Answer:
3x+24 more widgets
Step-by-step explanation:
A company owns two manufacturing plants:
1st plant: 8x+17 widgets;2nd plant: 5x-7 widgets.
To find how many more items the first plant produces daily than the second plant, we have to subtract from the number of widgets the first plant produces the second plant produces. So,
(8x+17)-(5x-7)\\ \\=8x+17-5x+7\ [\text{Eliminate brackets}]\\ \\=(8x-5x)+(17+7)\ [\text{Combine the like terms}]\\ \\=3x+24
hope this helps!
Step-by-step explanation:
Answer:
x = 7
Step-by-step explanation:
Notice that in the triangle, the angle is either known or in terms of x. This means we can make an equation: 82 + (9x - 6) + (6x - 1) = 180. Now, add up tthe terms to get 15x + 75 = 180, or 15x = 105 or x = 7.
Answer:
b
Step-by-step explanation:
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
Recall that
There are three cases to consider:
(1) When
, we have
and
, so
(2) When
and
, we get
and
, so
(3) When
, we have
and
, so
So
