To calculate: The factor of the expression
Answer to Problem 122E
The factor of the expression
Explanation of Solution
Given information:
The expression
Formula used:
To factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.
The special factoring formula for perfect square, which is mathematically expressed as,
Calculation:
Consider the given expression
Recall that to factor out the common factor from a polynomial, find out the greatest common factor and express the polynomial as a product of the simpler ones.
The common factor of these terms is
Simplify
Recall the special factoring formula for perfect square, which is mathematically expressed as,
Apply it to factorize
Thus, the factor of expression
Chapter 1 Solutions
Precalculus - A Custom Text for UNLV
- Submit answer Reset item Calculate the length of the astroid of x + y = 5. S = a Submit answer Answers Answer Related Queries: D T Weather DELL 1 Points UParrow_forwardIn the attached graph of f', and given that f(0) = -4 a) Approximate the slope of f at x = 4. b) Is it possible that f(2) = -1? c) Is f(5) - f(4) > 0?arrow_forwardI need some help with this problemarrow_forward
- please find the general solutions to the following ODEs: 1. dy/dx + k^(2)y where y is a function of x only and k^(2) is a constant 2. du/dt + k^(2)cu where u is a function of t only and k^(2) and c are constants Thanksarrow_forwardplease solve problem 4. Thank youarrow_forwardCalculus1 - area between r=2+sin(2theta) and r=2+cos(2theta) Hi! I'd be so so thankful if you can provide the correct answer.. (I asked AI too, but they all got it wrong so I'm asking here..!)arrow_forward
- Problem 1. Solving SDEs: Ornstein-Uhlenbeck process The purpose of this problem is to use Itô lemma to solve the Stochastic Differential Equation with Xo = dX+= (aX+) dt + σ dWt, xo. The solution is known as an Ornstein-Uhlenbeck process. (a) Find an explicit expression for Xt. Hint: use the function f(t, x) Formula. (b) Determine E[X] and Var(X+). (c) Determine lim E[X] and lim Var(X+). 00+7 0047 (d) Is X normally distributed? = etx in Itôarrow_forwardProblem 2. Feynman-Kac application We consider the stochastic process (X+)+20 given by X₁ = et, where (W₁) is a Brownian motion. (a) Determine the stochastic differential equation satisfied by the process (X+). (b) We want to determine g(t, X₁) = EXF] Use Feynman-Kac formula and the result of (a) to write the PDE (with its terminal condition) that the function g has to solve. (c) We guess that g has to be a polynomial of degree 2 in x. Determine g by solving the PDE. (d) We can directly calculate the result using properties of conditional expectation. Verify that you obtain the same solution.arrow_forwardProblem 3. A two-dimensional system. Let (W)to be a one-dimensional Brownian motion. We consider two processes (X+)+20 and (Y)to solutions of the system of stochastic differential equations = with Xo 1, Yo = 0. dXt = Xx₁ dt - Y₁dWt, dyt = -Y dt +X+dWt, 1 (a) We denote Rt and t the radius and the angle in polar coordinates for the point (X, Y) in the two-dimensional plane. Use the multidimensional Itô Lemma to find the differential equations satisfied by Rt and Ot. (b) Solve the differential equations provided in (a) and give an intuitive description of the solution of the system. (c) Write an expression for the solution (X, Y) to the system.arrow_forward
- In some urban locations, if one pollutant is found in the air, we often find others as well. Two commons pollutants in big cities are ozone and secondary carbon concentrations. Both of these pollutants are quite hazardous to the lungs in strong concentrations. The following 16 pairs of data were taken on random summer days near downtown Los Angeles. The data are on ozone concentrations in parts per million (x) and secondary carbon concentrations in micrograms per cubic meter (y): 066 088 120 .050 162 .186.057 .100 .112 .055 .154 .074 4.6 11.6 9.5 6.3 13.8 15.4 2.5 11.8 8.0 7.0 20.6 16.6 111 140 .071 .110 y 9.2 17.9 2.8 13.0 a) Create a scatterplot for these data. b) Using the pictures on a previous handout, guess the sample correlation coefficient. How Would you describe the relationship between the two pollutants? c) Using the scatterplot, what might be a good prediction for the secondary carbon concentration if on a particular day the ozone level is .125 ppm? Predict y if X=125 X…arrow_forward3. (i) Using the definition of the line integral of a vector field, calculate the line integral LF. F.dy of the vector field F: R2 R2 given by F(x, y) = (y, x), and where the curve is the unit semi-circle centred at the origin, located in the upper half-plane and oriented in the anticlockwise direction. Hint. Represent the curve y as the join of two curves 7 = 71 + 1/2 (see Example 8.9 in the Notes). [20 Marks] (ii) Calculate the same integral using Green's Theorem. [10 Marks]arrow_forwardCalculate the arc length of y = 5x + 1 as a varies from 0 to 1. S Submit answer Next item Answers Answer Report technical issue ⚫Email instructor Points 1 T The Weather Channel UParrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning