Find two vectors v1 and v2 whose sum is 〈−3,4〉〈−3,4〉, where v1 is parallel to 〈3,−3〉〈3,−3〉 while v2 is perpendicular to 〈3,−3〉〈3,−3〉.

∵ Vector is parallel to 〈3, -3〉,

⇒ = x〈3, -3〉 = 〈3x, -3x〉,

Where, x is any scalar,

According to the question,

= 〈-3,4〉

⇒ 〈3x, -3x〉+ = 〈-3,4〉

⇒ = 〈-3,4〉 - 〈3x,-3x〉

Now, is perpendicular to 〈3, -3〉,

⇒ .〈3, -3〉 = 0

⇒ ( 〈3,4〉 - 〈3x, -3x〉 ). 〈3, -3〉 = 0

⇒ 〈-3-3x,4+3x〉 . 〈3, -3〉 = 0

⇒ (-3-3x)(3) + (4+3x)(-3) = 0

⇒ - 9 - 9x - 12 - 9x = 0

⇒ -21 - 18x = 0

⇒ x =

Hence, required vectors are,

= 〈-7/2, 7/2〉

=〈3,4〉 - 〈-7/2, 7/2〉 = 〈13/2, 1/2〉

the amount you'd have after the work is $1.55

step-by-step explanation:

you subtract 95% from $31.

reduce the friction between its moving parts

step-by-step explanation:

in fact, by reducing the friction between the moving parts of the machine, it is possible to reduce the energy wasted due to this friction; therefore, more input energy is converted into useful work, and this will improve the efficiency of the machine.