Masses m 1 = 10 , m 2 = 3 , m 3 = 4 , and m are positioned on a weightless beam, with the fulcrum positioned at point 4 , as shown in the accompanying figure. (a) Suppose that m = 14 . Without computing the sum of the moments about 4 , determine whether the sum is positive, zero, or negative. Explain. (b) For what value of m is the beam in equilibrium?
Masses m 1 = 10 , m 2 = 3 , m 3 = 4 , and m are positioned on a weightless beam, with the fulcrum positioned at point 4 , as shown in the accompanying figure. (a) Suppose that m = 14 . Without computing the sum of the moments about 4 , determine whether the sum is positive, zero, or negative. Explain. (b) For what value of m is the beam in equilibrium?
Masses
m
1
=
10
,
m
2
=
3
,
m
3
=
4
,
and
m
are positioned on a weightless beam, with the fulcrum positioned at point
4
, as shown in the accompanying figure.
(a) Suppose that
m
=
14
. Without computing the sum of the moments about
4
, determine whether the sum is positive, zero, or negative. Explain.
(b) For what value of m is the beam in equilibrium?
After a great deal of experimentation, two college senior physics majors determined that when a bottle of French champagne is shaken several times, held upright, and uncorked,
its cork travels according to the function below, where s is its height (in feet) above the ground t seconds after being released.
s(t)=-16t² + 30t+3
a. How high will it go?
b. How long is it in the air?
+6x²+135x+1) (0≤x≤10). a) Find the number of units
The total profit P(x) (in thousands of dollars) from a sale of x thousand units of a new product is given by P(x) = In (-x²+6x² + 135x+
that should be sold in order to maximize the total profit. b) What is the maximum profit?
The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the
population in the year 2000 was 22600.
(a) Find a function that models the population t years after 2000 (t = 0 for 2000).
Your answer is P(t)
=
(b) Use the function from part (a) to estimate the fox population in the year 2008.
Your answer is (the answer should be an integer)
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