You are in a room 30 feet long with a heater at one end. In the morning the room is 65°F. You turn on the heater, which quickly warms up to 85°F. Let H(x, t) be the temperature x feet from the heater, t minutes after the heater is turned on. The figure below shows the contour diagram for H. t (minutes) 60 The room is i 50 The room is i 40 30 20 10 Round your answers to the nearest degree. 80 75 70 65 How warm is it 10 feet from the heater 10 minutes after it was turned on? 15 minutes after it was turned on? 5 10 15 20 25 30 x (feet) °F 10 feet from the heater 10 minutes after it was turned on. °F 10 feet from the heater 15 minutes after it was turned on.

Solve the following problems and show pertinent solutions. 1. A survey of a random sample of people leaving an amusement park showed an average expenditure of 1030 Php for the evening. The average expenditure for the 20 girls in the sample was 970 Php and for the boys it was 1110 Php. How many boys are there in the random sample?

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Use the four-step method in problem solving to solve the problem. A college cafeteria pays student cashiers $8.50 per hour. Cashiers earn an additional $1.40 per hour for each hour worked over 35 hours per week. A cashier worked 44 hours one week and 39 hours the second week. How much did this cashier earn in this two-week period? ..... О А. $613.20 В. $705.50 C. $7,171.20 D. $723.70

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2. You have some coins, each of which is a penny (1 cent), a nickel (5 cents), a dime (10 cents), or a quarter (25 cents). You know that • you have twice as many pennies as nickels, • the number of dimes is one more than the number of pennies and nickels combined, you have 34 coins in total, • and the total value of your coins is $2.70 (270 cents). (a) Set up a system of linear equations for the numbers of pennies, nickels, dimes, and quarters you have. (b) Determine how many coins of each type you have, by solving the system from part (a).

3.) Mr. Richards and Mr. Dolge each began improving their yards over the summer by buying bags of soil (fancy dirt) and bags of mulch (bark dust). Since Mr. Dolge has access to a truck, Mr. Richards got a ride and as a result they got their supplies from the same store. Mr. Dolge spent $97 on 3 bags of soil and 14 bags of mulch. Mr. Richards got 14 bags of soil and 7 bags of mulch for $161. They forgot to get a receipt, but just in case they need more supplies, they are wondering how much each bag of soil will cost, and how much each bag of mulch will cost. What should they find these prices to be?

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59. Car repairs Smith Chevrolet charges $50 per hour for labor on car repairs. Lopez Ford charges a diagnosis fee of $30 plus $40 per hour for labor. If the labor on an engine repair costs the same at either shop, how long does the repair take?

Write down the 4 by 4 matrix S that scales by a constant c. Multiply ST and also TS, where T is translation by (1, 4, 3). To blow up the picture around the center point (1, 4, 3), would you use vST or vT S?