91Ó°ÊÓ

Poiseuille's Law According to Poiseuille's law, the resistance to flow of a blood vessel, \(R\), is directly proportional to the length, \(l\), and inversely proportional to the fourth power of the radius, \(r .\) If \(R=25\) when \(l=12\) and \(r=0.2,\) find \(R\) to the nearest hundredth as \(r\) increases to \(0.3,\) while \(l\) is unchanged.

Graph each polynomial function. Factor first if the expression is not in factored form. $$f(x)=3 x^{4}-7 x^{3}-6 x^{2}+12 x+8$$

Solve each problem. Sum and Product of Two Numbers Find two numbers whose sum is 20 and whose product is the maximum possible value. (Hint: Let \(x\) be one number. Then \(20-x\) is the other number. Form a quadratic function by multiplying them, and then find the maximum value of the function.

For each polynomial function, find all zeros and their multiplicities. $$f(x)=\left(2 x^{2}-7 x+3\right)^{3}(x-2-\sqrt{5})$$

Use synthetic division to decide whether the given number \(k\) is a zero of the given polynomial function. If it is not, give the value of \(f(k) .\) See Examples 2 and 3 . $$f(x)=2 x^{3}-3 x^{2}-5 x ; k=0$$

Solve each problem. Sum and Product of Two Numbers Find two numbers whose sum is 32 and whose product is the maximum possible value.

Solve each problem. Minimum cost Brigette Cole has a taco stand. She has found that her daily costs are approximated by $$ C(x)=x^{2}-40 x+610 $$ where \(C(x)\) is the cost, in dollars, to sell \(x\) units of tacos. Find the number of units of tacos she should sell to minimize her costs. What is the minimum cost?

Find a polynomial function \(f(x)\) of degree 3 with real coefficients that satisfies the given conditions. See Example 4. Zeros of \(-3,1,\) and \(4 ; f(2)=30\)

Work each problem.What happens to \(y\) if \(y\) varies inversely as \(x,\) and \(x\) is doubled?

Solve each problem. Maximum Number of Mosquitos The number of mosquitos, \(M(x),\) in millions, in a certain area of Florida depends on the June rainfall, \(x,\) in inches. The function $$ M(x)=10 x-x^{2} $$ models this phenomenon. Find the amount of rainfall that will maximize the number of mosquitos. What is the maximum number of mosquitos?