Answer:
see explanation
Step-by-step explanation:
Given that M is directly proportional to r³ then the equation relating them is
M = kr³ ← k is the constant of proportion
To find k use the condition when r = 4, M = 160, thus
160 = k × 4³ = 64k ( divide both sides by 64 )
2.5 = k
M = 2.5r³ ← equation of variation
(a)
When r = 2, then
M = 2.5 × 2³ = 2.5 × 8 = 20
(b)
When M = 540, then
540 = 2.5r³ ( divide both sides by 2.5 )_
216 = r³ ( take the cube root of both sides )
r = = 6
Answer:
The angle to the nearest hundredths is 38. 66 °
Step-by-step explanation:
From the question above the events will form a right angle triangle. From the triangle above the opposite side is the height of the tree. The adjacent side is the length of the shadow. The x value is the angle formed.
From the triangle,
height of tree (opposite) = 96 ft
length of shadow(adjacent) = 120 ft
angle formed = x
Using the SOHCAHTOA principle,
tan x = opposite/adjacent
tan x = 96/120
tan x = 0.8
x = arctan(0.8)
x = 38.659808254
6, immediately after the decimal → tenth value
5 → hundredth value
9 → thousandth value
The thousandth value(9) is greater than 5 so we give 1 to the hundredth value(5) to make it 6.
To the nearest hundredth ,
x = 38. 66 °
