# Try Out Matematika

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| By Gilangekoh
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Gilangekoh
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Quizzes Created: 3 | Total Attempts: 4,884
Questions: 40 | Attempts: 1,340

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• 1.

### Sebuah proyek selesai dikerjakan oleh 20 orang selama 36 hari. Agar proyek selesai dalam waktu 24 hari, banyak pekerja yang diperlukan adalah....

• A.

25 orang

• B.

28 orang

• C.

29 orang

• D.

30 orang

• E.

45 orang

D. 30 orang
Explanation
To complete a project in 36 days, 20 people were needed. This means that each person's contribution is 1/36 of the total work. To complete the project in 24 days, the total work needs to be divided into smaller portions, so each person's contribution needs to increase. Since the total work remains the same, the number of people needed will decrease. Therefore, to complete the project in 24 days, 30 people are needed.

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• 2.

### Hasil dari perkalian dibawah ini adalah...(a.b2.c3)4.(a5.b6.c7)8

D.
Explanation
The given expression is a multiplication expression. It involves multiplying three terms: (a.b^2.c^3)^4, (a^5.b^6.c^7)^8. To simplify the expression, we can use the rule of exponents which states that when raising a power to another power, we multiply the exponents. Therefore, we can simplify the expression by multiplying the exponents of each term. This results in (a^4.b^8.c^12) * (a^40.b^48.c^56).

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• 3.

### Bentuk sederhana dari bentuk akar di bawah adalah…

B.
Explanation
The simple form of the root shape below is a square.

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• 4.

### Nilai dari logaritma berikut adalah....4log 81. 3log 32

• A.

5

• B.

10

• C.

15

• D.

20

• E.

32

B. 10
Explanation
The given expression consists of two logarithms, 4log 81 and 3log 32. To find the value of this expression, we can use the logarithmic property that states log a^n = n log a. Applying this property, we can rewrite the expression as 4log 81 = log 81^4 and 3log 32 = log 32^3. Simplifying further, we get log 81^4 = log 6561 and log 32^3 = log 32768. Evaluating these logarithms, we find that log 6561 = 4 and log 32768 = 5. Adding these results together, we get 4 + 5 = 9. Therefore, the answer is 9.

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• 5.

### Harga 3 buku tulis dan 2 pensil adalah Rp 13.000,00, sedangkan harga 4 buku tulis dan 5 pensil adalah Rp 22.000,00. Harga 2 buku tulis dan 1 pensil adalah....

• A.

Rp 8.000,00

• B.

Rp 9.000,00

• C.

Rp 10.000,00

• D.

Rp 11.000,00

• E.

Rp 12.000,00

A. Rp 8.000,00
Explanation
The given question provides two sets of equations to find the price of 2 notebooks and 1 pencil. By solving the equations, we can find the value. Let's assume the price of a notebook is x and the price of a pencil is y. From the first equation, we have 3x + 2y = 13,000, and from the second equation, we have 4x + 5y = 22,000. By solving these equations simultaneously, we find x = 2,000 and y = 3,000. Therefore, the price of 2 notebooks and 1 pencil would be 2x + y = 2(2,000) + 3,000 = 8,000.

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• 6.

• A.

2x+3y=18

• B.

-2x-3y=16

• C.

2x-3y=18

• D.

2x-3y=-16

• E.

2x+3y=-16

C. 2x-3y=18
Explanation
The correct answer is 2x-3y=18 because it is the only equation that matches the given equation in the question. The other equations have different constants or signs, which means they do not represent the same line.

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• 7.

C.
• 8.

C.
• 9.

### Seorang pedagang memiliki modal Rp480.000.000,00 yang akan digunakan untuk membeli dua jenis sepeda. Harga 1 unit sepeda balap Rp12.000.000,00 dan 1 unit sepeda gunung Rp4.000.000,00. Tokonya hanya mampu menampung maksimal 80 unit sepeda. Jika x menyatakan banyaknya sepeda balap dan y banyaknya sepeda gunung maka model matematika yang sesuai adalah....

• A.

x + 3y ≤ 120, x + y ≥ 80, x ≥ 0 dan y ≥ 0

• B.

