Answer:
15,872 mm³
Step-by-step explanation:
given:
A small square pyramid of height 6 cm was removed from the top of a large square pyramid of height 12cm forming the solid shown.
Find:
the exact volume of the solid
solution:
volume of square base pyramid = (base area)² * h/3
where total h = 12 cm
height of top pyramid (ht)= 6 cm
height of bottom pyramid (hb) = 6 cm
bottom volume = total volume - the volume on top
so,
total volume = 1/3 (base area)² h
= 1/3 (8*8)² * 12
= 16,384 mm³
volume on top = 1/3 (top base area)² h
= 1/3 (4*4)² * 6
= 512 mm³
finally: get the bottom volume:
bottom volume = total volume - the volume on top
bot. vol = 16,384 mm³ - 512 mm³
= 15,872 mm³
therefore,
the volume of the cut pyramid base = 15,872 mm³
(a) Using the table, give the values fo rthe inverse
1) original table of values:
x 1 2 3 4 5
f(x) 0 1 1 5 3
2) The inverse of the function is obtained by exchanging x and f(x), this is:
( x, f(x) ) → ( f(x), x)
3) So, the table of values of the inverse of the given function is:
x 0 1 1 5 3
f⁻¹ (x) 0 1 2 3 4
(b) Is the inverse a function?
No, the inverse is not a function, since the table of the inverse shows that the x -value 1 has two different images.
This ambigüity is opposite to the definition of a function, which requires that any input value has only one output. For that reason, the inverse is not a function. You cannot tell whether the image of 1 is 1 or 2, because both are images of the same value.
