Answer: see proof below
<u>Step-by-step explanation:</u>
Use the following Half-Angle Identities: tan (A/2) = (sinA)/(1 + cosA)
cot (A/2) = (sinA)/(1 - cosA)
Use the Pythagorean Identity: cos²A + sin²B = 1
Use Unit Circle to evaluate: cos 45° = sin 45° = 
<u>Proof LHS → RHS</u>
Given: 
Rewrite Fraction: 
Half-Angle Identity: 
Substitute: 
Simplify: 
= 2
LHS = RHS: 2 = 2 
Question:
A boy makes a cone of diameter 28 cm without a base. He then cuts a smaller cone of diameter 20 cm from the cone. He used the bottom part as a lampshade. If the height of the lampshade is 11cm,
(a) find the volume of the whole cone.
(b) find in cm2, the area of the material used to make the lampshade.
Answer:
(a) V ≈ 16420.1
(b) A ≈ 2690.1 cm²
Step-by-step explanation:
<u>Solution for (a)</u>
Formula: The formula for the volume of a cone is V = 1/3 hπr².
V= πr² h
/3 = π × 28/ 2 × 20/ 3 ≈ 16420.0576
16420.0576 in nearest tenths is 16420.1
Therefore, the volume of the whole cone is 16420.1 cm²
<u>Solution for (b)</u>
Formula: A = πrl + πr2.
l = r² + h²
Solving for A
A = πr (r + h²+ r²) = π × 20 × (20 + 112 + 202) ≈ 2690.80077
2690.80077 In nearest tenths, is 2690.1
Therefore, the area of the material used to make the lampshade is 2690.1 cm²
Answer:
Step-by-step explanation:
Convert both fractions to improper fractions
To subtract, find a common denominator of 3 and 5.
Answer:
the answer is A
Step-by-step explanation:
The line is the middle point of the graph/ the middle number of all therefore it's the median.
