Answer:
98 degrees
Step-by-step explanation:
HJ = (5x - 7)
Because it's a full circle:
61 + 34 + (5x - 7) + (9x - 22) = 360
95 + (14x - 29) = 360
14x = 360 - 95 + 29 = 294
x = 21
HJ = 5x - 7 = 5 * 21 - 7 = 105 - 7 = 98
Answer:
(i) 
(ii) 
(iii) $36.5
Step-by-step explanation:
Given that:
1. Total Number of fruits = 80
2. Number of mangoes = x
3. Both mangoes and oranges are there in the basket.
Solution (i):
Only mangoes and oranges are there in the basket and the basket is full.
so, Number of mangoes + Number of oranges = Total number of fruits
x + Number of oranges = 80
Number of oranges = 
Solution (ii):
<u>Given:</u>
Cost of an orange = 50 cents = $0.50
Cost of a mango = 40 cents = $0.40
Cost for x mangoes = 
Cost for (
) oranges = 

Solution (iii):
Put value of x = 35 in S(x)

Hence, answers are:
(i) 
(ii) 
(iii) $36.5
F(x) is a piecewise function defined as:
f(x) = (3/2)x when 0 <= x <= 2
or
f(x) = -(3/2)x+6 when 2 < x <= 4
g(x) is defined as:
g(x) = -(1/4)x+1 when 0 <= x <= 4
Based on the graph or through the equations we can say:
f(1) = (3/2)*1 = 1.5
g(1) = -(1/4)*1+1 = 0.75
f(3) = (3/2)*3 = 4.5
g(3) = -(1/4)*3+1 = 0.25
And the derivative values are:
f ' (1) = 3/2 = 1.5
f ' (3) = -3/2 = -1.5
g ' (1) = -1/4 = -0.25
g ' (3) = -1/4 = -0.25
which are the slopes of each line
So...
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x) ... product rule
h ' (1) = f ' (1)*g(1) + f(1)*g ' (1)
h ' (1) = 1.5*0.75 + 1.5*(-0.25)
h ' (1) = 0.75
and,
h(x) = f(x)*g(x)
h ' (x) = f ' (x)*g(x) + f(x)*g ' (x)
h ' (3) = f ' (3)*g(3) + f(3)*g ' (3)
h ' (3) = -1.5*0.25 + 4.5*(-0.25)
h ' (3) = -1.5