Answer:
Step-by-step explanation:
The equation of a straight line can be represented in the slope-intercept form, y = mx + c
Where c = intercept
For two lines to be perpendicular, the slope of one line is the negative reciprocal of the other line. The equation of the given line is
(5x-5y)/4= (4x-4)/2
Cross multiplying
2(5x - 5y) = 4(4x - 4)
10x - 10y = 16x - 16
10y = - 6x + 16
y = -6x/10 + 16/10
Comparing with the slope intercept form,
Slope, m = - 6/10
This means that the slope of the line that is perpendicular to it is 10/6
The given points are (10,7)
To determine c,
We will substitute m = 10/6, y = 7 and x = 10 into the equation, y = mx + c. It becomes
7 = 10/6 × 10 + c
7 = 100/6 + c
7 = 50/3 + c
c = 7 - 50/3
c = - 29/3
The equation becomes
y = 10x/6 - 29/3
Answer:
(D^2 + 9)y = cos 2x….(1). The corresponding homogeneous equation is (D^2 +9)y= 0,…(2), whose auxiliary equation is m^2 + 9 = 0, which has (+/-)3i as roots. The general solution of (2) is y = A.cos(3x) + B.sin(3x). Now to get a general solution of (1) we have just to add to the above, a particular solution of (1). One such solution is [cos(2x)]/[-2^2 +9] = (1/5).cos 2x. Hence a general solution of the given equation is given by y = A.cos(3x) + B.sin(3x) + (1/5)cos(2x), where A and B are arbitrary constants. The above solution incorporates all the solutions of the given equation.
Step-by-step explanation:
Answer:
Part A: after 9 days the radius of the algae would be 12.81mm so the domain is 9. you would plot the domain at (0,9)
Part B: the y-intercept (the 9) represents the amount of algae the experiment started off with.
Part C: the rate of change is 0.
Step-by-step explanation:
Answer:
Step-by-step explanation:
Somebody plays 30 times
L+W = 30, where L and W are number of losses and wins, respectively.
L = 30-W
Net after 30 plays is $6
2W - 1L = 6
2W - (30-W) = 6
3W = 36
W = 12
W = 18
17 wins
