Search & Filtering
a school administrator claims that less than 50% of the students of the school are dissatisfied by the community cafeteria service. Test this claim by using sample data obtained from a survey of 500 students of the school where 54% indicated their dissatisfaction of the community cafeteria service. use a 0.05.
Numbers and operation
Prove that
x<log(1/1-x)< x/1-x, 0<x<1
Find the equation of the normal to the parabola y 2 +4x = 0 at the point where the line y = x+c touches it.
Consider the equation xyz = 4x2 +y2 −z2. Use the Implicit Function Theorem to show that the given equation has a smooth unique local solution of the form z = g(x,y) about the point (2,0,4). Then find the local linearization of g about the point (2,0).
A function is defined by the polynomial 𝑓(𝑥) = 3𝑥 4 − 4𝑥 3 − 12𝑥 2 + 8. Find and classify all the stationary points of f(x)
Calculate the area of the region inside the cardioid r = a(1 + sin Ɵ) outside the r = a sinƟ circle and above the polar ray. Show by drawing.
In “x” years from now, one investment plan will be generating profit at the rate of R1(x) = 50 + x2 pesos per year, while a second plan will be generating profit at the rate R2(x) = 200 + 5x pesos per year. For how many years will the second plan be more profitable one? Compute also the net excess profit if the second plan would be used instead of the first.
Determine the location of all critical points and determine their nature for the function. f(x)=ln(x^2 + 1) - x
a firm estimates that it can sell q units of its product with an advertising expenditure of x thousand dollars when Q=Q(x) = -X2 +600x +25 i) over whta level of advertising expenditure is the number of units of products sold is incresing ? ii) over what level of advertising expenditure is the numbers of units of product sold decreasing?
