91Ó°ÊÓ

Write the standard form of the equation and the general form of the equation of each circle of radius \(r\) and center \((h, k)\). Graph each circle. $$ r=\frac{1}{2} ;(h, k)=\left(\frac{1}{2}, 0\right) $$

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. $$ y=3 x-9 $$

Plot each pair of points and determine the slope of the line containing the points. Graph the line. $$ (4,2) ;(-5,2) $$

write an equation that relates the quantities. The period of a pendulum is the time required for one oscillation; the pendulum is usually referred to as simple when the angle made to the vertical is less than \(5^{\circ} .\) The period \(T\) of a simple pendulum (in seconds) varies directly with the square root of its length \(l\) (in feet). The constant of proportionality is \(\frac{2 \pi}{\sqrt{32}}\)

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. $$ y=-x^{2}+4 $$

The velocity \(v\) of a falling object is directly proportional to the time \(t\) of the fall. If, after 2 seconds, the velocity of the object is 64 feet per second. what will its velocity be after 3 seconds?

The rate of vibration of a string under constant tension varies inversely with the length of the string. If a string is 48 inches long and vibrates 256 times per second, what is the length of a string that vibrates 576 times per second?

Find the intercepts and graph each equation by plotting points. Be sure to label the intercepts. $$ 5 x+2 y=10 $$

The cost \(C\) of roasted almonds varies directly with the number \(A\) of pounds of almonds purchased. If the cost is 23.75 when the number of pounds of roasted almonds purchased is \(5,\) find a linear equation that relates the cost \(C\) to the number \(A\) of pounds of almonds purchased. Then find the cost C when the number of pounds of almonds purchased is 3.5

Find the distance \(d\) between the points \(P_{1}\) and \(P_{2}\). $$ P_{1}=(1.2,2.3) ; \quad P_{2}=(-0.3,1.1) $$