X^3 + 5^3
(x+5)x(x^2-X x 5+5^2)
(x+5)x(x^2 -5x+5^2)
(x+5)x(x^2 -5x+25)
(x+5) x (x^2 -5x+25)
Answer:
<u>Sum of the 8 terms = 69.19</u>
Step-by-step explanation:
The sum of the geometric series is S
Where: a is the first term
n is the number of terms
r is the constant ratio.
For the giving geometric series: 120 - 80 + 160/3 - 320/9 + ...
a = 120 , n = 8
r = -80/120 = -2/3
∴ 
Then the area of the top and bottom are each x^2.
<span>Then the height of the box is 40/x^2. </span>
<span>Then each side of the box is 40/x square feet. </span>
<span>Then the area of all four sides is 160/x square feet. </span>
<span>Then the total cost is represented by: </span>
<span>0.30x^2 + 0.05 (160/x) + 0.20x^2 </span>
<span>Expand the middle term and combine x^2 terms: </span>
<span>0.50x^2 + 8/x </span>
<span>Rewrite for easy differentiation: </span>
<span>0.50x^2 + 8x^-1 </span>
<span>Take the derivative: </span>
<span>x - 8x^-2 </span>
<span>Set the derivative to zero: </span>
<span>x - (8/x^2) = 0 </span>
<span>Multiply by x^2 </span>
<span>x^3 - 8 = 0 </span>
<span>Add 8: </span>
<span>x^3 = 8 </span>
<span>Take the cube root: </span>
<span>x = 2 feet </span>
<span>So the height is 40/4 = 10 feet </span>
<span>So the dimensions with minimum cost are: </span>
<span>2 x 2 x 10 feet.</span>
Answer:
C. 15
Step-by-step explanation:
Absolute value is just how far away the number is on the number line and is always positive.
