(1 point) newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its temperature and that of its surroundings. suppose that the temperature of a cup of coffee obeys newton's law of cooling. let k> 0k> 0 be the constant of proportionality. assume the coffee has a temperature of 190 degrees fahrenheit when freshly poured, and 33 minutes later has cooled to 180 degrees in a room at 68 degrees.(a) write an initial value problem for the temperature t of the coffee, in fahrenheit, at time t in minutes. your answer will contain the uknown constant k : dtdt=equation editort(0)=equation editor(b) solve the initial value problem in part (a). your answer will contain the unknown constant k .t(t)=equation editor(c) determine the value of the constant kk=equation editorminutes.(d) determine when the coffee reaches a temperature of 150 degrees. equation editorminutes.

Me! 50 points! why does when we come home, our door is unlocked and there is grease on the door knob, me solve this , and i don't know what category this goes under

What are the solutions of the system? y = x^2 + 2x +3y = 4x - 2a. (-1, -6) and (-3, -14)b. (-1, 10) and (3, -6)c. no solutiond. (-1, -6) and (3, 10)

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