Westonci.ca is the premier destination for reliable answers to your questions, provided by a community of experts. Explore thousands of questions and answers from knowledgeable experts in various fields on our Q&A platform. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.
Sagot :
Certainly! Let's address the problem step by step:
### (a) [tex]$a^m$[/tex] लाई [tex]$a^n$[/tex] ले गुणा गर्दा कति हुन्छ ? (What is the product of [tex]$a^m$[/tex] and [tex]$a^n$[/tex]?)
When you multiply two exponential expressions with the same base, you add the exponents. Thus, the product of [tex]\(a^m\)[/tex] and [tex]\(a^n\)[/tex] is given by:
[tex]\[a^m \times a^n = a^{m+n}\][/tex]
### (b) उक्त गुणनफल पत्ता लगाउनुहोस् । (Find the product.)
We need to multiply [tex]\(\left(6.8 \times 10^5\right)\)[/tex] by [tex]\(\left(3.9 \times 10^{-7}\right)\)[/tex].
[tex]\[ (6.8 \times 10^5) \times (3.9 \times 10^{-7}) = 6.8 \times 3.9 \times 10^{5 + (-7)} = 26.52 \times 10^{-2} = 0.2652 \][/tex]
So, the product is:
[tex]\[0.2652\][/tex]
### (c) सो भागफल निकाल्नुहोस्। (Calculate the quotient.)
Next, we divide the product obtained in part (b) by [tex]\(7.8 \times 10^{-4}\)[/tex]:
[tex]\[ \frac{0.2652}{7.8 \times 10^{-4}} = \frac{0.2652}{0.00078} = 340.0 \][/tex]
Therefore, the quotient is:
[tex]\[340.0\][/tex]
### (d) 3400 लाई पञ्च आधार सड्ख्यामा बदल्नुहोस् । (Convert 3400 into quinary number system.)
To convert 3400 into the quinary (base-5) number system, we repeatedly divide the number by 5 and record the remainders:
- [tex]\(3400 \div 5 = 680\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(680 \div 5 = 136\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(136 \div 5 = 27\)[/tex] remainder [tex]\(1\)[/tex]
- [tex]\(27 \div 5 = 5\)[/tex] remainder [tex]\(2\)[/tex]
- [tex]\(5 \div 5 = 1\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(1 \div 5 = 0\)[/tex] remainder [tex]\(1\)[/tex]
Reading the remainders from bottom to top, we get [tex]\(3400_{10} = 102100_5\)[/tex].
So, 3400 in the quinary number system is:
[tex]\[102100_5\][/tex]
### (e) 34 लाई द्विआधार सड्ख्यामा बदल्नुहोस् । (Convert 34 into binary number system.)
To convert 34 into the binary (base-2) number system, we repeatedly divide the number by 2 and record the remainders:
- [tex]\(34 \div 2 = 17\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(17 \div 2 = 8\)[/tex] remainder [tex]\(1\)[/tex]
- [tex]\(8 \div 2 = 4\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(4 \div 2 = 2\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(2 \div 2 = 1\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(1 \div 2 = 0\)[/tex] remainder [tex]\(1\)[/tex]
Reading the remainders from bottom to top, we get [tex]\(34_{10} = 100010_2\)[/tex].
So, 34 in the binary number system is:
[tex]\[100010_2\][/tex]
### (a) [tex]$a^m$[/tex] लाई [tex]$a^n$[/tex] ले गुणा गर्दा कति हुन्छ ? (What is the product of [tex]$a^m$[/tex] and [tex]$a^n$[/tex]?)
When you multiply two exponential expressions with the same base, you add the exponents. Thus, the product of [tex]\(a^m\)[/tex] and [tex]\(a^n\)[/tex] is given by:
[tex]\[a^m \times a^n = a^{m+n}\][/tex]
### (b) उक्त गुणनफल पत्ता लगाउनुहोस् । (Find the product.)
We need to multiply [tex]\(\left(6.8 \times 10^5\right)\)[/tex] by [tex]\(\left(3.9 \times 10^{-7}\right)\)[/tex].
[tex]\[ (6.8 \times 10^5) \times (3.9 \times 10^{-7}) = 6.8 \times 3.9 \times 10^{5 + (-7)} = 26.52 \times 10^{-2} = 0.2652 \][/tex]
So, the product is:
[tex]\[0.2652\][/tex]
### (c) सो भागफल निकाल्नुहोस्। (Calculate the quotient.)
Next, we divide the product obtained in part (b) by [tex]\(7.8 \times 10^{-4}\)[/tex]:
[tex]\[ \frac{0.2652}{7.8 \times 10^{-4}} = \frac{0.2652}{0.00078} = 340.0 \][/tex]
Therefore, the quotient is:
[tex]\[340.0\][/tex]
### (d) 3400 लाई पञ्च आधार सड्ख्यामा बदल्नुहोस् । (Convert 3400 into quinary number system.)
To convert 3400 into the quinary (base-5) number system, we repeatedly divide the number by 5 and record the remainders:
- [tex]\(3400 \div 5 = 680\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(680 \div 5 = 136\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(136 \div 5 = 27\)[/tex] remainder [tex]\(1\)[/tex]
- [tex]\(27 \div 5 = 5\)[/tex] remainder [tex]\(2\)[/tex]
- [tex]\(5 \div 5 = 1\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(1 \div 5 = 0\)[/tex] remainder [tex]\(1\)[/tex]
Reading the remainders from bottom to top, we get [tex]\(3400_{10} = 102100_5\)[/tex].
So, 3400 in the quinary number system is:
[tex]\[102100_5\][/tex]
### (e) 34 लाई द्विआधार सड्ख्यामा बदल्नुहोस् । (Convert 34 into binary number system.)
To convert 34 into the binary (base-2) number system, we repeatedly divide the number by 2 and record the remainders:
- [tex]\(34 \div 2 = 17\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(17 \div 2 = 8\)[/tex] remainder [tex]\(1\)[/tex]
- [tex]\(8 \div 2 = 4\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(4 \div 2 = 2\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(2 \div 2 = 1\)[/tex] remainder [tex]\(0\)[/tex]
- [tex]\(1 \div 2 = 0\)[/tex] remainder [tex]\(1\)[/tex]
Reading the remainders from bottom to top, we get [tex]\(34_{10} = 100010_2\)[/tex].
So, 34 in the binary number system is:
[tex]\[100010_2\][/tex]
Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Thank you for choosing Westonci.ca as your information source. We look forward to your next visit.