James is four years younger than Austin. If three times James age is increased by the square of Austin's age, the result is 28. Find the ages of James and Austin.

James = 1 year

Austin = 5 years

Step-by-step explanation:

Let James age = x

Let Austin's age = y

James is four years younger than Austin.

x = y - 4

If three times James age is increased by the square of Austin's age, the result is 28.

3(x - 4) + y² = 28

Hence,

Note: x = y - 4

Hence,

3y - 12 + y² = 28

3y + y² - 12 - 28 = 0

y² + 3y - 40 = 0

y² + 8y - 5y - 40 = 0

y(y + 8) - 5(y + 8 ) = 0

(y + 8)(y - 5)

y = -8

y = 5 years

x = y - 4

x = 5 - 4

x = 1 years.

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

the equation cos(35) =a/25 can be used to find the length of bc what is the length of bc? round to the nearest tenth

step-by-step explanation: