The vector u has a magnitude ∥u ∥= 12 ft and direction with generalized angle α = 135°. Find the magnitude of its vertical and horizontal components

The magnitude of the vertical component of vector u is  

The magnitude of the horizontal component of vector u is  

Step-by-step explanation:

A vector quantity has, a magnitude and a direction

The horizontal component of vector is ║u║ cos α

The vertical component of vector is ║u║ sin α

∵ The magnitude of vector u is 12 ft

∵ The measure of angle α is 135°

- Substitute the magnitude and the angle in the rule of

   each component

∴ = 12 cos(135)

∴ = 12 sin(135)

∵ cos(135) =

∴ = 12 ( )

∴ =  

- The magnitude of a number means the number without its sign

∴ The magnitude of the horizontal component of vector u is  

∵ sin(135) =

∴ = 12 ( )

∴ =  

∴ The magnitude of the vertical component of vector u is  

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.