Step-by-step explanation:
Using similar triangles, the height and width of the water is proportional to the height and width of the trough.
w / h = 5 / 1
w = 5h
The volume of the water is:
V = AL
V = (½ wh) (14)
V = 7wh
Substituting:
V = 7(5h)h
V = 35h²
Take derivative with respect to time:
dV/dt = 70h dh/dt
Given that dV/dt = 15 and h = ⅓:
15 = 70 (⅓) dh/dt
dh/dt = 9/14
dh/dt ≈ 0.643 ft/min
A. More reasonable is 5 because the 4 is closest to the lowest number, being 5.
B. About 10 times more
Answer:
cos x = 30°
Step-by-step explanation:
2 cos x = √3
cos x = √3/2
<em><u>cos x = 30°</u></em>
This is deceptively simple: there are only three terms, one is a constant (1) and two are coefficients of q (4q, -2q). To simplify the like terms, just simplify the terms containing q.
Answer:
59.4 times greater to the nearest tenth.
Step-by-step explanation:
5,028,000,000,000,000,000,000,000
= 5.028 * 10^24
So the required ratio = 5.028 * 10^24 / 8.46 * 10^22
= 0.594326 * 10^2
= 5.94326 * 10
= 59.4326.
