Why do you think Neruda calls the "constancy that beats in your chest" (literally, his beloved's heartbeat) a "purer motion"? Interpret the remarkable visual image in line $11$.

Use a case $1$-case $2$ ratio box to solve this problem. Don's heart beats $225$ times in $3$ minutes. At that rate, how many times will his heart beat in $5$ minutes?

Starting with the identity $\sin ^2 \theta+\cos ^2 \theta=1$, derive the identity $1+\tan ^2 \theta=\sec ^2 \theta$.

"To tune your violin, you first tune the A string to the correct pitch of $440 \text{~Hz}$, and then you bow both it and an adjoining string simultaneously, all the while listening for beats. While bowing the A and E strings, you hear a beat frequency of $3.00 \text{~Hz}$ and note that the beat frequency increases as the tension on the E string are increased. (The E string is to be tuned to $660 \text{~Hz}$.) $(a)$ Why are beats produced by these two strings when bowed simultaneously?"

Verify the identity.

$$\arccos (-x) = \pi-\arccos x$$

Verify the identity. $\sin$ x $\csc$(-x) = -1

Determine whether the equality is an identity or an equation. If it is an identity, prove it. If it is an equation, solve it for $(0\leq x < 2\pi)$.

$$\sin x \cos x - 1 = \cos x - \sin x$$

A police siren contains two frequencies, producing a wavering sound (beats). Explain how the siren sound changes as a police car approaches, passes, and moves away from a pedestrian.

A lion's heart beats 12 times in 16 s. How many times does a lion's heart beat in 60 s?

$$F. \ 24 \\ G. \ 32 \\ H. \ 45 \\ J. \ 192$$

$-8(1)=$______ , multiplicative identity property

Recommended heart rates during exercise vary with age and physical condition. For a healthy person doing moderate to intense exercise, such as hiking. the inequality

$$0.5 ( 220 - a ) \leq R \leq 0.9 ( 220 - a )$$

gives a target range for the heart rate R (in beats per minute), based on age a (in years). a. What is the target range for heart rates for a person 15 years old? b. How old is a person whose target range is between 99 and 178.2 beats per minute?

Differentiate between a conditional equation and an identity?

Prove the identity $\sin(\pi - x) = \sin x$.

A hummingbird in flight beats its wings at a rate of 70 times per second. How many times does it beat its wings in an hour if it is in flight 70% of the time?