Answer:
10.5
Step-by-step explanation:
Answer:
First angle = 30°
Second angle = 60°
Third angle = 90°
Step-by-step explanation:
x + y + z = 180
y + z = 5x
z = y + 30
then:
y + (y+30) = 5x
2y + 30 = 5x
x = (2y+30)/5
then:
x + y + z = 180
{(2y+30)/5} + y + y+30 = 180
{(2y+30)/5} + 2y + 30 = 180
{(2y+30)/5} = 180 - 30 - 2y
{(2y+30)/5} = 150 - 2y
2y+30 = 5(150-2y)
2y+30 = 5*150 + 5*-2y
2y+30 = 750 - 10y
2y + 10y = 750 - 30
12y = 720
y = 720/12
y = 60°
x = (2y+30)/5
x = (2*60 + 30)/5
x = (120+30)/5
x = 150/5
x = 30°
z = y + 30
z = 60 + 30
z = 90°
Check:
x + y + z = 180°
30° + 60° + 90° = 180°
log(4) + log(2) - log(5)
= log(2²) + log(2) - log(5)
= 2 log(2) + log(2) - log(5)
= 3 log(2) - log(5)
= log(2³) - log(5)
= log (2³/5)
= log (8/5)
= log (1.6) = 0.2041... (rounded)
Answer:
Cavalier's principle can be used to find the volume of any solid.
Step-by-step explanation:
Cavalier's Principle:
- Cavalier introduced parallel planes and area to describe the relationship between solids.
- Cavalier stated if two solids have the same height and equal areas of the base everywhere along the height then the solids have the same volume.
- Suppose two regions are included between two parallel planes.
- If every plane parallel to these two planes intersects both regions in cross-sections of equal area, then the two regions have equal volumes.
- The formula for the volume of a prism is the area of the base times the height.