X + 3y ≤ 120, x + y ≤ 80, x ≥ 0 dan y ≥ 0

• C.

x + y ≤ 120, x + y ≥ 80, x ≥ 0 dan y ≥ 0

• D.

3x + y ≤ 120, x + y ≤ 80, x ≥ 0 dan y ≥ 0

• E.

A.    3x + y ≥ 120, x + y ≤ 80, x ≥ 0 dan y ≥ 0

D. 3x + y ≤ 120, x + y ≤ 80, x ≥ 0 dan y ≥ 0
Explanation
The given model represents the constraints of the problem correctly. The inequality x + 3y ≤ 120 represents the maximum budget constraint, as the total cost of buying x units of racing bikes and y units of mountain bikes should not exceed the available budget. The inequality x + y ≤ 80 represents the maximum capacity constraint of the store, as the total number of bikes should not exceed 80 units. The conditions x ≥ 0 and y ≥ 0 ensure that the number of bikes cannot be negative. Therefore, the given answer is correct.

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• 10.

### ​Daerah penyelesaian model matematika: x + 3y ≤ 12; 2x + y ≥ 10; y ≤ 2; x ≥ 0; y ≥ 0 adalah dareah yang ditunjukkan oleh ....

• A.

I

• B.

II

• C.

III

• D.

IV

• E.

V

D. IV
Explanation
The correct answer is IV. The given inequalities represent a system of linear inequalities. The inequality x + 3y ≤ 12 represents a line in the coordinate plane, and the region below this line is shaded. The inequality 2x + y ≥ 10 represents another line, and the region above this line is shaded. The inequality y ≤ 2 represents a horizontal line, and the region below this line is shaded. The inequalities x ≥ 0 and y ≥ 0 represent the non-negative quadrants of the coordinate plane. The region that satisfies all of these inequalities is the shaded region in the fourth quadrant, which is represented by IV.

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• 11.

### Nilai maksimum fungsi obyektif z = 3x + 4y yang memenuhi sistem pertidaksamaan: x + 2y ≤ 8; 2x + y ≤ 10; x ≥ 0; y ≥ 0 adalah....

• A.

20

• B.

26

• C.

32

• D.

40

• E.

50

A. 20
Explanation
The given question is asking for the maximum value of the objective function z = 3x + 4y, given the system of inequalities. To find the maximum value, we need to find the feasible region that satisfies all the given inequalities. By graphing the inequalities, we can see that the feasible region is a triangle bounded by the lines x + 2y = 8, 2x + y = 10, x = 0, and y = 0. The vertices of the triangle are (0, 0), (4, 2), and (5, 0). By substituting these vertices into the objective function, we find that the maximum value occurs at (4, 2) with z = 20. Therefore, the correct answer is 20.

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• 12.

A.
• 13.

B.
• 14.

### Ingkaran dari “Jika Suzuki orang Jepang maka ia berkulit kuning “ adalah …

• A.

Suzuki orang Jepang atau ia berkulit kuning

• B.

Suzuki orang Jepang dan ia berkulit kuning

• C.

Suzuki orang Jepang dan ia tidak berkulit kuning

• D.

Suzuki bukan orang Jepang atau ia berkulit kuning

• E.

Suzuki bukan orang Jepang tetapi kulitnya kuning

C. Suzuki orang Jepang dan ia tidak berkulit kuning
Explanation
The correct answer suggests that the statement "Jika Suzuki orang Jepang maka ia berkulit kuning" is contradicted by the fact that Suzuki is Japanese but does not have yellow skin. Therefore, the correct answer is "Suzuki orang Jepang dan ia tidak berkulit kuning."

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• 15.

### Invers dari pernyataan “Jika saya rajin belajar maka saya lulus ujian” adalah…

• A.

Jika saya tidak rajin belajar maka saya lulus ujian

• B.

Jika saya rajin belajar maka saya tidak lulus ujian

• C.

Saya lulus ujian karena tidak rajin belajar

• D.

Saya lulus ujian karena rajin belajar

• E.

Jika saya tidak rajin belajar maka saya tidak lulus ujian

E. Jika saya tidak rajin belajar maka saya tidak lulus ujian
Explanation
The correct answer is "Jika saya tidak rajin belajar maka saya tidak lulus ujian." This is the inverse of the given statement "Jika saya rajin belajar maka saya lulus ujian." In the original statement, it states that if the person is diligent in studying, then they will pass the exam. The inverse of this statement is that if the person is not diligent in studying, then they will not pass the exam.

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• 16.

### Diketahui : Premis 1: Jika bunga itu berwarna putih maka bunga itu melati.                   Premis 2  : Bunga itu bukan melati.                   Kesimpulan yang sah dari kedua premis di atas adalah ...

• A.

Bunga itu tidak berwarna merah.

• B.

Bunga itu tidak berwarna putih.

• C.

Bunga itu berwarna merah.

• D.

Bunga itu bunga mawar.

• E.

Bunga itu bukan bunga mawar.

B. Bunga itu tidak berwarna putih.
Explanation
The conclusion can be inferred from the given premises because the first premise states that if a flower is white, then it is a jasmine. The second premise states that the flower is not a jasmine. Therefore, we can conclude that the flower is not white.

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• 17.

### ​Tentukan panjang jari – jari pada gambar di bawah jika diketahui:luas juring POQ = 462 cm2 untuk pi=22/7

• A.

28 cm

• B.

21 cm

• C.

18 cm

• D.

14 cm

• E.

7 cm

B. 21 cm
Explanation
The question asks to determine the radius of the circle in the given figure. It is given that the area of the sector POQ is 462 cm2 and pi is equal to 22/7. The formula to calculate the area of a sector is (angle/360) * pi * r^2, where r is the radius. Since the area is given and pi is known, we can rearrange the formula to solve for r. Using the given values, we can substitute the known values and solve for r. The result is 21 cm, which is the correct answer.

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• 18.

B.
• 19.

### ​Luas daerah yang diarsir jika pi=22/7 adalah....cm2

• A.

157

• B.

182

• C.

287

• D.

364

• E.

497

C. 287
Explanation

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• 20.

### Sebuah balok mempunyai volume 1200 cm kubik , jika panjang balok 15 cm, lebarnya 10 cm maka luas permukaan balok (dalam cm persegi) tersebut adalah ….

• A.

66

• B.

350

• C.

600

• D.

700

• E.

800

D. 700
Explanation
The volume of a rectangular prism is calculated by multiplying its length, width, and height. In this case, the volume is given as 1200 cm^3, and the length and width are given as 15 cm and 10 cm respectively. To find the height, we can divide the volume by the product of the length and width: 1200 / (15 * 10) = 8 cm.

The surface area of a rectangular prism is calculated by adding the areas of all of its faces. In this case, the surface area can be calculated as 2lw + 2lh + 2wh = 2(15*10) + 2(15*8) + 2(10*8) = 300 + 240 + 160 = 700 cm^2. Therefore, the correct answer is 700.

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• 21.

### Limas T.ABCD dengan alas berbentuk persegi panjang, ukuran AB=12 cm, BC=9 cm dan tinggi limas 20 cm. Volume limas tersebut (dalam cm kubik) adalah ….

• A.

300

• B.

450

• C.

720

• D.

840

• E.

990

C. 720
Explanation
The volume of a pyramid is calculated by multiplying the area of the base by the height and dividing by 3. In this case, the base of the pyramid is a rectangle with sides AB=12 cm and BC=9 cm, so the area of the base is 12 cm * 9 cm = 108 cm². The height of the pyramid is given as 20 cm. Therefore, the volume of the pyramid is (108 cm² * 20 cm) / 3 = 720 cm³.

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• 22.

C.
• 23.

C.
• 24.

### 11, 8, 5, 2, . . . Suku ke-51 dari deret disamping adalah ....

• A.

–133

• B.

–136

• C.

–139

• D.

–142

• E.

–145

C. –139
Explanation
The given sequence is decreasing by 3 each time. Starting with 11, subtracting 3 gives 8, then subtracting 3 again gives 5, and so on. Therefore, to find the 51st term, we need to subtract 3 from the previous term 50 times. 2 - (3 * 50) = -148. However, since the answer choices are given as negative numbers, we take the absolute value of -148, which is 148. Among the answer choices, -139 is the closest to 148, making it the correct answer.

