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>
Answer:
<h3>28 4/7 % ≈ 29%</h3>
Step-by-step explanation:
4 kg - weight of sugar
10 kg - mass of water
4kg + 10kg = 14kg - weight of the syrup
The sugar is 2/7 of the weight of the syrup.
Convert to the percentage:
<h3>Point Y is the midpoint of segment XZ. Then value of x is 20</h3>
<em><u>Solution:</u></em>
Given that,
<em><u>Point Y is the midpoint of segment XZ</u></em>
XY = 2(3x +1)
YZ = 5x + 22
To find: Value of x
Since, Point Y is the midpoint of segment XZ,
Therefore,
XY = YZ
2(3x + 1) = 5x + 22
6x + 2 = 5x + 22
6x - 5x = 22 - 2
<h3>x = 20</h3>
Thus, value of x is 20
<u>Answer</u>:
It takes 5 seconds for the sandbag to hit the ground
<u>Explanation</u>:
Given:
Height at which the sand bag is released from the hot air balloon
To find:
Time taken for the sandbag to hit the ground, t =?
Solution:
The initial height =s
Initially the height will be 0
Hence
the falling object model equation
Substituting the values we get,
Result:
Thus it takes 5 seconds for the sandbag to hit the ground
An easy way to do this is to do trial and error.
All possible places to put the bracket:
a) (25 - 8) - 2 = 19 But since BEDMAS goes from left to right with Addition and Subtraction, the equation is unaffected.
b) 25 - (8 - 2) = 19
25 - 6 = 19
Therefore b) is correct.
