Answer:
x = 10 - 10sqrt(3)/3
Approximately 4.2265 cm
Volume = 1539.6 cm³
Step-by-step explanation:
Let the height be x
V = (20 - 2x)(40 - 2x)x
V = (800 - 80x - 40x + 4x²)x
V = 4x³ - 120x² + 800x
dV/dx= 12x² - 240x + 800 = 0
3x² - 60x + 200 = 0
x = [60 +/- sqrt(60² - 4(3)(200))]/6
x = [30 +/- 10sqrt(3)]/3
x = 10 +/- 10sqrt(3)/3
Approximately,
15.7735 and 4.2265
d²V/dx² = 24x - 240
For max, d²V/dx² < 0
So, x = 4.2265
V = (20 - 2x)(40 - 2x)x
Plug in x = 10 - 10sqrt(3)/3
V = 1539.600718
Answer: 74.6
we draw a right triangle ABC, have: ∠ABC = 90°, AB = 20 and ∠BAC = 75°, the height of the building is BC
we also have: tan 75° = BC/AB = BC/20
=> BC = tan 75°. 20 = 40 + 20√3 ≈ 74.6
Step-by-step explanation:
Since there are decimals you could round the decimals to the nearest tenth.
Answer:
Graph 1.
Step-by-step explanation:
The graph of f(x) will be compressed by a factor 4 and the vertex will be 4 units up from the origin.
