Determine whether the following statements are true and give an explanation or counter example. a. any point on the z-axis has more than one representation in both cylindrical and spherical coordinates. b. the sets { (r, θ,z ): r = z } and {(rho,θ): =π/4} are the samea. the statement is true. in cylindrical coordinates, any point (x, y,z) = (0,0,z) on the z-axis is represented by (r,θ,z) = (0,θ,z), where theta is arbitrary. in spherical coordinates, the point (x, y,z) = (0,0,z) can be represented by (p, θ) = (z,0,θ) or (p, θ) = (-z, pi,θ) where theta is arbitrary. b. the statement is false. the origin (x, y,z) = (0,0,0) has only one unique representation in cylindrical coordinates. c. the statement is false. the origin (x, y,z) = (0,0,0) has only one unique representation in any coordinate system. d. the system is false. the origin (x, y,z) = (0,0,0) has only one unique representation in spherical coordinates.

answer: the common difference is -0.10

hello from mrbilldoesmath!

answer:

25x^2 + 90x + 84

discussion:

mn(x) = m(n(x)) = m( 5x + 9) =

(5x + 9)^2 + 3 =>

25x^2 + 90x + 9^2 + 3 =

25x^2 + 90x + 84                 (as 9^2 = 9*9 = 81)

which is the second choice

regards,  

mrb

p.s.   i'll be on vacation from friday, dec 22 to jan 2, 2019. have a great new year!

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true