(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)
Let x = the width
then
2x = the length
:
The box dimensions: 2x by x by 4
Given the surface area:
2(2x*x) + 2(2x*4) + 2(x*4) = 220
:
4x^2 + 16x + 8x = 220
A quadratic equation:
4x^2 + 24x - 220 = 0
simplify, divide by 4
x^2 + 6x - 55 = 0
Factor
(x+11)(x-5) = 0
The positive solution is what we want here:
x = 5 ft is the width
then
2(5) = 10 ft is the length
:
Find the volume
10 * 5 * 4 = 200 cu/ft is the volume
Answer:
10 sides.
Step-by-step explanation:
Two same interior angles + 72 degrees = 360.
Thus, the interior angle of the polygon is 
.
The formula to find the interior angle of a polygon is 
Multiply both sides by n:
Expand:
Add 360 to both sides:
Subtract 144n from both sides:
Divide both sides by 36:
The value of f(-3) is 5.
In order to find this answer, we are going to input -3 in for x (this is what the notation f(-3) means).
f(x)=| x-2 |
f(-3)=| -3 -2 |
f(-3)=| -5 |
Now we have to take the absolute value.
f(-3) = 5
