The answer it 1. is A.
The answer to 2. is B.
Answer:
8 < x < 22
Step-by-step explanation:
If x is the third side , then
difference of 2 sides < x < sum of 2 sides , that is
15 - 7 < x < 15 + 7
8 < x < 22
which means there is some integer
for which
.
Because
and
, there are integers
such that
and
, and
We have
, which means there are four possible choices of
:
1, 42
2, 21
3, 14
6, 7
which is to say there are also four corresponding choices for
:
9, 378
18, 189
27, 126
54, 63
whose sums are:
387
207
153
117
So the least possible value of
is 117.
Let x =lenght, y = width, and z =height
<span>The volume of the box is equal to V = xyz </span>
<span>Subject to the surface area </span>
<span>S = 2xy + 2xz + 2yz = 64 </span>
<span>= 2(xy + xz + yz) </span>
<span>= 2[xy + x(64/xy) + y(64/xy)] </span>
<span>S(x,y)= 2(xy + 64/y + 64/x) </span>
<span>Then </span>
<span>Mx(x, y) = y = 64/x^2 </span>
<span>My(x, y) = x = 64/y^2 </span>
<span>y^2 = 64/x </span>
<span>(64/x^2)^2 = 64 </span>
<span>4096/x^4 = 64/x </span>
<span>x^3 = 4096/64 </span>
<span>x^3 = 64 </span>
<span>x = 4 </span>
<span>y = 64/x^2 </span>
<span>y = 4 </span>
<span>z= 64/yx </span>
<span>z= 64/16 </span>
<span>z = 4 </span>
<span>Therefor the dimensions are cube 4.</span>
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