Part A: Suppose Jackson hiked due north on the first trail, and due east on the second trail. Show that the magnitude of the resultant vector for the entire hike is . Part B: Describe the meaning of the magnitude you found in Part A in terms of the hike. Part C: Could Jackson have hiked in a different direction on the second trail without affecting the magnitude of the resultant vector? Explain.

A) √((distance travelled due north)²+(distance travelled due east)²)

B) distance from starting point

C) Yes due west

Step-by-step explanation:

A) According to pythagoras theorem

resultant vector= √((distance travelled due north)²+(distance travelled due east)²)

Also see 1st attachment

B) The resultant vector tells the distance from the starting point

C) The same amount of distance travelled in opposite direction that is westwards will give same magnitude of resutlant vector.

See 2nd attachment

i think the correct option is the second option.

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)