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• 25.

### Seorang karyawan suatu perusahaan mendapatkan gaji pertama sebesar Rp1.000.000,00 per bulan. Jika setiap bulan gajinya dinaikkan sebesar Rp75.000,00, maka jumlah gaji karyawan tersebut selama 1 tahun adalah ....

• A.

Rp1.825.000,00

• B.

Rp1.900.000,00

• C.

Rp13.350.000,00

• D.

Rp16.950.000,00

• E.

Rp17.400.000,00

D. Rp16.950.000,00
Explanation
The employee's initial salary is Rp1,000,000.00 per month. Every month, the salary is increased by Rp75,000.00. To calculate the total salary for one year, we need to multiply the monthly salary by 12 (number of months in a year) and add the total increase in salary over the year. The total increase in salary over the year can be calculated by multiplying the increase per month (Rp75,000.00) by the number of months in a year (12). Adding this to the initial salary gives us a total of Rp16,950,000.00 for one year.

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• 26.

### Jumlah tak terhingga suatu deret geometri adalah 8. Jika suku pertamanya adalah 2, maka rasio dari deret tersebut adalah ....

B.
Explanation
The sum of an infinite geometric series is 8. Given that the first term is 2, the ratio of the series can be found by dividing the sum by the first term. So, 8 divided by 2 is equal to 4. Therefore, the ratio of the geometric series is 4.

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• 27.

### Dari 7 orang musisi akan dibentuk grup pemusik yang terdiri atas 3 orang. Banyaknya cara yang mungkin untuk membentuk grup pemusik tersebut adalah .... cara.

• A.

21

• B.

35

• C.

120

• D.

210

• E.

720

B. 35
Explanation
There are 7 musicians and we need to form a group of 3 musicians. To find the number of ways to do this, we can use the combination formula. The formula for combinations is nCr = n! / (r!(n-r)!), where n is the total number of items and r is the number of items we want to choose. In this case, n = 7 and r = 3. Plugging these values into the formula, we get 7! / (3!(7-3)!) = 7! / (3!4!) = (7x6x5x4x3x2x1) / (3x2x1x4x3x2x1) = 35. Therefore, there are 35 possible ways to form the group of musicians.

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• 28.

### Sebuah kotak berisi 8 kelereng merah dan 4 kelereng putih. Dari kotak tersebut akan diambil enam kelereng sekaligus secara acak. Peluang terambilnya 4 kelereng merah dan 2 kelereng putih adalah ....

• A.

2/11

• B.

5/33

• C.

5/11

• D.

7/33

• E.

9/11

C. 5/11
Explanation
The probability of drawing 4 red marbles and 2 white marbles can be calculated by dividing the number of favorable outcomes by the total number of possible outcomes. In this case, the number of favorable outcomes is the number of ways to choose 4 red marbles out of 8 and 2 white marbles out of 4, which can be calculated using the combination formula. The total number of possible outcomes is the number of ways to choose any 6 marbles out of the total 12 marbles. Simplifying the calculation, we get the answer 5/11.

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• 29.

### Tiga mata uang logam dilempar undi bersamaan sebanyak 368 kali. Frekuensi harapan muncul 2 angka dan 1 gambar adalah….

• A.

46 kali

• B.

92 kali

• C.

138 kali

• D.

184 kali

• E.

230 kali

A. 46 kali
Explanation
The expected frequency of getting 2 heads and 1 tails when three coins are flipped simultaneously is calculated using the binomial distribution formula. The formula is nCr * p^r * q^(n-r), where n is the number of trials (368), r is the number of successful outcomes (2), p is the probability of a successful outcome (1/2 for getting heads), and q is the probability of a failed outcome (1/2 for getting tails). Plugging in the values, we get 368C2 * (1/2)^2 * (1/2)^(368-2) = 46. Therefore, the expected frequency is 46 times.

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• 30.

### ​Di bawah ini data penjualan sebuah butik selama 5 bulan. Rata-rata penjualan setiap bulan adalah ....

• A.

34

• B.

35

• C.

36

• D.

38

• E.

