While painting the interior of a large house, Gene is going to transfer some paint in a large 5 gallon container to a smaller bu
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Answer:
The diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Step-by-step explanation:
Dimensions of the rectangle
Height = 5cm
Rate of base = 3/2 cm/min
Area = 60cm^2
We know the area of a rectangle of given by = base* Height
b*h = 60
b*5 = 60
b = 12cm
Applying Pythagoras theorem while drawing a diagonal to the rectangle
so our diagonal will be 13cm
Upon differentiating the area of the rectangle we get
b*h = A=60cm^2
using the chain rule of differentiation
h*db/dt + b*dh/dt = 0
b*dh/dt = -h*db/dt
12*dh/dt = -5*3/2
dh/dt = -5/8 cm//min
so the height of the rectangle is decreasing at the rate of -5/8cm/min
now we have all the measurements we need
b = 12 , db/dt = 3/2cm/min
h = 5 , dh/dt = -5/8 cm/min
Upon differentiating we get
2b*db/dt + 2h*dh/dt = 2D*dD/dt
b*db/dt + h*dh/dt = D*dD/dt
12*3/2 + 5*(-5/8) = 13*dD/dt
18 -25/8 = 13*dD/dt
= 13*dD/dt
dD/dt =
Therefore the diagonal is increasing at the rate of 119/104cm/min of the given rectangle.
Answer:
The critical value of <em>z</em> for 99% confidence interval is 2.5760.
The 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).
Step-by-step explanation:
Let <em>X</em> = number of lightning strikes on each day.
A random sample of <em>n</em> = 23 days is selected to observe the number of lightning strikes on each day.
The random variable <em>X</em> has a sample mean of, and the population standard deviation,
.
The (1 - <em>α</em>)% confidence interval for population mean <em>μ</em> is:
Compute the critical value of <em>z</em> for 99% confidence interval is:
*Use a <em>z</em>-table.
The critical value of <em>z</em> for 99% confidence interval is 2.5760.
Compute the 99% confidence interval for population mean number of lightning strike as follows:
Thus, the 99% confidence interval for population mean number of lightning strike is (7.83 mn, 8.37 mn).
The 99% confidence interval for population mean number of lightning strike implies that the true mean number of lightning strikes lies in the interval (7.83 mn, 8.37 mn) with 0.99 probability.