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The resonant frequency of a vibrating shaft is given by: f =1/2π 2√k/l where K is the stiffness of the shaft and I is the moment of inertia of the shaft. Use the binomial theorem to determine the approximate percentage error in determining the frequency using the measured values of K and I when the measured value of K is 5% larger and the measured value of I is 3% smaller.
f(x)=2x^2+x and g(x)=x-2 find f(g(x))
Given Vin (t) = sin (wt) and Vin = Vc + Vr (out). Use laplace transform to show that Vout = CRw * cos (wt) / ( (C^2 * R^2 * w^2) + 1 ) + (C^2 * R^2 * w^2) * sin (wt) / ( (C^2 * R^2 * w^2) + 1 ) - ( (CRw * e^-t/CR) / ( (C^2 * R^2 * w^2 ) +1 )
3. If f(x) = 2x + 4 and g(x) = - 3. Given that h(x) = g(x) – f(x). Find h(x).
Suppose 4112 adults were asked if they were in favor of a proposition, and 6% were in favor. What is the 95% interval and margin of error for the percent of adults who are in favor of the proposition?
show each and every step

1. Kenya Multi-Products (kMP) Ltd. is planning on producing and selling three products: A, B, C. KMP sales manager estimates that the three products will sell in a mix such that 3 units of product B and 5 units of product C will be sold for each 2 units sold of product A. the Total fixed costs are estimated at Ksh. 3.7 million. The total contributions of product A,B, and C are (85-50)x1, (80-40)x2 and (95-67)x3, where x1, x2, and x3 are units of A, B, and C produced and sold respectively.
determine the number of units of each product that KMP should produce and sell to break-even
a worker earns $6 per hour for the first 40 hours a weeks he works and $9 per hour for any extra hours. assuming that he works at least 40 hours, the total hours worked per week and then simplify?
what is the linear equation of the graph with the slope of 5 and the line passes through the coordination (8;11)
with a mean mass of 60 g and a standard deviation of 4g. four male frogs are chosen at random. find the probability that their mean mass is less than 55g
find the linear equations and draw its line graph using the following information; slope is 4 and the line passes through thation point (8;11)
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