the soil (X1) and whether the plant is located in partial or full sun (X2). Height is measured in cm, bacteria is measured in thousand per ml of soil (so 1000 is 1 unit), and type of sun = sun and type of sun = between shrubs with a 5500 bacteria and those with a 4000 bacteria count. Assuming the sun is the 0 if the plant is in partial 1 if the plant is in full sun. What will be the height difference on average same for both. (b) Let's say after a few training steps your model is in this state: Y = 33 + 4.6 * X1+8* X2. Explain what the effect of the plant being in sun vs. partial shade will have on the average height of the shrub if there are no bacteria in the soil, based on the model.
Example: A tank initially contains 800 gallons of fresh water. Water containing 1/2 lb/gal of salt flows into the tank with the rate 6 gal/min and the well stirred mixture flows out at the rate of 2 gal/min. Write the initial value problem for Q(t), the amount of salt in pounds in the tank.

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS