Two chemical factories are discharging toxic waste into a large lake, and the pollution level at a point x miles from factory A toward factory B is P(x) = 3x2 − 36x + 512 parts per million (for 0 ≤ x ≤ 50). Find where the pollution is the least. x = _______________mi

Two chemical factories are discharging toxic waste into a large lake, and the pollution level at a point x miles from factory A toward factory B is P(x) = 3x2 − 36x + 512 parts per million (for 0 ≤ x ≤ 50). Find where the pollution is the least. x = _______________mi

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter5: Polynomial And Rational Functions

Section5.5: Zeros Of Polynomial Functions

Problem 51SE: Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph...

See similar textbooks

Related questions

Q: Find the equation of the plane through the point (3, -3,0) that is tangent to the surface xy² + 3ye²…

Q: If xy^2-y^3=x^2-5 , then dy/dx = ?

Q: Find the extreme values of g(x, y) = x² + y² + x²y on the circle x² + y² = 12 using the method of…

A: To find the extreme values of g(x,y)=x2+y2+x2y...(1) on the circle f(x,y)=x2+y2-12=0...(2)

Q: Check that the point (−2, 2, 4) lies on the surface cos(x + y) = exz+8 (a) View this surface as a…

A: To find the normal vector to the surface.

Q: Solve the ff. first order DE using Separation of Variables 2 a. xy¹dx + e*dy = 0

Q: Supply and Demand Suppose that the quantity supplied Sand the quantity demanded D of hot dogs at a…

A: Supply and demand is the relationship between the quantity of a commodity that producers wish to…

Q: 4. (16x + 5y)dx + (3x + y)dy = 0, when x = 1 and y = -3

Q: Consider the surface xyz = 16. A. Find the unit normal vector to the surface at the point (2, 2, 4)…

A: Given, xyz=16⇒xyz-16=0

Q: What is the slope of the tangent line to the curve y^2-2x^2=6-2xy at the point (2,3) ?

Q: 13. The graph of the first derivative f'(x) of a function is shown. Identify the graph of f. N

A: Given query is to find the the graph of the function from the derivative graph.

Q: x+2 2x²+5x+2 11. Find all x values at which f(x) discontinuity and redefine the function to make it…

Q: Use the Fundamental Counting Principle to solve:A television programmer is arranging the order that…

A: Fundamental Counting Principle:- The fundamental counting principle is a rule used to count the…

Q: f(x) = In (x + 9)

A: Given f(x) = ln ( x + 9 )

Q: Straight-line Depreciation Suppose that a company has justpurchased a new machine for its…

A: Note:- Slope intercept form of line: y =mx +b Here, m is the slope of line. Given…

Q: 55. Differentiate each trigonometric identity to obtain a new (or familiar) identity. sin x cos x…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: How many different four-letter passwords can be formed from the letters A, B, C, D, E, F, and G if…

A: The letters A, B, C, D, E, F, and G.

Q: Use algebra to rewrite the expression BEFORE you differentiate. 8x¹7 - 2x¹4 14 x11 A) 32x³ - 2x D)…

Q: x=t+3 and y=²+2t Part: 0/2 Part 1 of 2 (a) Eliminate the parameter and write an equation in…

A: The parametric equations are x = t+3 .........1y = t2+2t…

Q: (e) Write out the first five terms of the sequence, determine whether the sequence converges, and if…

Q: lim 60 SiA (-78) (10

Q: a. b. C. S e. sin ²0 S de cos²0 S dx x(x²+1) d. 0 cos(20 + 1 S 9dv 81-v4 x3 x2–2x+1

Q: PROBLEM: Write the general solution of the differential equation defined by x^2dy-…

Q: a. f(x)=²x-2 g={(1,-1),(-1,1), (2,3), (-3,2), (6,2), (-2,0), (0,√3)} h(x) = √2x - 1 b. g C.

Q: le's law states that if the temperature of an ideal gas is held constant, then the pressure P of the…

A: Given query is to find the expression for rate of change of pressure.

Q: Consider the curve given by Find all points on the curve (x,y) where the tangent line is horizontal.…

Q: Set f(x) = 1 7x³ + 3x + 2 . The point 1, 11/12) is on the graph of f. Find (ƒ-¹) (12)

A: we need to find f-1'112

Q: a. In 25-In 64 +In 27 3

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: These are the following jokes about books:. “Outside of a dog, a book is man’s best friend. Inside…

A: Given data There are six jokes about books

Q: Write an equation for the parabola whose graph is given below. Enter your answer in general form.…

A: Topic- Equation of a parabola We are given a graph of a parabola with vertex at (-4,3) and passing…

Q: 5. Bernoulli's Equations b. 2x³y' = y(y² + 3x²)

A: equation

Q: (a) cosh(sinh *(8))

A: U

Q: Compute the first three derivatives of f(x) and then state the formula for the nth derivative of…

Q: Find an equation of the tangent line to the curve y=4x at the point (1,4) Tangent line: y=

A: Given query is to find the equation of the tangent line.

Q: Find the limit. (If an answer does not exist, enter DNE.) lim arctan(eX) x → ∞0

A: We have, limx→∞ arctanex

Q: Solve the ff. first order DE using Exact Equations a. (x + y)dx + (x −y)dy = 0

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Evaluate: 1. lim [√x² + x − √x² + 4] = X→ +∞ 2. lim [(x²-In(x + 1)) cotx] -0-x

Q: DIRECTIONS Indicate the degree and determine the solution of the following equations. 3. (x² + 2xy…

Q: For the curve y = Inx, find the equation of a tangent line parallel to the line 3x-y = 5 *Note…

A: given curvey=ln(x)

Q: F(x) = psolute min solute max +25 on [-7,7] 11

A: Topic:- application of derivatives

Q: A runner begins training by running 5 miles in one week. The second week she runs a total of 6.5…

Q: २. px 17X 11 (X)7 gos

Q: Differentiate y with respect to a y cos²(a) + y sin²(a) = (cos(a)+37)² Select one: O a. y' =…

A: ycos2a+ysin2a=cosa+372

Q: Solve: cos 2x + 3 sin x - 2 = 0, 0≤ x<2π.

A: Given data:- The given trigonometry equation is, cos2x+3sinx-2=0, 0≤x<2π

Q: a. Graph the function ƒ(x) = sqrt(1 - x2), 0<= x <= 1. What symmetry does the graph have?b.…

A: The given function is: f(x)=1-x2,0≤x≤1. It is required to find the symmetry of graph.

Q: PLOT THE GRAPH FOR THE GIVEN CURVES AND CONDITIONS BELOW Need to find out the differential equation…

A: We have to plot the graph.

Q: What is a periodic function? Give examples. What are the periodsof the six basic trigonometric…

A: Function: In mathematics, a function is an expression, rule, or law that establishes the…

Q: The formula for nCr has the same numerator as the formula for nPr but contains an extra…

A: The NCR formula is used to calculate the number of possible combinations in which r objects are…

Q: A consumer purchased a computer after a 20% price reduction. If x represents the computer's…

A: A consumer purchased a computer after a 20% price reduction. If x represents the computer's…

Q: 10. x dy dx = y + √x² = y²₂ x>0

Q: 3 Each limit repr number a. State m -0 √9+h-3 h

A: Given query is to find f and a.

Question

Two chemical factories are discharging toxic waste into a large lake, and the pollution level at a point x miles from factory A toward factory B is P(x) = 3x² − 36x + 512 parts per million (for 0 ≤ x ≤ 50).
Find where the pollution is the least.

x = _______________mi

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

Sales A soft-drink vendor at a popular beach analyzes his sales records and find that if he sells x cans of soda pop in one day, his profit (in dollars) is given by P(x)=0.001x2+3x1800 What is his maximum profit per day, and how many cans must he sell for maximum profit?
Use Descartes’ Rule to determine the possible number of positive and negative solutions. Then graph to confirm whichof those possibilities is the actual combination. 51. f(x)=2x3+37x2+200x+300
Gravity If an imaginary line segment is drawn between the centers of the earth and the moon, then the net gravitational force F acting on an object situated on this line segment is F=Kx2+0.012K(239x)2 Where K0 is a constant and x is the distance of the object from the center of the earth, measured in thousands of miles. How far from the center of the earth is the dead spot where no net gravitational force acts upon the object? Express your answer to the nearest thousand miles.
APPLICATIONS Average Linh has obtained scores of 82, 75 and 71 on her midterm algebra exams. If the final exams counts twice as much as a midterm, what score must she make on her final exam to get an average score of 80? Assume that the maximum possible score on each test is 100.
The cost function for a certain company is C=60x+300 and the revenue is given by R=100x0.5x2. Recall that profit is revenue minus cost. Set up a quadratic equation and find two values of x (production level) that will create a profit of $300.