The center of a clock is $$(0,0)$$ in a coordinate system, and the hour hand is 8 inches long. It is 10:30 p.m. Which of the following are true of the end of the hour hand? Select all that apply.

Its coordinates are about $$(\text-5.7,5.7)$$

Its coordinates are $$(8\cos(\frac{3\pi}{4}),8\sin(\frac{3\pi}{4}))$$

Its coordinates are about $$(5.7,\text-5.7)$$

Its coordinates are about $$(\text-5.7,\text-5.7)$$

Its coordinates are $$(8\sin(\frac{3\pi}{4}),8\cos(\frac{3\pi}{4}))$$

Here is the initial position of a bike wheel before it starts to move. The vertical position, in inches, of $$P$$ is given by $$y = 10\boldcdot \sin\left(\frac{\pi}{2} + 6\pi s\right) + 10$$ , where $$s$$ is the number of seconds since the wheel began to move. Select all the true statements.

The wheel makes 3 revolutions per second.

After $$\frac{1}{4}$$ of a second, the point $$P$$ will be in the position marked $$Q$$ .

The radius of the wheel is 10 inches.

The wheel makes one revolution every 3 seconds.

After $$\frac{3}{4}$$ of a second, the point $$P$$ will be in the position marked $$Q$$ .

Algebra 2 | Unit 6 | Lesson 19: Beyond Circles | Practice Problems

Authored by Illustrative Mathematics

Mathematics

6th Grade

Algebra 2 | Unit 6 | Lesson 19: Beyond Circles | Practice Problems

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