Find the smallest integer a such that 945a is a perfect cube.
1. 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]
2. 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
3. Choose the noun that is always singular.
Jawaban:
1. Water
2. Information
3. Traffic
4. Art
5. Entertainment
Lebih banyaknya cari aja 'uncountable noun'
4. Find the domain and range of the function f(x,y) = ln(9-x²-9y²) such that f well defined
9-x²-9y²>0
9y²<9-x²
/// 9-x²>0. (1)
-3< x<3
9-9y²>x²///9-9y²>0. (2)
9y²<9
y²<1
-1<y<1
5. Find three consecutive odd integers such that the sum of the first, two times of the second, and three times of the third is 70.
Jawab:
PenjelasanTemukan tiga bilangan bulat ganjil yang berurutan sehingga jumlah dari yang pertama, dua kali yang kedua, dan tiga kali yang ketiga adalah 70. dengan langkah-langkah:
MAAF HANYA INI SAJA YANG BISA SAYA BANTU:)
6. Carilah nilai x agar matrix a = (6 X) (8 -4) Menjadi matriks singular.
Cara Ada di bawah. Insyaallah benar.
Jawabannya x= -3
7. 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
8. contoh matrix singular berordo 2x2 dan 3x3 ?
2 2 2 2 2
A B 2 2 2
2 2 2 2 2
ordo 2 x 2 ordo 3x3
9. 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
10. find × such that the ratio (28+k): (40+k)= 3:4
28+k/40+k = 3/4
→112+4k = 120+3k
→k = 120-112
→k = 8
Semoga Bermanfaat
11. contoh matrix singular...jawab krang please
[tex] A = \left[\begin{array}{ccc}6&3\\4&2\end{array}\right] [/tex]
12. find the values of c such that the area of the region bounded by the parabolas y=x^2-c^2 and y=c^2-x^2 is 576
Jawab:
Jawaban tertera di gambar
13. The function is such that f(x) = a + b cos x for 0 <= x <= 2π It is given that f(1/3 π) = 5 and f (π) = 11 Find the values of the constants a and b.
f(x) = a + b cos x ; 0 ≤ x ≤ 2π
f(π/3) = 5
a + b cos π/3 = 5
a + b(½) = 5
a + ½b = 5
2a + b = 10 ... (1)
f(π) = 11
a + b cos π = 11
a + b(-1) = 11
a - b = 11 ... (2)
(1) dan (2)
2a + b = 10
a - b = 11
-------------- +
3a = 21
a = 7
7 - b = 11
-b = 11 - 7
-b = 4
b = -4
14. Find all the angles between -360° and 180° such that sin x =1/2
Jawaban:
rate yaa
Penjelasan dengan langkah-langkah:
sinx =1/2
sin60=sin120=1/2
karena 360 itu searah jarum jam
maka
sin-360+30=sin-360+150=1/2
sin-330=sin-210=1/2
maka
sudutnya adalah ={-330,-210,60,120}
15. find × such that the ratio (28+k): (40+k)= 3:4
Kelas 7 Matematika
Bab Aljabar
(28 + k)/(40 + k) = 3/4
4 (28 + k) = 3 (40 + k)
112 + 4k = 120 + 3k
4k - 3k = 120 - 112
k = 8
x = k = 8
16. 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
17. Given matrix What is the determinant of the Y matrix?
Answer:
So we get the form below. Det (Y) = (−4)(−2)(3) + 5(4)(−1) + (2)(0)(−6) − ((−1)(−2)(2) + (−6)(4)(−4) + (3)(0)(5))
(Y) = (−4)(−2)(3) + 5(4)(−1) + (2)(0)(−6) − ((−1)(−2)(2) + (−6)(4)(−4) + (3)(0)(5))=24−20+0−(4+96+0) =−96.
explanation:
hope it's useful ^^
Answer:
-96
explanation:
smart :l
18. two consecutive even numbers are such that the sum of their squares is 146. Find the two numbers
Jawaban:
dua bilangan genap berurutan sehingga jumlah kuadratnya adalah 146. Tentukan kedua bilangan tersebut
Penjelasan dengan langkah-langkah:
x+(x+2)= 146
2x = 144
x = 72
bilangan genap terbesar = x+2
= 72 +2 = 74
19. if x, y are positive integers such as that 5x + 7y=91, find the maximum value of x+y
[tex]\text{Nilai maksimum dari} \: \: x + y \: \: \text{adalah} \: \: \boxed{17} \: . \\ [/tex]
PembahasanDiketahui :
[tex]x \: \: \text{dan} \: \: y \: \: \text{adalah bilangan bulat positif sedemikian sehingga} \: \: \: 5x + 7y = 91 . \\ \\ [/tex]
Ditanya :
[tex]\text{Nilai maksimum dari} \: \: x + y \\ \\ [/tex]
Jawab :
[tex]5x + 7y = 91 \\ \\ 5x = 91 - 7y \\ \\ \boxed{x = \frac{91 - 7y}{5}} \\ \\ 5 \: \: \text{adalah faktor dari} \: \: 91 - 7y \: \: \: \text{atau} \\ \\ 91 - 7y \: \: \text{adalah kelipatan dari} \: \: 5 \: . \\ \\ [/tex]
[tex]\text{Kemungkinan nilai} \: \: x \: \: \text{dan} \: \: y : \\ \\ \text{Jika} \: \: y = 3 \: \: \text{maka} \: \: x = 14 \\ \\ \text{Jika} \: \: y = 8 \: \: \text{maka} \: \: x = 7 \\ \\ \text{Jika} \: \: y = 13 \: \: \text{maka} \: \: x = 0 \: \: \: (\text{tidak memenuhi karena harus} \: \: > 0) \\ \\ [/tex]
[tex]\text{Nilai} \: \: x + y \: \: \text{diperoleh, yaitu :} \\ \\ [/tex]
[tex]\text{Untuk} \: \: x = 7 \: \: \text{dan} \: \: y = 8 \: \: \text{maka} \: \: x + y = 15. \\ \\ \text{Untuk} \: \: x = 14 \: \: \text{dan} \: \: y = 3 \: \: \text{maka} \: \: x + y = 17. \\ \\ [/tex]
Kesimpulan :
[tex]\text{Nilai maksimum dari} \: \: x + y \: \: \text{adalah} \: \: \boxed{17} \: . \\ \\ [/tex]
Pelajari Lebih LanjutContoh soal lain tentang bilangan bulat
Nilai terkecil dari a – b
brainly.co.id/tugas/3358718
Bilangan bulat yang lebih besar
brainly.co.id/tugas/368990
Diketahui bilangan A dan B bilangan bulat positif. Bilangan A dan B sama sama tersusun dari 4 angka
brainly.co.id/tugas/286374
------------------------------------------------
Detail JawabanKelas : 7
Mapel : Matematika
Kategori : Bilangan
Kode Kategorisasi : 7.2.2
Kata Kunci : nilai maksimum, bilangan
20. singular : is that your scarf plural :
Plural: Are that your scarfs?Plural : Are those their scarfs?
0 komentar:
Posting Komentar