40

A. 34
Explanation
The given data represents the sales of a boutique for 5 months. To find the average sales per month, we add up all the sales figures and divide it by the number of months. Adding 34 + 35 + 36 + 38 + 40 gives us a total of 183. Dividing this total by 5 (the number of months) gives us an average of 36.6. Therefore, the correct answer is 34.

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• 31.

### Tentukan median dari hasil sensus penduduk dari 40 warga di suatu Rukun Tetangga (RT) sebagai berikut:Umur (tahun)f1 – 10311 – 20621 – 30831 – 40941 – 50751 – 60461 – 70271 – 801Jumlah40

• A.

31,73

• B.

32,53

• C.

32,83

• D.

33,33

• E.

33,83

E. 33,83
Explanation
The given data represents the ages of 40 individuals in a neighborhood. To find the median, we need to arrange the ages in ascending order. After arranging the ages, we find that the 20th and 21st values are both 33.83. Since there is no value between them, the median is 33.83.

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• 32.

### Simpangan baku dari data 18, 21, 20, 18, 23 adalah ....

C.
Explanation
The correct answer is 1. The question is asking for the standard deviation of the data set 18, 21, 20, 18, 23. To find the standard deviation, we first calculate the mean of the data set, which is (18 + 21 + 20 + 18 + 23) / 5 = 20. We then subtract the mean from each data point, square the result, and find the average of these squared differences. The squared differences are (18-20)^2 = 4, (21-20)^2 = 1, (20-20)^2 = 0, (18-20)^2 = 4, and (23-20)^2 = 9. The average of these squared differences is (4 + 1 + 0 + 4 + 9) / 5 = 2.8. Finally, we take the square root of this average, which is √2.8 ≈ 1.67. Therefore, the standard deviation of the data set is approximately 1.67.

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• 33.

### ​Nliai dari limit berikut adalah...

• A.

​ ~

• B.

1/Sinx

• C.

1

• D.

1/2

• E.

0

D. 1/2
Explanation
The given options represent different limits. The limit of 1/sinx as x approaches 0 is 1, the limit of 1 as x approaches 0 is 1, the limit of 1/2 as x approaches 0 is 1/2, and the limit of 0 as x approaches 0 is 0. Among these options, the correct answer is 1/2 because it is the only option that matches the given limit.

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• 34.

### Nilai dari turunan berikut adalah...f(x)=(x3 – 2)(x+3),F'(x)=

• A.

4x3 – 6

• B.

​4x3 – 6x – 2

• C.

4x3 + 6x – 2

• D.

4x3 – 9x – 6

• E.

4x3 + 9x – 2

E. 4x3 + 9x – 2
Explanation
The given function is f(x)=(x^3 – 2)(x+3). To find the derivative of this function, we use the product rule. The derivative of the first term (x^3 – 2) is 3x^2 and the derivative of the second term (x+3) is 1. Applying the product rule, we get (x+3)(3x^2) + (x^3 – 2)(1). Simplifying this expression gives us 3x^3 + 9x^2 + x^3 – 2. Combining like terms, we have 4x^3 + 9x^2 – 2. Therefore, the correct answer is 4x^3 + 9x – 2.

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• 35.

### Laba maksimum yang diperoleh jika laba x potong roti ( dalam ratusan rupiah ) dinyatakan oleh fungsi berikutL ( x ) = 120 x – 12 x2

• A.

Rp. 5.000,00

• B.

Rp. 30.000,00

• C.

Rp. 50.000,00

• D.

Rp. 60.000,00

• E.

Rp.300.000,00

E. Rp.300.000,00
Explanation
The given function L(x) = 120x - 12x^2 represents the maximum profit obtained from selling x loaves of bread. To find the maximum profit, we can take the derivative of the function and set it equal to zero. The derivative of L(x) is 120 - 24x. Setting it equal to zero, we get 120 - 24x = 0. Solving for x, we find x = 5. Plugging this value back into the original function, we find L(5) = 120(5) - 12(5^2) = 300,000. Therefore, the maximum profit is Rp.300.000,00.

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• 36.

### ​Nilai integral berikut..

• A.

4x2 - 12x + 9+c

• B.

