If √7-3√5 = √x-√y, determine the value of x and y where x>y.

x = 45

y = 7

Step-by-step explanation:

To obtain the value of x and y, do the following:

√7 – 3√5

Rearrange

– 3√5 + √7

Multiply through by –1

3√5 – √7 ... (1)

Express 3√5 as a single surd

3√5 = √(3 × 3 × 5)

3√5 = √45

Replace 3√5 with √45 in equation 1

3√5 – √7

√45 – √7

Comparing

√45 – √7 and √x – √y i.e

√45 – √7 = √x – √y

x = 45

y = 7

the value of v.w= -12.

step-by-step explanation:

we are given three vector r,v and w as:

r = < 5, -5, -2> ; v = < 2, -8, -8> ; w = < -2, 6, -5>

we know that r,v and w could also be represented as:

r=5i-5j-2k

v=2i-8j-8k

and w= -2i+6j-5k

where i,j and k are the unit vectors of x,y and z-axis respectively.

also we know that it has the following property:

i.i=1 ; j.j=1; k.k=1

and i.=j.i=i.k=k.i=j.k=k.j=0

i.e. when we multiply two vectors or we find it's dot product we need to only multiply the components of x coordinates with each other; y with each other and z with each other.

hence, v.w= (2i-8j- -2i+6j-5k)

                  = 2×(-2)+(-8)×(6)+(-8)×(-5)

                  = -4-48+40

                  = -12

hence, v.w= -12