Answer:
Slope is 1/4 (0.25) while y-intercept is 5
Step-by-step explanation:
Here, we are interested in getting the y intercept and slope of the line joining the given points.
We can get the slope by using any two points
Let’s say (4,6) and (12,8)
Mathematically; slope
= (y2-y1)/(x2-x1) = (8-6)/(12-4) = 2/8 = 1/4 = 0.25
To get the y-intercept, we proceed
kindly recall that the equation of a straight line is;
y = mx + c
where m is the slope and c is the y-intercept
Let’s take any of the points (28,12)
Thus:
12 = 0.25(28) + c
12 = 7 + c
c = 12-7
c = 5
D. (8, -22) is the correct answer
Step-by-step explanation:
g(t) = (t + 1)² − 20.25
0 = (t + 1)² − 20.25
20.25 = (t + 1)²
±4.5 = t + 1
t = -1 ± 4.5
t = -5.5 or 3.5
The zeros are (-5.5, 0) and (3.5, 0).
Answer:
i)W = 2500 / T
ii) W = 500 Tons
iii) grad W(10°) = - 25î
iv) The formulation is not practical
Step-by-step explanation:
i) Write an equation describing the use of coal
As use of coal is inversely proportional to the average monthly temperature
if W is use of coal in tons/per month then
W(t) = k / T where k is a constant of proportionality and T is the average temperature in degrees. We have to determine k from given conditions
k = ?? we know that when T = 25° W = 100 tons the by subtitution
W = k/T 100 = k /25 k = 2500 Tons*degree
Then final equation is:
W = 2500 / T
ii) Find the amount of coal when T = 5 degrees
W = 2500 / 5
W = 500 Tons
iii)
The inverse proportionality implies that W will decrease as T increase.
The vector gradient of W function is:
grad W = DW(t)/dt î
grad W = - 2500/T² î
Wich agrees with the fact that W is decreasing.
And when T = 100°
grad W(10°) = - 2500/ 100 î ⇒ grad W(10°) = - 25î
iv) When T = 0 The quantity of coal tends to infinite and the previous formulation is not practical
