Finding the coefficient a of the term in the expansion of the binomial.

3,247,695

Step-by-step explanation:

We want the coefficient of  the term with  x^8

So  Use Newton's Binomial Expansion formula

Formula is  (x + y) ^n  =   Sum for i=0 to n     (n choose i)   x^(n-i)*y^i

here   (x^2  + 3) ^ 12

( 12 choose i) *  (x^2)^(12-i) * (3)^i

i needs to equal 8  for us to get  x^8

(12 choose 8) * (x^2)^(12-8) * (3^8)

= (12 choose 8) * x^8  * (3^8)

so  a = (12 choose 8) *

a =  (12! /(8! * 4!) ) *

a = ( 12*11*10*9/  4*3*2*1)  *

a =  (11*5*9) *

a = 11*5*9 * 6561

a = 3,247,695

45.36 feet per second.

step-by-step explanation:

to find the most accurate determination for the number of feet per second tyrone traveled on his way to work let us convert miles to feet and minutes to seconds.

1 mile = 5280 feet.

1 minute = 60 seconds.

now we will divide 158400 by 3492 to find the most accurate determination for the number of feet per second tyrone traveled on his way to work.

therefore, tyrone traveled on his way to work at the rate of 45.36 feet per second.