It would be 67 because its the same decrease as the other.
Here L = W, but H can be different.
The sum L+H+W must be less than or equal to 192 cm.
We can solve L + H + W = 192 for H: H = 192 - W - L. Remembering that W = L, the formula for H becomes 192 - 2W.
The formula for volume would be V = L*W*H.
This becomes V = W*W*H, or V = W^2*(192-2W)
Multiplying this out: V = w^2*192 - 2W^3
Two ways of determining W:
1) graph V = 192W^2 - 2W^3 and determine the value of W at which V is at a max with the constraint W + L + H is equal to or smaller than 192.
2) Differentiate V with respect to W and set the result equal to zero:
384W - 6W^2 = 0. Solving for W: W(384 - 6W) = 0.
W = 0 is trivial, so just solve 384 - 6W = 0 for W: 6W = 384, and W = 64.
The width is 64 cm, the length is 64 cm also, and the height is (192-2W) cm, or 64 cm.
These dimensions produce the max volume.
Answer:
We conclude that all the points of the table satisfy the equation y = x²
Hence, the option containing the equation y = x² is true.
The graph of y = x² is also attached below.
Step-by-step explanation:
Given the table
x y
-2 4
-1 1
0 0
1 1
2 4
Let us substitute the x-values of the table in the equation
y = x²
plun in x = -2
y = (-2)² = 4
so the point (2, 4) lies on the graph of y = x²
y = x²
plun in x = -1
y = (-1)² = 1
so the point (-1, 1) lies on the graph of y = x²
y = x²
plun in x = 0
y = (0)² = 0
so the point (0, 0) lies on the graph of y = x²
y = x²
plun in x = 1
y = (1)² = 1
so the point (1, 1) lies on the graph of y = x²
y = x²
plun in x = 2
y = (2)² = 4
so the point (2, 4) lies on the graph of y = x²
Therefore, we conclude from the above calculations that all the points of the table satisfy the equation y = x²
Hence, the option containing the equation y = x² is true.
The graph of y = x² is also attached below.
Step-by-step explanation:
a) i) original cuboid = 3×5×2 = 30 cm³......(i)
ii) ratio : 3×2 = 6cm (width), 5×2 = 10 cm (length),
2×2 = 4 cm (height).
enlarged cuboid = 6×10×4 = 240 cm³....(ii)
b) ratio = 240cm³/30cm³ = 8:1.
hope this helps you.