9514 1404 393
Answer:
5/9 m/min
Step-by-step explanation:
The depth of the water is 2/5 of the depth of the trough, so the width of the surface will be 2/5 of the width of the trough:
2/5 × 2 m = 4/5 m
Then the surface area of the water is ...
A = LW = (18 m)(4/5 m) = 14.4 m²
The rate of change of height multiplied by the area gives the rate of change of volume:
8 m³/min = (14.4 m²)(h')
h' = (8 m³/min)/(14.4 m²) = 5/9 m/min
Answer: A
Explanation:
(6x^2 - x + 8) - (x^2 + 2)
6x^2 - x + 8 - x^2 - 2
= 5x^2 - x + 6
Answer:
Factoring
Step-by-step explanation:
(x+4)² = 15
x² + 8x + 16 = 15
x² + 8x + 1 = 0
I hope this helps you :)
Answer:
311.41 degrees
Step-by-step explanation:
If 4 sin Ф = -3 and Ф is between 0 and 360 degrees, then we conclude that Ф must be either in Quadrant III or Quadrant IV (because the sine is negative).
Let's assume we're in Quadrant IV. Then sin Ф = opp / hyp = -3/4; that is, the opp side is negative and has length 3, and the hypo is positive 4.
According to the Pythagorean Theorem, (-3)^2 + x^2 = 4^2, or,
x^2 = 16 - 9 = 7.
Then x is either √7 or -√7.
To find the angle Ф, use the inverse sine function:
Ф = arcsin (-3/4). Using a calculator we get the angle -40.59 degrees, which corresponds to (360 degrees - 40.59 degrees), or 311.41 degrees. We can check this by finding the sine of 311.41 degrees; the result is -0.75, which matches "If 4sintheta = -3."
Answer:
17.11%
Step-by-step explanation:
since 43.2 months is the mean, and the standard deviation is 7.7 months
that means if we take the z score:
z=(36-43.2)/7.7
now that we know how many standard deviations you are away from the mean: -0.9351
using the zscore table you can find the proportion, or you can use the calculator if you have one that can do that.
you get 0.1711 which in percentages is 17.11%
