Answer:
linear
Step-by-step explanation:
Step-by-step explanation:
a. The point estimate is the mean, 47 days.
b. The margin of error is the critical value times the standard error.
At 31 degrees of freedom and 98% confidence, t = 2.453.
The margin of error is therefore:
MoE = 2.453 × 10.2 / √32
MoE = 4.42
c. The confidence interval is:
CI = 47 ± 4.42
CI = (42.58, 51.42)
d. We can conclude with 98% confidence that the true mean is between 42.58 days and 51.42 days.
e. We can reduce the margin of error by either increasing the sample size, or using a lower confidence level.
Performing laplace transform of the equation.
sY(s) - y(0) + 6Y(s) = 1/(s-4)
(s+6)Y(s) - 2 = 1/(s-4)
Y(s) = 2/(s+6) + 1/(s-4)(s+6), by partial fraction decomposition
Y(s) = 2/(s+6) + 1/10 * (1/(s-4) + 1/(s+6))
Y(s) = 0.1/(s-4) + 2.1/(s+6)
Performing inverse laplace transform,
y(t) = 0.1e^4t + 2.1e^(-6t)
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I think it’s direct variation y= 12/x i’m note 100% sure tho
Answer:
9 cm
Step-by-step explanation:
Since the container is a cylinder of base diameter d₁ = 12 cm and thus radius r = 12/2 = 6 cm. The water height is 8 cm. The initial volume of water is thus V₁ = πr²h = π × 6² × 8 = 288π cm³.
The sphere of diameter d = 6 cm has radius r₁ = 6/2 = 3 cm. Its volume V₂ = 4πr³/3 = 4π × 3³/3 = 36π cm³
Since the sphere displaces it own volume of liquid, the new volume V = V₁ + V₂ = 288π cm³ + 36π cm³ = 324π cm³
This is the new volume of water in the cylinder. Since the water level rises by h' cm and V = πr²h'
h' = V/πr²
= 324π cm³/π(6)²
= 324π cm³/36π cm²
= 9 cm
So, the water level is 9 cm above the base
