4.3 Calculate the following without the use of a calculator: $$ 4.3 .1-2+(-4)(-2)-3 $$ $$ 4.3 .28+9 imes 10+(3+7) $$ $$ 4.3 .33^{3}-11^{2}+\sqrt[4]{-256}-(-5)^{3} $$ $$ 4.3 .4 \frac{-3(2)+(-2)^{3}(-2)-12(2)}{-3(2)+8(-2)-12(-2)} $$ A submarine is at a depth of 22 meters below sea level. It then descends another 19 meters. What is its new depth? QUESTION 5 5.1 Anine buys a new camera. The camera cost R8 400. She pays a deposit of R2 000,00 and the rest she pays over 2 years at $$ 18 \% $$ interest. How much does she pay each month? M. Mhlengi borrows R98 000 to pay for his student fees at 7\% Compound Interest. How much will he have to pay back after 36 months when he starts working? [7]

Question

4.3 Calculate the following without the use of a calculator: $$ 4.3 .1-2+(-4)(-2)-3 $$ $$ 4.3 .28+9 	imes 10+(3+7) $$ $$ 4.3 .33^{3}-11^{2}+\sqrt[4]{-256}-(-5)^{3} $$ $$ 4.3 .4 \frac{-3(2)+(-2)^{3}(-2)-12(2)}{-3(2)+8(-2)-12(-2)} $$ A submarine is at a depth of 22 meters below sea level. It then descends another 19 meters. What is its new depth? QUESTION 5 5.1 Anine buys a new camera. The camera cost R8 400. She pays a deposit of R2 000,00 and the rest she pays over 2 years at $$ 18 \% $$ interest. How much does she pay each month? M. Mhlengi borrows R98 000 to pay for his student fees at 7\% Compound Interest. How much will he have to pay back after 36 months when he starts working? [7]

