Find the inequalities system and find the maximum and minimum values for the objective quantity : z = x+ y
1. Find the inequalities system and find the maximum and minimum values for the objective quantity : z = x+ y
Sub Chapter : Inequalities
Ways/Answer : Put on the Pict
2. Find the maximum and minimum point for y=3+4x³-x⁴. Sketch the graph of the curve.
Jawab:
Penjelasan dengan langkah-langkah:
[tex]y = 3+4x^3 - x^4\\\\y' = 12x^2 - 4x^3 = 0\\\\x^3 - 3x^2 = 0\\\\x^2(x-3) = 0\\\\x = 0 \;\cup\; 3\\\\y'' = 24x - 12x^2 = 0\\\\x^2 - 2x = 0\\\\x(x-2) = 0\\\\x = 0 \;\cup\; 2\\\\y''' = 24-24x = 0 => x = 1\\\\ y'''' = -24\\\\\begin{minipage}{15em}berdasarkan turunan keempat, ketiga, kedua, dan pertama :\\\\- f(x) terbuka keatas dan memiliki minimum pada interval $0 < x < 2$ \\\\- f(x) terbuka kebawah dan \\memiliki maksimum pada \\interval $x < 0$ atau $x > 2$ \\\\\end{minipage}[/tex]
[tex]\begin{minipage}{15 em}- f(x) memiliki perubahan kecekungan parabola singgung terbesar pada x = 1\\\\- berdasarkan turunan kedua maka f(x) memiliki maksimum lokal di x = 3\\\\- x = 0 pada interval $ 0< x < 2 $ bukan merupakan maksimum maupun minimum, tetapi secara keseluruhan tanpa interval x = 0 merupakan minimum f(x) (karena maksimum f(x) sudah ditemukan)\end{minipage}[/tex]
[tex]\begin{minipage}{15 em}- Nilai turunan keempat negatif dan mempengaruhi sifat turunan diatasnya \\- f(x) monoton turun ketika $x > 3$ dan monoton naik untuk \\$x < 0 \;\cap\; 0<x<3$ \\(netral pada x = 0)\end{minipage}[/tex]
maximum = f(3), "minimum" = f(0) = 3 = titik potong sumbu y
maximum = 3+4(3)³ - 3⁴ = 30
3. Find the values of the unknown. Wayss
Jawaban:
x 27,5°
y 10°
Penjelasan dengan langkah-langkah:
tengkyuu ngabbb
4. Please help The equation of a curve is y=x^3+3x^2-9x+k, where k is a constant. i) Find the coordinates of the stationary points on the curve and their natures. ii) Find the values of k for which the curve has a stationary point on the x-axis. iii) Find the equation of the tangent to the curve at the point where the curve intersects the y-axis. iii) Find the set of values for x for which y=x^3+3x^2-9x+k is increasing function.
[tex]EQ\rightarrow\ y=x^3+3x^2-9x+k\\\\i.\\Stationary\ points:\\\ f(x)=x^3+3x^2-9x+k\\f'(x)=3x^2+6x-9\\f'(x)=0=3x^2+6x-9\\0=(3x-3)(x+3)\\x_1=1\\x_2=-3\\\\Nature:\\f'(x)=3x^2+6x-9\\f''(x)=6x+6\\for\ x=1\rightarrow\ f''(x)=12(positive)\\for\ x=-3\rightarrow\ f''(x)=-12(negative)\\hence\ x_2\ is\ the\ maximum\ point\ and\ x_1\ the\ minimum[/tex]
[tex]ii.\\subsititute\ x_1\ and\ x_2\ to\ f(x)\\x_1\rightarrow (1)^3+3(1)^2-9(1)+k=0\\k_{x_1}=5\\x_2\rightarrow (-3)^3+3(-3)^2-9(-3)+k=0\\k_{x_2}=-27[/tex]
[tex]iii.\\intersects \rightarrow\ x=0\\y=(0)^3+3(0)^2-9(0)+k\\y=k\\y=\ 5/-27\\f'(x)=3x^2+6x-9\\3(0)^2+6(0)-9\\hence\ m_{curve}=-9\\\\for\ k=5\\\rightarrow y-5=-9(x-0)\\\rightarrow y=-9x+5\\\\for\ k=-27\\\rightarrow y+27=-9(x-0)\\\rightarrow y=-9x-27[/tex]
[tex]iv.\\because\ x_2\ is\ the\ maximum\ point,\\the\ function\ will\ incerase\ up\ to\ that\ point.\\\\because\ x_1\ is\ the\ minimum\ point,\\the\ function\ will\ decrease\ up\ to\ that\ point.\\\\Hence,\ the\ set\ values\ for\ x\ which\ f(x)\ is\ incerasing\ are:\\(-\infty,-3)\ and\ (1,\infty)[/tex]
hope these helps :)
5. the lines 2x-5 = ky and (k+1)x = 6y-3 have the same gradient. Find the possible values of k.
Jawab:
Penjelasan dengan langkah-langkah:
2x - 5 = ky m1 = 2/k
(k + 1) x = 6y - 3
(k + 1) x + 3 = 6y m2 = (k + 1)/6
same gradient ⇒ m1 = m2
2/k = (k + 1) /6
2 = k (k + 1) /6
12 = k² + k
k² + k - 12 = 0
(k - 3) (k + 4) =
k = {-4, 3}
6. Find the values of p
f(x) = -x² + 14x + p²
a = -1
b = 14
c = p²
y max = 74
(b² - 4ac)/(-4a) = 74
[14² - 4 . (-1) . p²]/[-4 . (-1)] = 74
(196 + 4p²)/4 = 74
196 + 4p² = 74 . 4
196 + 4p² = 296
4p² = 296 - 196
4p² = 100
p² = 100 : 4
p = ±√25
p = ±5
7. Given that o is the centre of each of the followingcircles, find the values of the unknowns.
Penjelasan dengan langkah-langkah:
C² = 17²-13²
= 289 -169
= 120
C = √120
= 2√30
17² = 17²+16² -2.17.16.cosd
8. Find 10 Indonesian proverbs and write the cultural values
Proverbs is a simple and brief phrase that gives us advice based on practical experience and common sense. These are 10 common Indonesian proverbs and their values:
“Di mana kaki berpijak, di situ langit dijunjung.” The values of this proverbs are culture and society.“Sekali mendayung, dua tiga pulau terlampaui.” The values of this proverbs are opportunity and smart thinking.“Beruk di hutan disusukan, punai di tangan dilupakan.” The value of this proverbs is greed.“Kemalasan adalah kunci kemelaratan.” The values of this proverbs are opportunity and causal effect.“Siapa cepat, dia dapat.” The values of this proverbs are opportunity and dilligence.“Pikir dahulu pendapatan, sesal kemudian tiada guna.” The value of this proverbs is carelessness.“Air beriak tanda tak dalam.” The values of this proverbs are social and humanity.“Berat sama dipikul, ringan sama dijinjing.” The values of this proverbs are community and teamwork.“Pagar makan tanaman.” The values of this proverbs are socials and family.“Jauh di mata, jauh di hati.” The value of this proverbs is relationship.PembahasanProverbs adalah pepatah dalam bahasa Inggris. Sehingga, jika makna pepatah berbahasa Indonesia di atas kita alih bahasa, maka kita akan menemukan English proverbs yang setara, sesuai dengan urutan nomornya:
“When in Rome, do as Romans do.”“Make a hay while the sun shines.”“A bird in hand is worth two in the bush.”“When you lie on roses while young, you’ll lie on thorns while you’re old.”“The early birds catches the worm.”“Look before you leap.”“Barking dogs never bite.”“Birds of feather flock together.”“The rotten apple injures its neighbors.”“Out of sight, out of mind.”Pelajari lebih lanjutMateri tentang 15 contoh proverbs dan artinya https://brainly.co.id/tugas/15897846Materi tentang social function dari proverbs https://brainly.co.id/tugas/10163609Materi tentang 10 proverb https://brainly.co.id/tugas/9889125Detail jawabanKelas : SMA
Mapel : Bahasa Inggris
Bab : Proverbs
Kode : -
#AyoBelajar #SPJ2
9. The LCM of 9, 12 and n is 252. If n is odd, find all the possible values of n.
Jawab:
Penjelasan dengan langkah-langkah:
9 = 3²
12 = 2² x 3
LCM (n, 9, 12) = 252
252 = 3² x 2² x n
252 = 9 x 4 x n
n = 252/36
n = 7
The possible values of n are :
n₁ = 7
n₂ = 2 x 7 = 14
n₃ = 3 x 7 = 21
n₄ = 2² x 7 = 28
n₅ = 2 x 3 x 7 = 42
n₆ = 3² x 7 = 63
n₇ = 2² x 3 x 7 = 84
n₈ = 2 x 3² x 7 = 126
n₉ = 2² x 3² x 7 = 252
10. two forces of magnitude 3N and 7N respectively act on body. What are the maximum and minimum resultant forces that act on the body?
