a) Determine an equation, in simplified form, for the family of cubic functions with zeros 2 +- sqrt5 and 0
20. Determine an equation, in simplified form, for a cubic function with zeros 2± v5 and 0 and graph passing through the point (2, 20) [A, 3m
Use the given conditions to write an equation for the line in point-slope form and slope-intercept form. Passing through (-3,-2) and (3,14) Type the point-slope form of the equation of the line. (Use integers or simplified fractions for any numbers in the equation.) Type the slope-intercept form of the equation of the line. (Use integers or simplified fractions for any numbers in the equation.)
For the following specifications of lines find the equation of the line in (a) General form (b) Point-gradient form (c) Gradient intercept form i. Passing through (2,2) with gradient 3 ii. Passing through (-3,7) parallel to the line 38-4y+1=0 Passing through (1.1) perpendicular to the line 7x+3y-5=0
Factor the quadratic functions below to determine the zeros of each function. 3. 49x2 = -21x-2 4. 12x2 + 4x - 8 = 0
Write the cubic polynomial function f(x)in expanded form with zeros −5, −2,and 2, given that f(−1)= −24. f (x) = ______ Suppose $3,500 is compounded annually for 42 years. If no other deposits are made, what rate is needed for the balance to triple in that time? Round the answer to the nearest hundredth of a percent. Interest Rate = _______%
For the following specifications of lines find the equation of the line in (a) General form (b) Point-gradient form (c) Gradient intercept form i. Passing through (2.2) with gradient 3 ii. Passing through (-3,7) parallel to the line 3x-4y+1=0 Passing through (1.1) perpendicular to the line 7x+3y-5=0 For each of the above lines find both the x intercept and the y intercept
5. (a) The natural spline S(a) passing through the n+ points is a collection of n cubic functions S,(x) defined in the n intervals x, Sxx Suppose that all the points are equally spaced, with uniform point spacing h=5m-x, for jso,1,..,,n. Ifthe symbols M,, 0, represent the second derivatives of the spline at cach of the mesh points, show that in each intervl-.R-1 For the natural cubic spline (for which M, O and M-=0 ), show that the moments M...
Problem 4: (a) (5 points) Find the equation for the line that passes through the points (-4,-2) and (8, 1). Write your equation in se form, slope-intercept form, or point- slope form. (Extra Credit: Write the equation for the line in all three forms) (b) (5 points) Graph the line. Problem 5: (10 points) Find the equation for the line passing through the point (3.2) and perpendicular to the line y = ',x + 7. The the line Problem 6:...
3. Express each of the following in simplified Cartesian form. a) (v2- V60)0 (V2 + V65)25 (b) 21010(-1 +)0(+) 4. Find the complex number z, in Cartesian form, such that it satisfies the equation 5. Find all solutions of the equation r 160 Express any complex solutions in Cartesian form, simplified as much as possible.
Determine the simplest form of an equation for the graph. Choose b>0, and include no phase shifts. (Midpoints and quarter-points are identified by dots). The simplest form of an equation for the graph is y = -1 tanx (Use integers or fractions for any numbers in the expression.)