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Gravity
Terms in this set (6)
Law of Sines Formula
Angle: sinA/a = sinB/b = sinC/c
Side: a/sinA = b/sinB= c/sinC
Law of Cosines
a²=b²+c²-2bcCosA
Pythagorean Theorem
a²+b²=c²
a²=c²-b²
Law of Cosines
Cos A= (b²+c²-a²)/2bc
Area of an Oblique Triangle
Area = (1/2)(bc)(Sin A)
Heron's Formula
A=√s(s-a)(s-b)(s-c)
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Verified questions
TRIGONOMETRY
A coin is dropped from the top of a 120-foot building. The height of displacement s (in feet) of the coin can be modeled by the position function $s(t)=-16 t^{2}+120$, where t is the time in seconds since it was dropped. (a) Find a formula for the instantaneous rate of change of the coin. (b) Find the average rate of change of the coin after the first two seconds of free fall. Explain your results. (c) Velocity is given by the derivative of the position function. Find the velocity of the coin as it impacts the ground. (d) Find the time when the coin's velocity is - 70 feet per second. (e) Use a graphing utility to graph the model and verify your results for parts (a)-(d).
TRIGONOMETRY
The laser that read a DVD uses constant linear velocity. This means that the laser will read the DVD at the same rate no matter where on the DVD the formation is stored. To maintain the constant velocity, the DVD player changes the rate that the DVD spins. When information is stored at the outermost track, a DVD spins at a rate of 200RPM (rotation per minute). If the innermost track is 2 cm from the center and the outermost track is 5.25 cm from the center, how many RPMs must the DVD spin at to maintain constant linear velocity when the laser is on the innermost track? Complete the parts below to help you answer the question. a. What does it mean to have constant linear velocity? Express your response in terms of distance and time. b. Will the DVD spin faster when the laser is on the inside track or on the outside track? Why? c. How far does a point on the outside track travel in one rotation? That is, how many centimeters per rotation are there? d. What is the constant velocity, in cm/min, of a point on the outside track of the DVD? e. How far does a point on the inside track travel in one rotation? That is, how many centimeters per rotation are there? f. How fast does the DVD need to spin when it is reading information from the inside track if it needs to maintain the same velocity you calculated in part (d)?
TRIGONOMETRY
Most days, Shane is frequently interrupted just after he puts his mid-morning cup of coffee into the microwave. By the time he remembers to remove it, it, it is usually cold (actually room temperature, $70^{\circ} F$). But Shane is very picky and will not drink coffee that is less than $160^{\circ} \mathrm{F}$. Since the interruptions are never consistent, Shane returns to the coffee cup at different times each day to find it undrinkable by his standards. He wonders just how long it takes the coffee to drop below his acceptable temperature. He decides to take some readings and analyze the results. His temperature readings are given in the table below. " $$ \begin{matrix}\text{Time (min)} & \text{0} & \text{2} & \text{4} & \text{5} & \text{6} & \text{8} & \text{10}\\\mathrm{Temp (^ \circ F)} & \mathrm{190^{\circ}} & \mathrm{185.5^{\circ}} & \mathrm{181.9^{\circ}} & \mathrm{180^{\circ}} & \mathrm{178.2^{\circ}} & \mathrm{174.3^{\circ}} & \mathrm{171^{\circ}}\\\end{matrix} $$ " a. Give your best estimate for how rapidly the coffee is cooling when t = 5 minutes. Be sure to include units in your answer. b. After carefully analyzing the data, Shane concludes that the function $c(t)=70+120(0.983)^{t}$ approximates the temperature of the coffee t minutes after it has been removed from the microwave. Using this function, calculate the rate that the coffee is cooling when t = 5 minutes. c. How long will it take for Shane's coffee to cool to $160^{\circ} \mathrm{F}$? How fast is the temperature changing at this time? d. Is the temperature of the coffee changing more quickly or more slowly over time? How do you know?
TRIGONOMETRY
rotate the axes to eliminate the xy-term in the equation. Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. $$ 7x^2-6√3xy+13y^2-64=0 $$
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