Use the inner product〈f, g〉=∫10f(x)g(x)dxin the vector space c0[0,1] of continuous functions on the domain [0,1] to find 〈f, g〉, ∥f∥, ∥g∥, and the angle αf, g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f, g〉= ,∥f∥= ,∥g∥= ,αf, g .

a) <f,g> = 2605/3

b) ∥f∥ = 960

c) ∥g∥ = 790

d) α = 90  

Explanation

a) We calculate  <f,g> using the definition of the inner product:

b) How

∥f∥ = <f,f> then:

∥f∥ =

c)

∥g∥ = <g,g>

∥g∥ =

d) Angle between f and g

<f,g> = ∥f∥∥g∥cosα

Thus

only 10/60 isn't equivalent

hope this : )

the given 6 = w/p is equivalent to 6p = w, where w is the total area of the walls and p is the area covered by a single can of paint.

knowing that 6 cans of paint will be needed, 6p = w becomes 6(6) = w = 36.   this tells us that the total area to be painted is 36 square units.