UpStudy AI · Accepted Answer

Calculate the value by following steps:
- step0: Calculate:
  $$98000\left(1+0.07ight)^{3}$$
- step1: Add the numbers:
  $$98000	imes 1.07^{3}$$
- step2: Convert the expressions:
  $$98000\left(\frac{107}{100}ight)^{3}$$
- step3: Simplify:
  $$98000	imes \frac{107^{3}}{100^{3}}$$
- step4: Rewrite the expression:
  $$1000	imes 98	imes \frac{107^{3}}{100^{3}}$$
- step5: Rewrite the expression:
  $$10^{3}	imes 98	imes \frac{107^{3}}{10^{6}}$$
- step6: Reduce the numbers:
  $$98	imes \frac{107^{3}}{10^{3}}$$
- step7: Rewrite the expression:
  $$2	imes 49	imes \frac{107^{3}}{10^{3}}$$
- step8: Rewrite the expression:
  $$2	imes 49	imes \frac{107^{3}}{2^{3}	imes 5^{3}}$$
- step9: Reduce the numbers:
  $$49	imes \frac{107^{3}}{2^{2}	imes 5^{3}}$$
- step10: Multiply:
  $$\frac{49	imes 107^{3}}{500}$$
Calculate or simplify the expression $$ (-3*2) + (-2)^3*(-2) - 12*2 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-3	imes 2ight)+\left(-2ight)^{3}\left(-2ight)-12	imes 2$$
- step1: Multiply the numbers:
  $$\left(-6ight)+\left(-2ight)^{3}\left(-2ight)-12	imes 2$$
- step2: Remove the parentheses:
  $$-6+\left(-2ight)^{3}\left(-2ight)-12	imes 2$$
- step3: Multiply the terms:
  $$-6+2^{4}-12	imes 2$$
- step4: Multiply the numbers:
  $$-6+2^{4}-24$$
- step5: Evaluate the power:
  $$-6+16-24$$
- step6: Calculate:
  $$-14$$
Calculate or simplify the expression $$ 22 + 19 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$22+19$$
- step1: Add the numbers:
  $$41$$
Calculate or simplify the expression $$ (-3*2) + 8*(-2) - 12*(-2) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\left(-3	imes 2ight)+8\left(-2ight)-12\left(-2ight)$$
- step1: Multiply the numbers:
  $$\left(-6ight)+8\left(-2ight)-12\left(-2ight)$$
- step2: Remove the parentheses:
  $$-6+8\left(-2ight)-12\left(-2ight)$$
- step3: Multiply the numbers:
  $$-6-16-12\left(-2ight)$$
- step4: Multiply the numbers:
  $$-6-16+24$$
- step5: Calculate:
  $$2$$
Calculate or simplify the expression $$ 4.3 + 9 * 10 + (3 + 7) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4.3+9	imes 10+\left(3+7ight)$$
- step1: Add the numbers:
  $$4.3+9	imes 10+10$$
- step2: Multiply the numbers:
  $$4.3+90+10$$
- step3: Add the numbers:
  $$104.3$$
Calculate or simplify the expression $$ 4.3 - 2 + (-4)*(-2) - 3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4.3-2+\left(-4ight)\left(-2ight)-3$$
- step1: Remove the parentheses:
  $$4.3-2-4\left(-2ight)-3$$
- step2: Multiply the numbers:
  $$4.3-2+8-3$$
- step3: Calculate:
  $$7.3$$
Calculate or simplify the expression $$ 4.3 * 3^3 - 11^2 + \sqrt[4]{-256} - (-5)^3 $$.
Calculate the value by following steps:
- step0: Calculate:
  $$4.3	imes 3^{3}-11^{2}+\sqrt[4]{-256}-\left(-5ight)^{3}$$
- step1: Simplify the root:
  $$4.3	imes 3^{3}-11^{2}+2\sqrt{2}+2\sqrt{2}	imes i-\left(-5ight)^{3}$$
- step2: Multiply the numbers:
  $$116.1-11^{2}+2\sqrt{2}+2\sqrt{2}	imes i-\left(-5ight)^{3}$$
- step3: Evaluate the power:
  $$116.1-121+2\sqrt{2}+2\sqrt{2}	imes i-\left(-5ight)^{3}$$
- step4: Evaluate the power:
  $$116.1-121+2\sqrt{2}+2\sqrt{2}	imes i-\left(-125ight)$$
- step5: Subtract the numbers:
  $$-4.9+2\sqrt{2}+2\sqrt{2}	imes i-\left(-125ight)$$
- step6: Remove the parentheses:
  $$-4.9+2\sqrt{2}+2\sqrt{2}	imes i+125$$
- step7: Calculate:
  $$120.1+2\sqrt{2}+2\sqrt{2}	imes i$$
- step8: Simplify:
  $$122.928427+2\sqrt{2}	imes i$$
Calculate or simplify the expression $$ (8400 - 2000) * (1 + 0.18)^(2) / (2 * 12) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{\left(8400-2000ight)\left(1+0.18ight)^{2}}{\left(2	imes 12ight)}$$
- step1: Remove the parentheses:
  $$\frac{\left(8400-2000ight)\left(1+0.18ight)^{2}}{2	imes 12}$$
- step2: Add the numbers:
  $$\frac{\left(8400-2000ight)	imes 1.18^{2}}{2	imes 12}$$
- step3: Subtract the numbers:
  $$\frac{6400	imes 1.18^{2}}{2	imes 12}$$
- step4: Convert the expressions:
  $$\frac{6400\left(\frac{59}{50}ight)^{2}}{2	imes 12}$$
- step5: Multiply the numbers:
  $$\frac{6400\left(\frac{59}{50}ight)^{2}}{24}$$
- step6: Reduce the fraction:
  $$\frac{800\left(\frac{59}{50}ight)^{2}}{3}$$
- step7: Simplify:
  $$\frac{800	imes \frac{59^{2}}{50^{2}}}{3}$$
- step8: Calculate:
  $$\frac{\frac{27848}{25}}{3}$$
- step9: Multiply by the reciprocal:
  $$\frac{27848}{25}	imes \frac{1}{3}$$
- step10: Multiply the fractions:
  $$\frac{27848}{25	imes 3}$$
- step11: Multiply:
  $$\frac{27848}{75}$$
Let's solve each part step by step.

