Answer: The required inverse transform of the given function is
![f(t)=8t^2e^{4t}.](https://tex.z-dn.net/?f=f%28t%29%3D8t%5E2e%5E%7B4t%7D.)
Step-by-step explanation: We are given to find the inverse Laplace transform, f(t), of the following function :
![F(s)=\dfrac{16}{(s-4)^3}.](https://tex.z-dn.net/?f=F%28s%29%3D%5Cdfrac%7B16%7D%7B%28s-4%29%5E3%7D.)
We have the following Laplace formula :
![L\{t^ne^{at}\}=\dfrac{n!}{(s-a)^{n+1}}\\\\\\\Rightarrow L^{-1}\{\dfrac{1}{(s-a)^{n+1}}\}=\dfrac{t^ne^{at}}{n!}.](https://tex.z-dn.net/?f=L%5C%7Bt%5Ene%5E%7Bat%7D%5C%7D%3D%5Cdfrac%7Bn%21%7D%7B%28s-a%29%5E%7Bn%2B1%7D%7D%5C%5C%5C%5C%5C%5C%5CRightarrow%20L%5E%7B-1%7D%5C%7B%5Cdfrac%7B1%7D%7B%28s-a%29%5E%7Bn%2B1%7D%7D%5C%7D%3D%5Cdfrac%7Bt%5Ene%5E%7Bat%7D%7D%7Bn%21%7D.)
Therefore, we get
![f(t)\\\\=L^{-1}\{\dfrac{16}{(s-4)^3}\}\\\\\\=16\times\dfrac{t^{3-1e^{4t}}}{(3-1)!}\\\\\\=\dfrac{16}{2}t^2e^{4t}\\\\\\=8t^2e^{4t}.](https://tex.z-dn.net/?f=f%28t%29%5C%5C%5C%5C%3DL%5E%7B-1%7D%5C%7B%5Cdfrac%7B16%7D%7B%28s-4%29%5E3%7D%5C%7D%5C%5C%5C%5C%5C%5C%3D16%5Ctimes%5Cdfrac%7Bt%5E%7B3-1e%5E%7B4t%7D%7D%7D%7B%283-1%29%21%7D%5C%5C%5C%5C%5C%5C%3D%5Cdfrac%7B16%7D%7B2%7Dt%5E2e%5E%7B4t%7D%5C%5C%5C%5C%5C%5C%3D8t%5E2e%5E%7B4t%7D.)
Thus, the required inverse transform of the given function is
![f(t)=8t^2e^{4t}.](https://tex.z-dn.net/?f=f%28t%29%3D8t%5E2e%5E%7B4t%7D.)
Answer: First option.
Step-by-step explanation:
To solve for "h" from the given the equation
, you need to:
Apply the Subtraction property of equality and subtract
to both sides of the equation.
Then you need to apply the Division property of equality and divide both sides of the equation by
.
Then:
![S-2\pi r^2=2\pi rh+2\pi r^2-2\pi r^2\\\\S-2\pi r^2=2\pi rh\\\\\frac{S}{2\pi r}-\frac{2\pi r^2}{2\pi r}=\frac{2\pi rh}{2\pi r}\\\\\frac{S}{2\pi r}-r=h](https://tex.z-dn.net/?f=S-2%5Cpi%20r%5E2%3D2%5Cpi%20rh%2B2%5Cpi%20r%5E2-2%5Cpi%20r%5E2%5C%5C%5C%5CS-2%5Cpi%20r%5E2%3D2%5Cpi%20rh%5C%5C%5C%5C%5Cfrac%7BS%7D%7B2%5Cpi%20r%7D-%5Cfrac%7B2%5Cpi%20r%5E2%7D%7B2%5Cpi%20r%7D%3D%5Cfrac%7B2%5Cpi%20rh%7D%7B2%5Cpi%20r%7D%5C%5C%5C%5C%5Cfrac%7BS%7D%7B2%5Cpi%20r%7D-r%3Dh)
Answer:
x < -8
Step-by-step explanation:
Step 1: Translate
Product = multiplication = -8(x)
More than = >
64 = 64
Step 2: Write out inequality
-8x > 64
Step 3: Solve
x < -8
Answer:
Probability that deliberation will last between 12 and 15 hours is 0.1725.
Step-by-step explanation:
We are given that a recent study showed that the length of time that juries deliberate on a verdict for civil trials is normally distributed with a mean equal to 12.56 hours with a standard deviation of 6.7 hours.
<em>Let X = length of time that juries deliberate on a verdict for civil trials</em>
So, X ~ N(
)
The z score probability distribution is given by;
Z =
~ N(0,1)
where,
= mean time = 12.56 hours
= standard deviation = 6.7 hours
So, Probability that deliberation will last between 12 and 15 hours is given by = P(12 hours < X < 15 hours) = P(X < 15) - P(X
12)
P(X < 15) = P(
<
) = P(Z < 0.36) = 0.64058
P(X
12) = P(
) = P(Z
-0.08) = 1 - P(Z < 0.08)
= 1 - 0.53188 = 0.46812
<em>Therefore, P(12 hours < X < 15 hours) = 0.64058 - 0.46812 = 0.1725</em>
Hence, probability that deliberation will last between 12 and 15 hours is 0.1725.
inside angles need to equal 180
180-75-40 = 65
now the question mark and 65 need to equal 180
180-65 = 115
answer is 115