In each of the following questions: a Write the calculation represented by each problem. b Work out the answer to each calculation. 1 The temperature of water in a beaker is initially $$ 48^{\circ} \mathrm{C} $$. It is allowed to cool by $$ 16^{\circ} \mathrm{C} $$ before being heated up again. When heated up, the temperature of the water is trebled. What is the temperature $$ \left(T^{\circ} \mathrm{C}\right) $$ of the water once it has been heated up? 2 A submarine is initially at a depth of 400 m below the water's surface. It then dives a further distance so that it is at a depth double what it was initially. The submarine later climbs 620 m . Calculate the depth $$ D(\mathrm{~m}) $$ the submarine climbs to. 3 Luis arranges five counters in a line. He squares the number of counters, then adds a further 11 counters. Finally, he divides the number of counters equally between himself and Dari, so they each receive $$ N $$ counters. Calculate the number of counters $$ (N) $$ they each receive.

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UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$5^{2}+11$$
- step1: Evaluate the power:
  $$25+11$$
- step2: Add the numbers:
  $$36$$
Calculate or simplify the expression $$ 400 * 2 - 620 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$400\times 2-620$$
- step1: Multiply the numbers:
  $$800-620$$
- step2: Subtract the numbers:
  $$180$$
Calculate or simplify the expression $$ (48 - 16) * 3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(48-16\right)\times 3$$
- step1: Subtract the numbers:
  $$32\times 3$$
- step2: Multiply the numbers:
  $$96$$
Calculate or simplify the expression $$ (5^2 + 11) / 2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(5^{2}+11\right)}{2}$$
- step1: Remove the parentheses:
  $$\frac{5^{2}+11}{2}$$
- step2: Add the numbers:
  $$\frac{36}{2}$$
- step3: Reduce the numbers:
  $$\frac{18}{1}$$
- step4: Calculate:
  $$18$$
Let's break down each problem step by step:

### Problem 1
1. **Calculation**: The initial temperature of the water is $$ 48^{\circ} \mathrm{C} $$. It cools by $$ 16^{\circ} \mathrm{C} $$, so the new temperature is $$ 48 - 16 $$. Then, this temperature is trebled.
   $$
   T = (48 - 16) \times 3
   $$
2. **Answer**: 
   $$
   T = 32 \times 3 = 96^{\circ} \mathrm{C}
   $$

### Problem 2
1. **Calculation**: The submarine starts at a depth of $$ 400 \, \mathrm{m} $$. It dives further to double its initial depth, which is $$ 400 \times 2 $$, and then climbs $$ 620 \, \mathrm{m} $$.
   $$
   D = (400 \times 2) - 620
   $$
2. **Answer**: 
   $$
   D = 800 - 620 = 180 \, \mathrm{m}
   $$

### Problem 3
1. **Calculation**: Luis arranges five counters, squares that number, adds $$ 11 $$, and then divides the total by $$ 2 $$ to find how many counters each receives.
   $$
   N = \frac{5^2 + 11}{2}
   $$
2. **Answer**: 
   $$
   N = \frac{25 + 11}{2} = \frac{36}{2} = 18
   $$

### Summary of Answers
1. The temperature of the water after heating is $$ 96^{\circ} \mathrm{C} $$.
2. The depth the submarine climbs to is $$ 180 \, \mathrm{m} $$.
3. Each receives $$ 18 $$ counters.
1. The water's temperature after heating is $$ 96^{\circ} \mathrm{C} $$. 2. The submarine climbs to a depth of $$ 180 \, \mathrm{m} $$. 3. Each person receives $$ 18 $$ counters.

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