Plsss help asap no wrong answers pls
1 answer:
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Answer:
the absolute maximum value is 89.96 and
the absolute minimum value is 23.173
Step-by-step explanation:
Here we have cotangent given by the following relation;
so that the expression becomes
f(t) = 9t +9/tan(t/2)
Therefore, to look for the point of local extremum, we differentiate, the expression as follows;
f'(t) = =
Equating to 0 and solving gives
Where n is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively
Or we have by chain rule
f'(t) = 9 -(9/2)csc²(t/2)
Equating to zero gives
9 -(9/2)csc²(t/2) = 0
csc²(t/2) = 2
csc(t/2) = ±√2
The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or
in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2
We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;
f(x) for x = π/4, π/2, 3π/2, 7π/2
f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965
f(π/2) = 9·π/2 +9/tan(π/4) = 23.137
f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412
f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96
Therefore the absolute maximum value = 89.96 and
the absolute minimum value = 23.173.
Answer:
23
Step-by-step explanation:
From the graph, derive the best fit equation :
Using the points ;
(0,2.5) (100 ,35)
x1 = 0 ; y1 = 2.5 ; x2 = 100 ; y2 = 35
Slope formula, m = (y2-y1)/(x2-x1)
m = (35-2.5)/(100-0)
m= (32.5)/100
m = 0.325
The y intercept, value on the graph where best fit line crosses the y axis = 2.5
The equation :
y = mx + c
c = intercept ; m = slope
y = 0.325x + 2.5
y = Number of cars
x = number of customers
The number of customers if there are 10 cars parked :
10 = 0.325x + 2.5
10 - 2.5 = 0.325x
7.5 = 0.325x
x = 7.5 / 0.325
x = 23.076
x = 23