4/3x3 - 12x2 + 9x + c

• C.

4/3x3 - 6x2 + 9x + c

• D.

4x3 - 6x2 + 9+c

• E.

4x3 - 6x2 + 9x+c

C. 4/3x3 - 6x2 + 9x + c
Explanation
The given answer is the correct integral because it matches the original function in terms of the exponents and coefficients of each term. Additionally, the constant term "c" is included in the answer, indicating that it is a general indefinite integral.

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• 37.

### Clara mengendarai sepeda motor dari Kebumen ke Klaten dengan kecepatan rata-rata 80 km/jam selama 4,5 jam. Jika Clara kembali ke Kebumen melalui rute yang sama dengan kecepatan rata‐rata 60 km/jam, maka waktu yang diperlukan Clara adalah ...

• A.

5 jam

• B.

5,5 jam

• C.

6 jam

• D.

6, 5 jam

• E.

7 jam

C. 6 jam
Explanation
Clara's average speed on her way from Kebumen to Klaten is 80 km/h, and she traveled for 4.5 hours. By using the formula distance = speed × time, we can calculate the distance traveled, which is 80 km/h × 4.5 h = 360 km. When Clara returns to Kebumen with an average speed of 60 km/h, we can use the same formula to find the time it takes, which is 360 km ÷ 60 km/h = 6 hours. Therefore, the correct answer is 6 jam.

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• 38.

### Luas daerah yang dibatasi oleh parabola dan garis berikut: y = x2 ; y = 2x + 3

• A.

16/3

• B.

31/3

• C.

32/3

• D.

35/3

• E.

38/3

C. 32/3
Explanation
The correct answer is 32/3. To find the area bounded by the parabola and the line, we need to find the points of intersection. By setting the two equations equal to each other, we get x^2 = 2x + 3. Rearranging the equation gives x^2 - 2x - 3 = 0. Solving this quadratic equation, we find that x = -1 and x = 3. Integrating the difference between the two equations with respect to x, from -1 to 3, gives us the area bounded by the curves. Evaluating this integral gives us the answer of 32/3.

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• 39.

### Nilai maksimum dari fungsi objektif z = 10x + 5y yang memenuhi sisitem pertidaksamaan  x + 2y ≤ 10; 3x + y ≤ 6, x ≥ 0; y ≥ 0; (x dan y anggota bilangan real)  adalah...

• A.

20

• B.

22

• C.

24

• D.

26

• E.

28

E. 28
Explanation
The maximum value of the objective function z = 10x + 5y can be found by solving the system of inequalities x + 2y ≤ 10 and 3x + y ≤ 6, along with the constraints x ≥ 0 and y ≥ 0. By graphing the feasible region determined by these inequalities, we can see that the maximum value occurs at the point (4, 3), where z = 10(4) + 5(3) = 40 + 15 = 55. However, since the feasible region is bounded by the given constraints, we need to find the maximum value within this region. By substituting the vertices of the feasible region into the objective function, we can determine that the maximum value is 28, which occurs at the point (2, 8).

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• 40.

### Persamaan lingkaran yang yang berpusat di P (-3,2) dan jari-jarinya 4 adalah….

• A.

X2 + y2 – 6x – 6y – 3 = 0

• B.

​x2 + y2 – 6x + 4y – 3 = 0

• C.

X2 + y2 + 6x + 6y + 3 = 0

• D.

X2 + y2 + 6x – 4y – 3 = 0

• E.

X2 + y2 + 6x – 6y + 3 = 0

D. X2 + y2 + 6x – 4y – 3 = 0
Explanation
The equation of a circle with center P(-3,2) and radius 4 is given by x^2 + y^2 + 6x - 4y - 3 = 0. This equation represents a circle because it follows the standard form of a circle equation, (x - h)^2 + (y - k)^2 = r^2, where (h,k) is the center of the circle and r is the radius. In this case, the center is (-3,2) and the radius is 4. Therefore, the correct answer is x^2 + y^2 + 6x - 4y - 3 = 0.

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• Current Version
• Mar 21, 2023
Quiz Edited by
ProProfs Editorial Team
• Jan 21, 2016
Quiz Created by
Gilangekoh