Find X Such That The Four Points Are Coplanar
April 05, 2023
if x, y are positive integers such as that 5x + 7y=91, find the maximum value of x+y
1. 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
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Bilangan bulat yang lebih besar
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Diketahui bilangan A dan B bilangan bulat positif. Bilangan A dan B sama sama tersusun dari 4 angka
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Detail JawabanKelas : 7
Mapel : Matematika
Kategori : Bilangan
Kode Kategorisasi : 7.2.2
Kata Kunci : nilai maksimum, bilangan
2. A,B, and C are Concecutive whole number such that A x B x C = 504 Find the value of A.
Jawaban dengan langkah-langkah:
a x b x c = 504
Persamaan berada dalam bentuk standar
bca = 504
bagi kedua sisi dengan bc
bca/bc = 540/bc
Membagi dengan bc membatalkan perkalian dengan bc
Kesimpulan/Jawaban
a = 504/bc
3. Find the x coordinates of the points p and q on y = (x-7)^2 + 3 such that the tangents at p and q have gradients 1 and -1 respectively
gak ngerti bahasa Inggris
4. 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]
5. They are …. a bad citizen … they often break the law.Complete the sentence above by using the right conjunctions ! That...such...That..so...So...that...Not only...but also...such … that …
Answer:
Not only...but also...
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. 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
8. A. Choose the correct italic word.1. There's so/such little crime now that2. They have got so/such poor hospitals that3. Fuel prices are hiking so/such quickly that4. Our situation sometimes looks so/such bleak that5. So/such few women are having babies these days that6. The incumbent local governor was allegedly involved in so/such a big corruption that7. The government has lied so/such many times that8. The earthquake caused so/such widespread damage that9. The aceg tsunami in 2004 left so/such an unforgettable memory that 10. so/such many children are forced to work that
Jawaban:
1. so
2. such
3. so
4. such
5.such
6. such
7. so
8. such
9. such
10. so
Penjelasan:
Jawaban:
1. so
2. so
3. so
4. so
5. such
6. such
7. so
8. such
9. such
10. so
maaf kalo ada yg salah
9. 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
10. Find x so that the distance between the points (-2,-3) and (-8,-x) is equal to 10. How far up is heaven?
Jawaban:
Find x so that the distance between the points (-2,-3) and (-8,-x) is equal to 10. How far up is heaven?
11. basket holds nine flowers: two are pink, three are yellow and four are red. Four of these flowers are chosen at random. Find the probability that at least two of them are red.
Jawab:
Penjelasan dengan langkah-langkah:
12. 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
13. TOLONG BANTU YA KAK!Find x so that the distance between the points (-2,-3) and (-8,-x) is equal to 10.
D=√(x2-x1)²+(y2-y1)²
D²=(x2-x1)²+(y2-y1)²
10²=(-8+2)²+(-x+3)²
100=36+(x-3)²
(x-3)²=64
(x-3)²=(±8)²
x-3=8 or x-3=-8
x=11 or x=-5
14. It p and q are whole numbers such that p x q = 37, find the value of p + q. Explain your answer.
p dan q adalah whole number (bilangan cacah).
bilangan cacah = 0,1,2,3,....
karena p×q = 37 dan 37 prima, maka kemungkinan p dan q nya adalah 1 dan 37 sebab 1×37 = 37.
misal p = 1, dan q = 37 (dibalik juga boleh).
maka, p+q = 1+37 = 38
15. 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
16. There are four birds _____ the tree. *10 pointsinonatunder
Jawaban:
In
Penjelasan:
There are four birds in the tree.
Jawaban:
There are four birds in the tree
17. 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}
18. A curve is such that dy/dx =3x² + kx where k is a constant. Given that the curve passes through the points (1,6) and (2, 1), find a) the value of k b) the equation of the curve.
mungkin seperti itu ...
jawab:
integral dy = y = f(x)
[tex]{x}^{3} + \frac{k}{2} {x}^{2} + c[/tex]
point (1,6) ->
[tex]f(1) = {1}^{3} + \frac{k}{2} {1}^{2} + c = 6 \\ = > 1 + \frac{k}{2} + c = 6 \\ = > 2 + k + 2c = 12 \\ = > k + 2c = 10...(i)[/tex]
point (2,1)
[tex]f(2) = {2}^{3} + \frac{k}{2} {2}^{2} + c = 1 \\ = > 8 + 2k + c = 1 \\ = > 2k + c = - 7...(ii)[/tex]
from (i) and (ii):
3c = 27 --> c = 9
a. the value of k --> k = 10-18= -8
b. the equation of the curve:
[tex]f(x) = {x}^{3} - 4 {x}^{2} + 9[/tex]
19. Find x so that the distance between the points (-2,-3) and (-8,-x) is equal to 10.
Penjelasan dengan langkah-langkah:
distance [tex]=\sqrt{(-2-(-8))^2+(-3-(-x))^2}[/tex]
[tex]10=\sqrt{6^2+(-3+x)^2}[/tex]
[tex]100=36+(x^2-6x+9)[/tex]
[tex]x^2-6x+45-100=0[/tex]
[tex]x^2-6x-55=0[/tex]
[tex](x-11)(x+5)=0[/tex]
[tex]x_1=11[/tex]
[tex]x_2=-5[/tex]
So, x is -5 or 11.
20. 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
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