Westonci.ca is the Q&A platform that connects you with experts who provide accurate and detailed answers. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.
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]
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.
