Answer:
3.14
Step-by-step explanation:
Circumference of a circle is given by
and making 
the subject then
Here d is the diameter and C is the circumference.
Given that d=10cm and C=31.4 then
Answer:
the answer is 1: the illustration shows the captain's worry and the ship's distress
Answer:
B. Angle D and Angle E
C. Angle C and Angle F
Step-by-step explanation:
Alternative Interior angles are not adjacent and are at opposite sides of the transversal.
Answer:
A) (-8, -16)
B) (0, 48)
C) (-4, 0), (-12, 0)
Step-by-step explanation:
A) the vertex is the minimum y value.
extremes of a function we get by using the first derivation and solving it for y' = 0.
y = x² + 16x + 48
y' = 2x + 16 = 0
2x = -16
x = -8
so, the vertex is at x=-8.
the y value is (-8)² + 16(-8) + 48 = 64 - 128 + 48 = -16
B) is totally simple. it is f(0) or x=0. so, y is 48.
C) is the solution of the equation for y = 0.
the solution for such a quadratic equation is
x = (-b ± sqrt(b² - 4ac)) / (2a)
in our case here
a=1
b=16
c=48
x = (-16 ± sqrt(16² - 4×48)) / 2 = (-16 ± sqrt(256-192)) / 2 =
= (-16 ± sqrt(64)) / 2 = (-16 ± 8) / 2 = (-8 ± 4)
x1 = -8 + 4 = -4
x2 = -8 - 4 = -12
so the x- intercepts are (-4, 0), (-12, 0)
The disposable income increases by $100, this means aggregate consumption will increase by $75 and autonomous consumption remains at $1000.
We are given the following in the question:
C(Y D )= 1000+0.75 YD
where C is the consumption and YD is the disposable income.
If the disposable income increases by $100, then we can write
C( Y D +100 ) - C(Y D) = 1000+ 0.75(Y D+100)- (1000 + 0.75 Y D)
C( Y D +100 ) - C(Y D)= 75
Thus, the aggregate consumption will increase by $75.
Autonomous consumption is the consumption when customer makes no disposable income.
Thus, we put YD = 0
C(0) = 1000+ 0.75(0)
C(0)= 1000
Thus, the autonomous consumption is $1000.
The disposable income increases by $100, this means aggregate consumption will increase by $75 and autonomous consumption remains at $1000.
learn more about of consumption here
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