A calculator is broken so that the only keys that still work are the $\sin$, $\cos$, $\tan$, $\cot$, $\arcsin$, $\arccos$, and $\arctan$ buttons. Assume that the calculator does real number calculations with infinite precision. All functions are in terms of radians, and you may assume all the values of $x$ below are positive. (a) Find, with proof, a sequence of buttons that will transform $x$ into $\frac{1}{x}$ . (b) Find, with proof, a sequence of buttons that will transform $\sqrt x$ into $\sqrt{x 1}$. (c) The display initially shows $1$. Prove that there is a sequence of buttons that will produce $\frac{3}{\sqrt{5}}$.

Find the slope and the y-intercept if there's one and the equation of the line given these two points( 3, 2) and( 3, -4)

The measure of an angle is 117°. what is the measure of a supplementary angle?

At river bank, checking account customers earn 0.75% interest a month on their account balances, pay no service fees for writing checks, and pay a monthly $2.00 financial charge. calculate the income earned in one month on the checking account for a customer with an account balance of $1,000. a. $4.25 b. $5.50 c. $6.75 d. $7.25 checking account earnings at baker’s bank are expressed by the equation: i = -0.09x + 10.2. while the earnings at elite bank are modeled by: i = -0.02x + 7.5. in both cases, x is the number of checks written. at what number of checks will elite bank start generating more checking account income than baker's bank? a. 12 b. 25 c. 39 d. 42 emilio’s checking account had a balance of 728.32 at the beginning of the week. he wrote checks for the following amounts throughout the week: $99.48, $33.50, $18.23, and $72.05. he also deposited his paycheck in the amount of $1,109.90. what is his account balance at the end of the week? a. $1,192.35 b. $1,222.86 c. $1,540.52 d. $1,614.96