The correct answer is D.
The symbol you are looking at is sigma, which means sum of all. Because the number on the bottom is 1 and the top is 6, these are the start and end numbers for our n value. Therefore, it means to add together all of the values of your expression (n -3), for all of the values with n equaling between 1 and 6. So let's plug in all of the numbers for n they ask for and see what we have.
1
1 - 3 = -2
2
2 - 3 = -1
3
3 - 3 = 0
4
4 - 3 = 1
5
5 - 3 = 2
6
6 - 3 = 3
Now, when we add all of these numbers up, we look for the answer.
-2 + -1 + 0 + 1 + 2 + 3 = 3
This is the answer we see in D
If the length, breadth and height of the box is denoted by a, b and h respectively, then V=a×b×h =32, and so h=32/ab. Now we have to maximize the surface area (lateral and the bottom) A = (2ah+2bh)+ab =2h(a+b)+ab = [64(a+b)/ab]+ab =64[(1/b)+(1/a)]+ab.
We treat A as a function of the variables and b and equating its partial derivatives with respect to a and b to 0. This gives {-64/(a^2)}+b=0, which means b=64/a^2. Since A(a,b) is symmetric in a and b, partial differentiation with respect to b gives a=64/b^2, ==>a=64[(a^2)/64}^2 =(a^4)/64. From this we get a=0 or a^3=64, which has the only real solution a=4. From the above relations or by symmetry, we get b=0 or b=4. For a=0 or b=0, the value of V is 0 and so are inadmissible. For a=4=b, we get h=32/ab =32/16 = 2.
Therefore the box has length and breadth as 4 ft each and a height of 2 ft.
Answer:
-2
Step-by-step explanation:
0 + -2 = -2
Answer:
yes
Step-by-step explanation:
