N is a positive integer such that N and N+27 are both perfect squares.What is the positive integer N?
1. N is a positive integer such that N and N+27 are both perfect squares.What is the positive integer N?
34
sorry dikalau saya salah
2. what is the smallest integer a such that a√115 will be greater than 115
Subject: Numbering
aV115 >= 115
a >= 115 / V115
a >= V115
The integer that greater than V115 is 11 (whose squared number is 121)
V = square root/akar kuadrat
3. Find the smallest integer a such that 945a is a perfect cube.
There is no smallest integer [tex]a[/tex] such that [tex]945a[/tex] is a perfect cube.
However, if [tex]a[/tex] or the perfect cube is a positive integer, the smallest integer a such that [tex]945a[/tex] is a perfect cube is 1225.
Let [tex]b[/tex] be the root of the perfect cube which is the value of [tex]945a[/tex]. Thus,
[tex]\large\text{$\begin{aligned}b^3=945a\end{aligned}$}[/tex]
By prime factorization, we get:
[tex]\large\text{$\begin{aligned}b^3&=3\cdot315\cdot a\\&=3\cdot3\cdot105\cdot a\\&=3\cdot3\cdot3\cdot35\cdot a\\&=3^3\cdot5\cdot7\cdot a\\\end{aligned}$}[/tex]
The integer [tex]a[/tex] should be in the form of [tex]{}\pm 35^{(3k-1)}[/tex], [tex]k=1,2,3,{\dots}[/tex]. Unlike perfect squares, perfect cubes could be negative. Hence, temporary solution we can get is:
[tex]\large\text{$\begin{aligned}&a=-\left(35^{(3k-1)}\right )\\&\quad k=1,2,3,{\dots}\end{aligned}$}[/tex]
The larger the [tex]k[/tex] is, the smaller the [tex]a[/tex] will be.
THEREFORE, there is no smallest integer [tex]a[/tex] such that [tex]945a[/tex] is a perfect cube.
However, if [tex]a[/tex] or the perfect cube is a positive integer, the smallest integer [tex]a[/tex] such that [tex]945a[/tex] is a perfect cube is:
[tex]\large\text{$\begin{aligned}a&=35^{(3\cdot1\:-\:1)}\\&=35^2\\&=\bf1225\end{aligned}$}[/tex]
[tex]\blacksquare[/tex]
4. 1). The classical music is so ...... that it's such a (n) ...... that ........ 2). Upin dan Ipin are so ....... that ...... It's such ........ that ...... 3). Lumpia is so .......... that ...... It's such a (n) ........ that ........
1). Musik klasik sangat ...... bahwa itu seperti (n) ...... yang ........
2). Upin dan Ipin sangat ....... itu ...... itu seperti ........ itu ......
3). Lumpia begitu .......... itu ...... itu seperti (n) ........ itu ........
1). Classical music is very soothing that it's like aromatherapy candles that make the body comfortable and relaxed
2). Upin and Ipin are very similar, the twins are like split betel nuts which are really difficult to distinguish
3). The lumpia is so crunchy and I really like it because it's like crispy crackers
5. BANTU JAWAB KK__^ 12. Work in groups. Based on each picture provided, complete each sentence with 'so.... that... or 'such.....that.....' see the example. 1) the latest collection is so______ that_____________. It was such ___________ that ____________. 2) the classical music concert is so ____________ that __________. It's such a(n) _________ that _____________. 3) upin and ipin are so __________ that ____________. It's such ________ that ___________. 4) lumpia is so _____________ that ___________________. It's such a(n) __________ that _________________________________.
Jawaban:
12. Bekerja dalam kelompok. Berdasarkan setiap gambar yang diberikan, lengkapi setiap kalimat dengan 'jadi ... itu ... atau' seperti ... itu. ' lihat contohnya. 1) Koleksi terbaru sehingga 2) Konser musik klasik yang begitu (n) ipin begitu seperti 3) upin dan 4) lumpia adalah sedemikian rupa sehingga seperti (n) ). bahwa
Penjelasan:
maaf klo Salah^_^
pelajari lebih lanjut dngn follow me untuk menanyakan soal yg tidk bisa d jawab^_^
6. Find the smallest value of such that the LCM of n and 54 is 108.
Jawaban:
54 = 2 × 3³
108 = 2² × 3³
LCM = 2² × 3³ = 108
7. The smallest even integer that satisfies 2x > 16 is
Jawaban:
10
Penjelasan dengan langkah-langkah:
2x > 16
x> 16/2
x> 8.
Bilangan yang memenuhi: 9, 10, 11, 12.
Genap terkecil yang memenuhi= 10
8. What is the month that has the least days? It is
february
28 days per 4 year
9. The smallest possible value of n such that 126n is a perfect square
Jawab: The answer of n is square root of 126 : 11.23
Penjelasan dengan langkah-langkah:
10. apa jawaban what is the month that has the least days ? it is
Jawaban:
february
Penjelasan:
karna ada yang namanya Tahun kabisat yang terjadi 4 tahun sekali, dan tanggal nya cuman sampai tgl 28
11. What is the smallest positive integer that is neither prime nor square and that has no prime factor less than 90 ?
Jawaban:
9797
Penjelasan dengan langkah-langkah:
Solution :
Find smallest two prime number above 90 :
97 and 101
then
97 × 101 = 9797
So, the number is 9797
12. 4. Let P(n) be the statement that 13 +23 +···+n3 = (n(n+1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f) Explain why these steps show that this formula is true whenever n is a positive integer. mohon bantuannya ya kaka , aku udah bingng banget dikumpul besok :(
a. P(1) is 1³ = (1(1+1)/2)²
b.1³ = 1
and (1(1+1)/2)² = (2/2)² = 1² = 1 thus P(1) is true
c. The inductive hypothesis is 1³ + ... + n³ = (n(n+1)/2)²
D. You need to prove P(n+1) so
1³ + ... + n³ + (n+1)³ = ((n+1)(n+1+1)/2)² = ((n+1)(n+2)/2)²
E. 1³ + ... + n³ + (n+1)³ = (n(n+1)/2)² + (n+1)³
= n²(n+1)²/4 + (n+1)³
= (n+1)² [n²/4 + (n+1)]
= (n+1)² [(n² + 4n + 4)/4]
= (n+1)² (n+2)² / 4 = ((n+1)(n+2)/2)²
F. So, if P(n) is true, then P(n+1) is true
Thus P(n) is true for all positive integer n.
13. 1.the latest collection is so amazing that all of them are sold out before the show. it was such..... that........ 2.the classical music cocncert is so ..... that... it's such a(n)......that.... 3.upin and ipin are so......that ...... it's such.....that..... 4.lumpia is so .....that .... it's such a(n).......that....
1. Expensive, not everyone can buy it
2. Amazing, I was startled, beautiful concert , I can't forget it
3. Naughty, I hate them , the bad boys, I wanna kill them ,
4. Tasty, I love it , a heavenly food , I recommend to anyone
14. If N be the positive integer such that the sum of its two smallest factors is 3 and the sum of its two largest factors is 294, then the value of N is?.
The value of N is 196. To solve this problem, we use the formula for the factors of the number N.
Penjelasan dengan langkah-langkah:
Is known:
If N be the positive integer such that the sum of its two smallest factors is 3 and the sum of its two largest factors is 294,
Asked
Then the value of N is?
Answer:
Suppose the factors are a, b, c and d.
a + b = 3
c + d = 294
a x d = b x c
We are looking for the sum of 2 integers whose result is 3.
1 + 2 = 3
so that a = 1 and b = 3
a x d = b x c
1 x d = 2 x c
d = 2c
c + d = 294
c + 2c = 294
3c = 294
c = 294 : 3
c = 98
c + d = 294
98 + d = 294
d = 294 - 98
d = 196.
N = a x d = 1 x 196 = 196.
Pelajari Lebih LanjutMateri tentang faktor, faktor prima, faktorisasi prima dapat disimak juga di https://brainly.co.id/tugas/7005564#BelajarBersamaBrainly
#SPJ1
15. 11. What is the least positive integer thatis divisible by both 2 and 5 and leavesa remainder of 2 when it is divided by7?A. 30B. 50C. 65D. 75E. 80
Jawaban:
apa bilangan bulat paling positif yang dapat dibagi oleh 2 dan 5 dan meninggalkan sisa 2 ketika dibagi dengan 7
Jawab:
A. 30
Karena selain bilangan itu bisa dibagi dengan 2 dan 5, lalu bilangan itu bila dibagi dengan 7 haruslah sisa 2
16. What is the different the use such that and in a sentence?
smga bermanfaat....
Penjelasan:
it used to point something example : There it is!! or there we have it
it's shows u where (idk how to explain it lol)example :
q : where's my chocolate?
a : it's inthe fridge not in 'a'
17. 2. What is the difference between so that and such as in the sentence?
i'm is the lier hnte nyaho
18. what is the least contained substance per 100 gram
Jawaban:
artinya;
apa zat yang paling sedikit terkandung per 100 gram
Penjelasan:
semoga membantu
19. if n is a whole number such that n×(n+28) is a prime number, find the prime number.explain your answer
Jawaban:
n = 1
Prime number = 29
Penjelasan dengan langkah-langkah:
Why n =1?
It cause if n is a multiplier, then the result not prime
If n our substitution on that function, then the result : 1 ( 1+28) = 1 x 29 = 29
29 is prime number
20. 4. Let P(n) be the statement that 13 +23 +···+n3 = (n(n+1)/2)2 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of the proof. c) What is the inductive hypothesis? d) What do you need to prove in the inductive step? e) Complete the inductive step, identifying where you use the inductive hypothesis. f) Explainwhythesestepsshowthatthisformulaistrue whenever n is a positive integer. ka tolong bantuin dong :(
susah bahasa inggris campur matematika
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