Let the side of the square base be x, and the height of the box be h.
<span>The material of the base is x^2, and the material of the four sides is 4xh. </span>
<span>4000 = hx^2 </span>
<span>h = 4000/x^2 </span>
<span>The total material is </span>
<span>M = x^2 + 4x(4000/x^2) = x^2 + 16000/x </span>
<span>Take the first derivative of M and set equal to 0. </span>
<span>M' = 2x - 16000/x^2 = 0 </span>
<span>Multiply by x^2: </span>
<span>2x^3 = 16000 </span>
<span>x^3 = 8000 </span>
<span>x = 20; h = 10; M = 1200</span>
Its a rate with 1as the second term
The answer is 30°.
Rule: All three sides must add up to 180°.
Since A=60 and the side vertical to the angle which is 90° then side C would be C=90° and that adds up to 150°, so you can conclude that angle B is 30°.
I hope I helped!
Answer:
9
Step-by-step explanation:
The possible dimensions of the larger piece of paper that could give us 1000 square inches for area are:
1×1000; 2×500; 4×250; 5×200; 8×125; 10×100; 20×50; 25×40
We want to use dimensions that will allow us to cut 8 1/2 by 11 sheets. This means that the smallest dimension needs to be larger than 8 1/2 inches; this leaves us with
10×100; 20×50; 25×40
For the first one, 10×100, we can have 1 row across the 10 inch dimension, and 100/11 = 9 columns across the other dimension. This gives us 1×9 = 9 sheets.
For the 20×50, we can have 2 rows across the 10 inch dimension and 50/11 = 4 columns; this gives us 2×4 = 8 sheets.
For the 25×40, we can have 2 rows across the 25 inch dimension (we lack half an inch of having 3) and 40/11 = 3 columns; this gives us 2×3 = 6 sheets.
The largest number of sheets was 9.
