(1+x^2)^8
=(1+8x^2+8*7/(1*2)x^4+8*7*6/(1*2*3)x^6+8*7*6*5/(1*2*3*4)x^8+....)
=1+8x^2+28x^4+56x^6+70x^8+....)
For x<1, higher power terms diminish in value, hence we can approximate powers of numbers.
1.01=(1+0.1^2) => x=0.1 in the above expansion
(1.01)^8
=1+8(0.1^2)+28(0.1^4)+56(0.1^6) [ limited to four terms, as requested]
=1+0.08+0.0028+0.000056 (+0.00000070)
=1.082856 (approximately)
Answer:
Reduction
Step-by-step explanation:
Answer:
a=1 or a=5/6
Step-by-step explanation:
I'm going to attempt to factor 6a^2-a-5
a=6
b=-1
c=-5
Find two numbers that multiply to be a*c and add to be b.
a*c=-30 =-6(5)
b=-1 =-6+5
So replace -a with -6a+5a in the expression we started with
6a^2-6a+5a-5
now we factor by grouping
6a(a-1)+5(a-1)
(a-1)(6a-5)
Now let's solve the equation:
(a-1)(6a-5)=0
So a=1 or a=5/6
Answer:
2.5 is closer
Step-by-step explanation:
Had this on a worksheet for math.
