Subjects algebra

Tank Capacity Quinary

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Tank Capacity Quinary


1. Problem: Find how much less the capacity of tank B is than the capacity of tank A. Step 1: Let the capacity of tank A be $C_A$ and tank B be $C_B$. Step 2: The difference in capacity is $C_A - C_B$. Without specific values given, the answer is the difference $C_A - C_B$. 2. Problem: Convert 484 to a quinary (base 5) number. Step 1: Divide 484 by 5 repeatedly and record remainders: $484 \div 5 = 96$ remainder $4$ $96 \div 5 = 19$ remainder $1$ $19 \div 5 = 3$ remainder $4$ $3 \div 5 = 0$ remainder $3$ Step 2: Write remainders in reverse order: $3 4 1 4$. Step 3: Therefore, $484_{10} = 3414_5$. 3. Problem: If the ratio of boys to girls is 4:5 and girls are 400, find number of boys. Step 1: Ratio is $\frac{boys}{girls} = \frac{4}{5}$. Step 2: Girls = 400, so boys $= \frac{4}{5} \times 400 = 320$. 4. Problem: Check if numbers 5, 8, 10, 15 are proportional. Step 1: For proportion $a:b = c:d$, check if $a\times d = b \times c$. Check: $5 \times 15 = 75$ and $8 \times 10 = 80$. Since $75 \neq 80$, numbers are not proportional. 5. Problem: Is a triangle a rational or irrational number? Step 1: A triangle is a geometric figure, not a number. Answer: Not applicable. 6. Problem: Write formula to calculate area of parallelogram. Answer: $\text{Area} = \text{base} \times \text{height}$. 7. Problem: Calculate area of parallelogram with sides 30 cm and 40 cm, and smaller segment 15 cm. Step 1: Given, base $b=40$ cm and height $h=15$ cm. Step 2: Area $= b \times h = 40 \times 15 = 600$ cm$^2$. 8. Problem: Express $x^a \times x^b$ as a power of $x$. Step 1: Use law of exponents: $x^a \times x^b = x^{a+b}$. Final answers: - Capacity difference: $C_A - C_B$ - $484_{10} = 3414_5$ - Boys = 320 - Numbers 5,8,10,15 are not proportional - Triangle: geometric figure, not a number - Area of parallelogram $= \text{base} \times \text{height}$ - Area of given parallelogram $= 600$ cm$^2$ - $x^a \times x^b = x^{a+b}$