Answer:
r = 0.0424 cm (3sf)
Step-by-step explanation:
it makes 150 rev/sec
1 revolution = 1 circumference = 2pi*r
so every second the spool goes through 2*pi*r*150 of distance
we know that the rate of pulling is 40cm/sec
so 2pi*r*150 = 40
r = 40/(2pi*150), which is 0.04244131816 cm.
check: Circumference is 2pi*r = 0.2666
now multiply by 150rev/sec = 40 cm/sec
5:2:3
5+2+3=10
If she has double of plum juice the ratio will be
10:4:6
10+4+6=20
So she can make 20 cups of fruit punch.
Answer:
3:6
Step-by-step explanation:
8:24 and 24:72 reduce down to 1:3. 3:6 is 1:2.
F ( x ) = 3 sim x + 3 cos x
f ` ( x ) = 3 cos x - 3 sin x
f `` ( x ) = - 3 sin x - 3 cos x = - 3 ( sin x + cos x )
The inflection points:
- 3 ( sin x + cos x ) = 0
sin x + cos x = 0
sin x = - cos x / : cos x
tan x = - 1
x 1 = 3π / 4
x 2 = 7π / 4
The function is concave up when f``(x) > 0
- 3( sin x+ cos x ) > 0
sin x + cos x < 0
tan x < - 1
f is concave up for:
x ∈ ( π/2, 3π/4 ) ∪ ( 3π/2, 7π/4)
f is concave down for:
x ∈ ( 0, π/2 ) ∪ ( 3π / 4, 3π/2 ) ∪ ( 7π / 4, 2 π ).
