Search
Show that if x is a real number, then x − 1 < ⌊x⌋ ≤ x ≤
⌈x⌉ < x + 1.
Show that if x is a real number, then ⌈x⌉ − ⌊x⌋ = 1 if x is
not an integer and ⌈x⌉ − ⌊x⌋ = 0 if x is an integer.
A water bottle company produces bottles with a net volume 400ml each. It is known that the standard deviation of the volume is 12ml. A sample of 50 bottles is tested.
If the sample yields mean volume of 420ml, construct a hypothesis test at the \alpha =0.01 level of significance for the null hypotheses H_(0):\mu =400ml against the alternative hypothesis H_(A):\mu !=400ml. State your conclusion and give a reason for your answer.
Jenny is planning to deposit 17,000.00 pesos Quezon Metropolitan Bank is offering 7.5% compounded semi-annually for 5 years while Quezon Premier Bank is offering 7% compounded monthly for 5 years. Wich bank should she deposit her money? Justify you answer by computing and comparing the maturity value for each bank.
1. Marinel received 1,450,500.00 pesos as her inheritance from her parents. She deposited the said amount in a time a deposit with 1% simple interest rate per annum, how much money will be accumulated after 7years?
A new car costs ₱450.000.00. This value subsides by 10% each year.
A 16 lb weight is suspended from a spring having spring constant 5 lbft. Assume that an external force given by 24 sin (10t) and a damping force with damping constant 4, are acting on the spring Initially the weight is at rest at its equilibrium position. Find the position of the weight at any time. Find the steady state solution. Find the amplitude, period and frequency of the steady state solution. Determine the velocity of the weight at any time
x^ 2 y^ " - 2xy'-4y=x^ 2 +2 log x
Determine the critical numbers of the given function and classify each critical point
as a relative maximum, a relative minimum, or neither.
ff(tt) = tt2
tt2 + tt − 2 .
TISSUE GROWTH Suppose a particular tissue culture has area AA(tt) at time tt and a
potential maximum area MM. Based on properties of cell division, it is reasonable to assume that
the area AA grows at a rate jointly proportional to �AA(tt) and MM − AA(tt); that is
dddd
dddd = kk�AA(tt) [MM − AA(tt)]
where kk is a positive constant.
a. Let RR(tt) = AA′
(tt) be the rate of tissue growth. Show that RR′
(tt) = 0 when AA(tt) = MM/3.
b. Is the rate of tissue growth greatest or least when AA(tt) = MM/3? [Hint: Use the first
derivative test or second derivative test.]
c. Based on the given information and what you discovered in part (a), what can you say
about the graph of AA(tt)?
