(1) y² + x² = 53
(2) y - x = 5 ⇒ y = x + 5
subtitute (2) to (1)
(x + 5)² + x² = 53 |use (a + b)² = a² + 2ab + b²
x² + 2x·5 + 5² + x² = 53
2x² + 10x + 25 = 53 |subtract 53 from both sides
2x² + 10x - 28 =0 |divide both sides by 2
x² + 5x - 14 = 0
x² - 2x+ 7x - 14 = 0
x(x - 2) + 7(x - 2) = 0
(x - 2)(x + 7) = 0 ⇔ x - 2 = 0 or x + 7 = 0 ⇔ x = 2 or x = -7
subtitute the values of y to (2)
for x = 2, y = 5 + 2 = 7
for x = -7, y = 5 + (-7) = 5 - 2 = 3
Answer: x = 2 and y = 7 or x = -7 and y = 3
R(x) = 60x - 0.2x^2
The revenue is maximum when the derivative of R(x) = 0.
dR(x)/dx = 60 - 0.4x = 0
0.4x = 60
x = 60/0.4 = 150
Therefore, maximum revenue is 60(150) - 0.2(150)^2 = 9000 - 4500 = $4,500
Maximum revenue is $4,500 and the number of units is 150 units
Answer:
Adult= $11
Children = $7.5
Step-by-step explanation:
Let x represent adult ticket and y represent children ticket
2x + 3y= 44.50........equation 1
3x + 6y= 78........equation 2
From equation 1
2x + 3y= 44.50
2x= 44.50-3y
x= 44.50-3y/2
Substitute 44.50-3y/2 for x in equation 2
3x+ 6y= 78
3(44.50-3y/2) + 6y= 78
66.75- 4.5y +6y= 78
66.75 + 1.5y= 78
1.5y= 78-66.75
1.5y= 11.25
y= 11.25/1.5
y = 7.5
Substitute 7.5 for y in equation 1
2x + 3y = 44.50
2x + 3(7.5)= 44.50
2x + 22.5= 44.50
2x = 44.50-22.5
2x= 22
x= 22/2
x= 11
Hence the price of adult ticket is $11 and the price of children ticket is $7.5
Answer:
Since in option B, the bacteria are growing exponentially, B would be the correct answer to this question.
Step-by-step explanation:
Keeping in mind that the area of a circle is πr².
the actual area will just be the area of the rectangular backyard plus the pool, namely (10*20) + (π15²), which gives us an actual area of
200 + 225π.
now, we know the model and actual are on a 1:20 ratio.
