Value of b is 11.25
<u>Step-by-step explanation:</u>
Step 1:
Use the trigonometric ratio sine to find z.
⇒ sin 60° = opposite side/hypotenuse = z/15
∴ z = 15 sin 60° = 15√3/2
Step 2:
Use the trigonometric ratio sine to find y.
⇒ sin 30° = opposite side/hypotenuse = y/z
∴ y = z sin 30° = 15√3/2 × 1/2 = 15√3/4
Step 3:
Use Pythagoras theorem to find value of b.
⇒ y² + b² = z²
⇒ b² = z² - y² = (15√3/2)² - (15√3/4)²
= (15 × 15 × 3/4) - (15 × 15 × 3/4²)
= 15²×3/4 [1 - 1/4] (taking common factor out)
= 15² × 3/4 × 3/4 = 15² × 3²/4²
∴ b = √15² × 3²/4² = 15 × 3/4
= 45/4 = 11.25
16 = 1/4x + 2.5...where x stands for diameter of large gear
16 - 2.5 = 1/4x
13.5 = 1/4x....multiply both sides by 4, eliminating the 1/4 on the right side
13.5 * 4 = x
54 = x.....the large gear is 54 cm
Answer:
3879.24
Step-by-step explanation:
The formula to find the volume of a cone is V = 
= 3879.24
Answer: AB=√17, AD=√98,6
Step-by-step explanation:
AB²=BC²+AC²-2*BC*AC*cosACB
AB²=5²+4²-2*5*4*0,6=25+16-24=17
AB=√17
AD²=AC²+CD²-2*AC*CD*cosACD
cosACD=cos(180°-ACB)=-cosACB
AD²=4²+7²-2*4*7*(-0,6)=16+49+33,6=98,6
AD=√98,6
For this case we have the following equation:
s = root (S.A / 6)
Substituting values we have:
For S.A = 180:
s = root (180/6)
s = root (30)
For S.A = 120:
s = root (120/6)
s = root (20)
s = root (4 * 5)
s = 2 * root (5)
Subtracting both values we have:
root (30) - 2 * root (5)
Answer:
root (30) - 2 * root (5)
option 2
