(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:
Step-by-step explanation:
Split the trapezoid as pictured below
Find its height and the upper base, then find the area of the trapezoid.
There are 3 pieces, two of them are 45°×45° and 30°×60°×90° triangles
- The ratio of sides of a 30°×60°×90° triangle is 1 : √3 : 2
- The legs of a 45x45 triangle are equal
<u>The above mentioned properties give us:</u>
- h = 16/2 = 8 m
- b = 8√3 ≈ 13.85 m
- a = h = 8 m
<u>Now find the area:</u>
- A = 1/2( 13 + 8 + 13.85 + 13)*8 = 191.4 m²
Correct choice is B
Answer:
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