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Round answers to the nearest unit. You may use 3.14 as an approximate value of \(\pi .\) If you have a \(\pi\) button on your calculator, use that value and then round your final answer. A satellite in a nearly circular orbit is \(2000 \mathrm{km}\) above Earth's surface. The radius of Earth is approximately \(6400 \mathrm{km}\). If the satellite completes its orbit in 12 hours, calculate the speed of the satellite in kilometers per hour.

Round answers to the nearest unit. You may use 3.14 as an approximate value of \(\pi .\) If you have a \(\pi\) button on your calculator, use that value and then round your final answer. Here is a tiring problem. The diameter of a car tire is approximately \(60 \mathrm{cm}(0.6 \mathrm{m}) .\) The warranty is good for \(70,000 \mathrm{km}\). About how many revolutions will the tire make before the warranty is up? More than a million? A billion? ( \(1 \mathrm{km}=1000 \mathrm{m}\) ) (PICTURE CANT COPY)

Developing Proof In Exercises \(1-4,\) the four conjectures are consequences of the Inscribed Angle Conjecture. Prove each conjecture by writing a paragraph proof or a flowchart proof. Use reasoning strategies, such as think backwards, apply previous conjectures and definitions, and break a problem into parts to develop your proofs. The opposite angles of a cyclic quadrilateral are supplementary. Given: Circle \(O\) with inscribed quadrilateral \(L I C Y\) Show: \(\angle L\) and \(\angle C\) are supplementary (GRAPH CANT COPY)

Round answers to the nearest unit. You may use 3.14 as an approximate value of \(\pi .\) If you have a \(\pi\) button on your calculator, use that value and then round your final answer. If the front tire of this motorcycle has a diameter of \(50 \mathrm{cm}(0.5 \mathrm{m}),\) how many revolutions will it make if it is pushed \(1 \mathrm{km}\) to the nearest gas station? In other words, how many circumferences of the circle are there in 1000 meters? (PICTURE CANT COPY)

Leave your answer in terms of \(\pi\). If a circle has a circumference of \(46 \pi \mathrm{m}\) what is its diameter?

If a trapezoid is inscribed within a circle, then the trapezoid is isosceles. Given: Circle \(R\) with inscribed trapezoid \(G A T E\) Show: \(G A T E\) is an isosceles trapezoid (GRAPH CANT COPY)

Astronaut Polly Hedra circles Earth every 90 minutes in a path above the equator. If the diameter of Earth is approximately 8000 miles, what distance along the equator will she pass directly over while eating a quick 15 -minute lunch?

Angular velocity is a measure of the rate at which an object revolves around an axis, and can be expressed in degrees per second. Suppose a carousel horse completes a revolution in 20 seconds. What is its angular velocity? Would another horse on the carousel have a different angular velocity? Why or why not?

Tangential velocity is a measure of the distance an object travels along a circular path in a given amount of time. Like speed, it can be expressed in meters per second. Suppose two carousel horses complete a revolution in 20 seconds. The horses are \(8 \mathrm{mand} 6 \mathrm{m}\) from the center of the carousel, respectively. What are the tangential velocities of the two horses? Round your answers to the nearest 0.1 \(\mathrm{m} / \mathrm{s}\). Explain why the horses have equal angular velocities but different tangential velocities.

Each year a growing tree adds a new ring to its cross section. Some years the ring is thicker than others. Why do you suppose this happens? Suppose the average thickness of growth rings in the Flintstones National Forest is \(0.5 \mathrm{cm} .\) About how old is "Old Fred," a famous tree in the forest, if its circumference measures \(766 \mathrm{cm} ?\) (IMAGE CAN'T COPY)