### 4.3 Calculations

**4.3.1** Calculate $$ 4.3 - 2 + (-4)(-2) - 3 $$

1. Calculate $$ (-4)(-2) = 8 $$.
2. Substitute back into the expression: $$ 4.3 - 2 + 8 - 3 $$.
3. Perform the operations: 
   - $$ 4.3 - 2 = 2.3 $$
   - $$ 2.3 + 8 = 10.3 $$
   - $$ 10.3 - 3 = 7.3 $$

Final result: $$ 7.3 $$

---

**4.3.2** Calculate $$ 4.3 + 9 	imes 10 + (3 + 7) $$

1. Calculate $$ 9 	imes 10 = 90 $$.
2. Calculate $$ (3 + 7) = 10 $$.
3. Substitute back into the expression: $$ 4.3 + 90 + 10 $$.
4. Perform the operations:
   - $$ 4.3 + 90 = 94.3 $$
   - $$ 94.3 + 10 = 104.3 $$

Final result: $$ 104.3 $$

---

**4.3.3** Calculate $$ 4.3 \cdot 3^{3} - 11^{2} + \sqrt[4]{-256} - (-5)^{3} $$

1. Calculate $$ 3^{3} = 27 $$.
2. Calculate $$ 11^{2} = 121 $$.
3. Calculate $$ (-5)^{3} = -125 $$.
4. The term $$ \sqrt[4]{-256} $$ involves complex numbers:
   - $$ \sqrt[4]{-256} = 4\sqrt{2}i $$ (where $$ i $$ is the imaginary unit).
5. Substitute back into the expression:
   - $$ 4.3 \cdot 27 - 121 + 4\sqrt{2}i + 125 $$.
6. Calculate $$ 4.3 \cdot 27 = 116.1 $$.
7. Combine all terms:
   - $$ 116.1 - 121 + 125 + 4\sqrt{2}i = 120.1 + 4\sqrt{2}i $$.

Final result: $$ 122.928427 + 2\sqrt{2}i $$

---

**4.3.4** Calculate $$ \frac{-3(2) + (-2)^{3}(-2) - 12(2)}{-3(2) + 8(-2) - 12(-2)} $$

1. Calculate the numerator:
   - $$ -3(2) = -6 $$
   - $$ (-2)^{3} = -8 $$ and $$ -8(-2) = 16 $$
   - $$ -12(2) = -24 $$
   - Combine: $$ -6 + 16 - 24 = -14 $$

2. Calculate the denominator:
   - $$ -3(2) = -6 $$
   - $$ 8(-2) = -16 $$
   - $$ -12(-2) = 24 $$
   - Combine: $$ -6 - 16 + 24 = 2 $$

3. Substitute back into the fraction:
   - $$ \frac{-14}{2} = -7 $$

Final result: $$ -7 $$

---

### Submarine Depth Calculation

A submarine is at a depth of 22 meters below sea level and descends another 19 meters.

1. Calculate the new depth:
   - $$ -22 - 19 = -41 $$

Final depth: $$ -41 $$ meters (41 meters below sea level).

---

### 5.1 Camera Payment Calculation

The camera costs R8,400, with a deposit of R2,000. The remaining amount is paid over 2 years at 18% interest.

1. Remaining amount after deposit:
   - $$ 8400 - 2000 = 6400 $$

2. Total amount with interest:
   - Using the formula for compound interest: $$ A = P(1 + r/n)^{nt} $$
   - Here, $$ P = 6400 $$, $$ r = 0.18 $$, $$ n = 12 $$ (monthly), $$ t = 2 $$.
   - Calculate $$ A = 6400(1 + 0.18/12)^{12 \cdot 2} $$.

Final monthly payment: $$ \frac{A}{24} $$.

---

### Mhlengi's Loan Calculation

Mhlengi borrows R98,000 at 7% compound interest for 36 months.

1. Total amount to pay back:
   - Using the same compound interest formula: $$ A = P(1 + r/n)^{nt} $$
   - Here, $$ P = 98000 $$, $$ r = 0.07 $$, $$ n = 12 $$, $$ t = 3 $$.
   - Calculate $$ A = 98000(1 + 0.07/12)^{12 \cdot 3} $$.

Final amount to pay back: $$ A $$.

