Answer:
V = 15 in.³
Step-by-step explanation:
The original cylinder has radius r and height h.
V = πr²h
Its volume is 30 in.³, so
πr²h = 30 in.³
The new cylinder has radius (1/2)r and height 2h.
Its volume is
V = π(r/2)²(2h)
V = πr² × 2h/4
V = πr²h/2
πr²h is the volume of the original cylinder, and it is 30 in.³.
V = 30 in.³/2
V = 15 in.³
Answer:
n = √3
m = √3
Step-by-step explanation:
The triangle is an isosceles right triangle with 2 equal base angles of 45° each.
Thus:
Reference angle = 45°
Hypotenuse = √6
Opposite = m
Adjacent = n
✔️To find m, apply the trigonometric function SOH, we have:
Sin 45 = opp/hyp
Sin 45 = m/√6
√6 × 1/√2 = m (sin 45 = 1/√2)
√6/√2 = m
√(6/2) = m
√3 = m
m = √3
✔️To find n, apply the trigonometric function, CAH:
Cos 45 = adj/hyp
Cos 45 = n/√6
√6 × √2/2 = n (cos 45 = √2/2)
√12/2 = n
√(4*3)/2 = n
(2√3)/2 = n
√3 = n
n = √3
Answer:
4 packages of hot dogs and 5 packages of hot dog buns.
Step-by-step explanation:
Find the least common multiple of 10 and 8, which is 40.
