BackIn Exercises 65–66, an object moves in simple harmonic motion described by the given equation, where t is measured in seconds and d in centimeters. In each exercise, find: a. the maximum displacement b. the frequency c. the time required for one cycle. d = 20 cos π/4 t
In each figure, there are two similar triangles. Find the unknown measurement. Give approximations to the nearest tenth.
In Exercises 67–68, an object is attached to a coiled spring. In Exercise 67, the object is pulled down (negative direction from the rest position) and then released. In Exercise 68, the object is propelled downward from its rest position. Write an equation for the distance of the object from its rest position after t seconds.
Solve each problem. Solar Eclipse on Earth The sun has a diameter of about 865,000 mi with a maximum distance from Earth's surface of about 94,500,000 mi. The moon has a smaller diameter of 2159 mi. For a total solar eclipse to occur, the moon must pass between Earth and the sun. The moon must also be close enough to Earth for the moon's umbra (shadow) to reach the surface of Earth. (Data from Karttunen, H., P. Kröger, H. Oja, M. Putannen, and K. Donners, Editors, Fundamental Astronomy, Fourth Edition, Springer-Verlag.) a. Calculate the maximum distance, to the nearest thousand miles, that the moon can be from Earth and still have a total solar eclipse occur. (Hint: Use similar triangles.)
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 30°
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 45°
Find the measure of each marked angle. See Example 2.
Find the measure of each marked angle. See Example 2.
Find the measure of each marked angle. See Example 2.
Find the measure of each marked angle. See Example 2 supplementary angles with measures 10𝓍 + 7 and 7𝓍 + 3 degrees
Find the measure of each marked angle. See Example 2 complementary angles with measures 9𝓍 + 6 and 3𝓍 degrees
Find the measure of each marked angle. See Example 2 complementary angles with measures 3𝓍 ― 5 and 6𝓍 ― 40 degrees
Find the measure of (a) the complement and (b) the supplement of an angle with the given measure. See Examples 1 and 3. 10°