---

Now, let's calculate the final amounts for the camera payment and Mhlengi's loan.
Calculate the value by following steps:
- step0: Calculate:
  $$98000\left(1+\frac{0.07}{12}ight)^{12	imes 3}$$
- step1: Divide the terms:
  $$98000\left(1+\frac{7}{1200}ight)^{12	imes 3}$$
- step2: Add the numbers:
  $$98000\left(\frac{1207}{1200}ight)^{12	imes 3}$$
- step3: Multiply the numbers:
  $$98000\left(\frac{1207}{1200}ight)^{36}$$
- step4: Simplify:
  $$98000	imes \frac{1207^{36}}{1200^{36}}$$
- step5: Rewrite the expression:
  $$400	imes 245	imes \frac{1207^{36}}{1200^{36}}$$
- step6: Rewrite the expression:
  $$400	imes 245	imes \frac{1207^{36}}{400^{36}	imes 3^{36}}$$
- step7: Reduce the numbers:
  $$245	imes \frac{1207^{36}}{400^{35}	imes 3^{36}}$$
- step8: Rewrite the expression:
  $$5	imes 49	imes \frac{1207^{36}}{400^{35}	imes 3^{36}}$$
- step9: Rewrite the expression:
  $$5	imes 49	imes \frac{1207^{36}}{25^{35}	imes 16^{35}	imes 3^{36}}$$
- step10: Rewrite the expression:
  $$5	imes 49	imes \frac{1207^{36}}{5^{70}	imes 16^{35}	imes 3^{36}}$$
- step11: Reduce the numbers:
  $$49	imes \frac{1207^{36}}{5^{69}	imes 16^{35}	imes 3^{36}}$$
- step12: Multiply the fractions:
  $$\frac{49	imes 1207^{36}}{5^{69}	imes 16^{35}	imes 3^{36}}$$
Calculate or simplify the expression $$ 6400 * (1 + 0.18/12)^(12*2) / (2*12) $$.
Calculate the value by following steps:
- step0: Calculate:
  $$\frac{6400\left(1+\frac{0.18}{12}ight)^{12	imes 2}}{\left(2	imes 12ight)}$$
- step1: Remove the parentheses:
  $$\frac{6400\left(1+\frac{0.18}{12}ight)^{12	imes 2}}{2	imes 12}$$
- step2: Divide the terms:
  $$\frac{6400\left(1+\frac{3}{200}ight)^{12	imes 2}}{2	imes 12}$$
- step3: Add the numbers:
  $$\frac{6400\left(\frac{203}{200}ight)^{12	imes 2}}{2	imes 12}$$
- step4: Multiply the numbers:
  $$\frac{6400\left(\frac{203}{200}ight)^{24}}{2	imes 12}$$
- step5: Multiply the numbers:
  $$\frac{6400\left(\frac{203}{200}ight)^{24}}{24}$$
- step6: Reduce the fraction:
  $$\frac{800\left(\frac{203}{200}ight)^{24}}{3}$$
- step7: Simplify:
  $$\frac{800	imes \frac{203^{24}}{200^{24}}}{3}$$
- step8: Calculate:
  $$\frac{\frac{203^{24}}{2^{67}	imes 25^{23}}}{3}$$
- step9: Multiply by the reciprocal:
  $$\frac{203^{24}}{2^{67}	imes 25^{23}}	imes \frac{1}{3}$$
- step10: Multiply the fractions:
  $$\frac{203^{24}}{2^{67}	imes 25^{23}	imes 3}$$
- step11: Multiply:
  $$\frac{203^{24}}{3	imes 2^{67}	imes 25^{23}}$$
### Final Results

1. **Camera Payment Calculation:**
   - Monthly payment: Approximately $$ R381.20 $$.

2. **Mhlengi's Loan Calculation:**
   - Total amount to pay back after 36 months: Approximately $$ R120,826.71 $$.

### Summary of All Calculations

- **4.3.1:** $$ 7.3 $$
- **4.3.2:** $$ 104.3 $$
- **4.3.3:** $$ 122.928427 + 2\sqrt{2}i $$
- **4.3.4:** $$ -7 $$
- **Submarine Depth:** $$ -41 $$ meters
- **Camera Monthly Payment:** Approximately $$ R381.20 $$
- **Mhlengi's Total Payback:** Approximately $$ R120,826.71 $$

If you have any further questions or need additional calculations, feel free to ask!
- **4.3.1:** 7.3 - **4.3.2:** 104.3 - **4.3.3:** 122.93 + 2√2i - **4.3.4:** -7 - **Submarine Depth:** 41 meters below sea level - **Camera Monthly Payment:** R381.20 - **Mhlengi's Total Payback:** R120,826.71

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