The polynomial x3+8 = (x+2)(x2-2x+4)
Given:
The equation of a line is:
A line parallel to the above line passes through the point P(2,5).
To find:
The equation of the parallel line.
Solution:
The slope intercept form of a line is:
...(i)
Where, m is the slope and b is the y-intercept.
The given equation is:
It can be rewritten as
...(ii)
On comparing (i) and (ii), we get
It means the slope of the given line is 4.
We know that the slopes of two perpendicular lines are equal. So, the slope of the required parallel line is also 4.
The parallel line passes through the point P(2,5) with slope 4, thus the equation of the parallel line is
Therefore, the equation of the required parallel line is .
Answer:
(a) When 400 donuts are made daily the company's profits is 250 dollars.
(b) The Company should produce 950 donuts daily in order to maximize its profits.
Step-by-step explanation:
Profit function P(x) = - 0.001 x² + 1.9x - 350
where p is the profit and x is the quantity of donuts made daily.
(a) If x = 400, the company's profit is:
P(x) = - 0.001 x² + 1.9x - 350
= - 0.001 (400)² + 1.9(400) - 350
=
= - 160 + 760 - 350
= 760 - 510
= 250
(b) The profit of a firm is maximum when MR = MC or MR - MC = 0 which is also known as break even point. In other words, at break-even point the profit function equals to zero. ∴,
Therefore, the Company should produce 950 donuts daily in order to maximize its profits.
(f ○ g)(0) = - 3
evaluate g(0) and substitute the value into f(x)
g(0) = 0 + 4 = 4
f(4) = 1 - 4 = - 3
thus (f ○ g)(0) = - 3
Perimeter = a + b + c = 30
Area = 1/2 x a x b = 30
Multiples of 30: 2, 3, 5, 6, 10, 12, 15
For perimeter c = 30- (a+b)
C= sqrt( a^2 + b^2)
Using the possible combinations of the above:
5 and 12:
C = sqrt(5^2 + 12^2) = 13
5 + 12 + 13 = 30 for the perimeter
Area = 1/2 x 5 x 12 = 30
The sides are 5, 12 and 13 cm