Answer:
Lateral area of the smaller cylinder = 33.6
π mm²
Step-by-step explanation:
Circumference of the base of a cylinder is 24π mm . A similar cylinder has a base with circumference of 60π mm. Since we are dealing with the circumference of two similar cylinder we need to know the scale factor.
The square factor can be expressed as follow
Scale factor is the ratio between the larger circumference of the larger cylinder to the circumference of the smaller cylinder.
Scale factor = 60π/24π = 2.5
The lateral area of the larger cylinder = 210π mm².
The scale factor squared is equal to the ratio of the larger cylinder surface area to the smaller cylinder surface area.
Therefore,
2.5² = 210π/a
where
a = surface area of the smaller cylinder
cross multiply
6.25
a = 210π
divide both sides by 6.25
a = 210π/6.25
a = 33.6
π mm²
Lateral area of the smaller cylinder = 33.6
π mm²
Answer:
9) y=3x+11
10) y=-3x-6
Step-by-step explanation:
plug the numbers in to find your y intercepts
Answer: see proof below
<u>Step-by-step explanation:</u>
Use the Double Angle Identity: sin 2Ф = 2sinФ · cosФ
Use the Sum/Difference Identities:
sin(α + β) = sinα · cosβ + cosα · sinβ
cos(α - β) = cosα · cosβ + sinα · sinβ
Use the Unit circle to evaluate: sin45 = cos45 = √2/2
Use the Double Angle Identities: sin2Ф = 2sinФ · cosФ
Use the Pythagorean Identity: cos²Ф + sin²Ф = 1
<u />
<u>Proof LHS → RHS</u>
LHS: 2sin(45 + 2A) · cos(45 - 2A)
Sum/Difference: 2 (sin45·cos2A + cos45·sin2A) (cos45·cos2A + sin45·sin2A)
Unit Circle: 2[(√2/2)cos2A + (√2/2)sin2A][(√2/2)cos2A +(√2/2)·sin2A)]
Expand: 2[(1/2)cos²2A + cos2A·sin2A + (1/2)sin²2A]
Distribute: cos²2A + 2cos2A·sin2A + sin²2A
Pythagorean Identity: 1 + 2cos2A·sin2A
Double Angle: 1 + sin4A
LHS = RHS: 1 + sin4A = 1 + sin4A 
Answer: x and y intercepts are where the line crosses over the x and y axis.
Step-by-step explanation:
The third equation is the correct one. After 100 years, about 115 grams will remain.
