Carefully consider and answer the following questions. Suppose someone claims that ⌊ 3 √ 82 ⌋ = 4 . How would you verify whether ⌊ 3 √ 82 ⌋ = 4 using powers of 4 and powers of 5? Is ⌊ 3 √ 82 ⌋ = 4 ? Suppose that n, r, and root denote integer values where n ≥ 0 and r > 0. Further, suppose that ( root ) r ≤ n < ( root + 1 ) r . Can we conclude that root = ⌊ r √ n ⌋ ? Carefully justify your answer. Suppose that n and r denote integer values where n ≥ 0 and r > 0. Further, suppose you would like to know ⌊ r √ n ⌋ . When finding ⌊ r √ n ⌋ by a guess and verify method, is there any reason to try a guess, say g, where g < 0? Explain your answer. Similarly, is there any reason to try a guess g where g > n? Explain. Again, suppose that n and r denote integer values where n ≥ 0 and r > 0. What are two "simple" values, say lowEnough and tooHigh, such that lowEnough ≤ ⌊ r √ n ⌋ < tooHigh. Explain based on your answer to the previous question. Suppose you would like to know ⌊ 5 √ 47226 ⌋ . Explain how you could find ⌊ 5 √ 47226 ⌋ using a guess and verify method. Note: Explain your answer by relating this problem to the number guessing game described earlier. Think about what would be an appropriate question to use in place of "Is secret_number < guess_number?" and think about good choices for the starting values of lowEnough and tooHigh.

In this lab, you complete a prewritten c++ program for a carpenter who creates personalized house signs. the program is supposed to compute the price of any sign a customer orders, based on the following facts: the charge for all signs is a minimum of $35.00. the first five letters or numbers are included in the minimum charge; there is a $4 charge for each additional character. if the sign is made of oak, add $20.00. no charge is added for pine. black or white characters are included in the minimum charge; there is an additional $15 charge for gold-leaf lettering. instructions ensure the file named housesign.cppis open in the code editor. you need to declare variables for the following, and initialize them where specified: a variable for the cost of the sign initialized to 0.00 (charge). a variable for the number of characters initialized to 8 (numchars). a variable for the color of the characters initialized to "gold" (color). a variable for the wood type initialized to "oak" (woodtype). write the rest of the program using assignment statements and ifstatements as appropriate. the output statements are written for you. execute the program by clicking the run button. your output should be: the charge for this sign is $82. this is the code, // housesign.cpp - this program calculates prices for custom made signs. #include #include using namespace std; int main() { // this is the work done in the housekeeping() function // declare and initialize variables here // charge for this sign // color of characters in sign // number of characters in sign // type of wood // this is the work done in the detailloop() function // write assignment and if statements here // this is the work done in the endofjob() function // output charge for this sign cout < < "the charge for this sign is $" < < charge < < endl; return(0); }

Melissa needs to add a topic to an email that she will send to her teacher. choose the name of the field where she should type her topic.

How to do this programming flowchart?