Jawaban:
Max = 10 N
Min = 4 N
Penjelasan:
If there are two force act on the same body, the value will be maximum if both of them in same direction so we can add to calculate. Otherwise if one another isn't in same direction, it will be minimum (because we can subtract the big one with the little one)
11. The values of the expression ax^2+bx+1 are 1 and 4 when x takes the value of 2 and 3 respectively. Find the value of the expression when x=4
Jawab:
9
Penjelasan dengan langkah-langkah:
Given : ax^2 + bx + 1 = y, (x,y) = (2,1) and (3,4)
if x = 2 , y = 1
then 4a + 2b + 1 = 1
4a + 2b = 0
-2a = b........(1)
if x = 3, y =4
then 9a + 3b + 1 = 4
9a + 3b = 3
3a + b = 1........(2)
(subtitute (1) to (2))
3a -2a = 1,
a = 1 and b = -2
so, the new equation is x^2 -2x + 1
x = 4, then 16 - 8 + 1 = 9
12. from the weather forecast of big cities in the world,the maximum and the minimum temperature are:swiss:minimum -5 c and maximum 18 c ,bombay :minimum 17 c and maximum 34 c : paris:minimum -3 c and maximum 17 c ,Hongkong minimum -2 c and maximum 25 c. which city has the greatest temperature's differences
bombay and Paris city's
13. Find the values of the unknown in each of the following figures:
Jawaban:
segitiga bca = segitiga sama kaki
jika sudut B= 27° maka sudut A= 27°
sehingga sudut C= 180°- 27°-27°=126°
sudutACD=180°-126°=54°
Penjelasan dengan langkah-langkah:
semoga membantu :)
14. the lcm of 6, 12 and n is 660. Find the possible values of n.
sorry if wrong
I hope this helps.....
:):)
15. The diatance between the points (14,0) and ( 5 , y ) is 15 units , find the possible values of y
Jawaban:
y=12
Penjelasan dengan langkah-langkah:
Jarak antara titik (14,0) dan (5,y) adalah 15 satuan, tentukan nilai y yang memungkinkan
---------------------------------------------------------------------
(5-14,y-0)
=(-9,y)
Jarak terdekat antara dua titik menggunakan pitagoras
c²=a²+b²
a²=c²-b²
[tex]a = \sqrt{ {c}^{2} - {b}^{2} } [/tex]
[tex]y = \sqrt{ {15}^{2} - {( - 9)}^{2} } [/tex]
[tex]y = \sqrt{225 - 81} [/tex]
[tex]y = \sqrt{144} [/tex]
y=12
16. 2. In the diagram, PRT and QRS are straight lines. Find the values of a and b.
Jawaban:
a= 75
b= 23
Penjelasan dengan langkah-langkah:
Cari PRQ:
= 180°-26°-79°
= 154°-79°
= 75°
Karena betolak belakang, maka a= 75.
180= a + b + 82
98= a + b
98= 75 + b
23= b
17. The sum of two numbers x and y is 82. Find the maximum value of its p. Where p = xy
x + y = 82
nilai kali maksimal = 82/2 = 41
p = xy = (41×41) = 1681Bahasa Indonesia
untuk membuat hasil kali tertinggi
maka selisih x dan y harus sekecil mungkin
selisih terkecil = 0
berarti x = y
x + y = 82
x + x = 82
2x = 82
x = 82:2
= 41
y = 41
P = xy
= 41 x 41
= 1681
Bahasa Inggris (In English)
we wanted to make the highest possible of the product
which means the difference of x and y must be as least as possible
smallest difference = 0
which means x = y
x + y = 82
x + x = 82
2x = 82
x = 82:2
= 41
y = 41
P = xy
= 41 x 41
= 1681
18. Given that m-n=6 and 4m+ n= 4, find the values of m and n.
Jawaban:
m=2/-3 n=20/3
Penjelasan dengan langkah-langkah:
Eliminasi
m-n=6
4m+n=4
_______ -
-3m = 2
m= 2/-3
substitusi
m-n= 6
2/-3-n=6
n=6+2/3
n=20/3
19. Find the sum of the values of the digit 8 in 83 845 is................
Jawaban:
8+8 =16
semoga membantu tolong jadikab jawaban tercerdas
20. Find the value of 1/2 for given values of x
Jawaban:
tidak tau jajajamkslsos0soakkanabjaidjd
Penjelasan dengan langkah-langkah:
shdjsjsksklalapqlm2oe8urndjkslapa0papa
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