Answer:
32mm
Step-by-step explanation:
6 + 8 + 6 + 12 = 32mm
If the dimensions were all the same number ... the box was a cube ...
then each dimension would be (the cube root of 13,800) cm.
∛13,800 = 23.986... (rounded)
so the place to look is around 23 .
(22 x 23 x 24) = 12,144 <== too small; go up one integer
(23 x 24 x 25) = 13,800 <== Eureka !
The consecutive integers are 23, 24, and 25 .
Answer:
g(x) = x+1
Step-by-step explanation:
Informally, you can see that the function h(x) takes the root of a value that is 1 more than the value under the same radical in f(x). This suggests that adding 1 to x in f(x) will give you h(x). That is, ...
h(x) = f(x+1) = f(g(x))
so
g(x) = x+1
_____
More formally, you can apply the inverse of the function f(x) to the equation ...
h(x) = f(g(x))
f^-1(h(x)) = f^-1(f(g(x))) . . . inverse function applied
f^-1(h(x)) = g(x) . . . . . . . . . simplified
Now f^-1(x) can be found by solving for y in ...
x = f(y)
x = ∛(y+2) . . . . . . . . . definition of f(y)
x^3 = y+2 . . . . . . . . . cube both sides
x^3 -2 = y = f^-1(x) . . . subtract 2 from both sides
So, f^-1(h(x)) is ...
f^-1(h(x)) = g(x) = (∛(x+3))^3 -2 = x+3 -2
g(x) = x+1
Answer:
20 cm
Step-by-step explanation:
1. Multiply the actual depth my the scale factor of 1/15.
2. Multiply the resulting depth after multiply by the scale factor by the conversion factor of meters to centimeters.
