Answer:
Option A is correct.
Step-by-step explanation:
The height of the rectangular pack is h1 = 4r
The height of the parallelogram = 2r + the height of equilateral triangles with a side of 2r
The height of equilateral triangle with a side of 2r = (side)/2*√3
=(2r)/2 *√3 = r√3
The height of the parallelogram h2 = 2r+r√3 = r(2+√3)
So,the ratio of h1 to h2 is :
4r : r(2 +√3)
Cancelling r we get
Hence, the ratio is 4 : 2 +√3
Answer:
12
Step-by-step explanation:
a² + b² = c²
5² + b² = 13²
25 + b² = 169
b² = 144
b = 12
Answer: 12
<span>When given 3 triangle sides, to determine if the triangle is acute, right or obtuse:
</span>1) Square all 3 sides.
2) Sum the squares of the 2 shortest sides.
3) Compare this sum to the square of the 3rd side.
if sum > 3rd side² Acute Triangle
if sum = 3rd side² Right Triangle<span>
if sum < 3rd side² Obtuse Triangle
1) 1,296 2,401 3,600
2) Sum = 3,697
3) </span><span>3,697 is greater than 3,600
Therefore, the triangle is acute.
Source:
http://www.1728.org/triantest.htm
</span>
To find the median, put the numbers in order to least to greatest, which would be 5, 5, 5, 7, 8, 8, 9. the median is the number in the middle, which is seven. the mode is the number that occurs most often in the set, which is 5 in this case (appears three times). 2. 543.24 in expanded form is essentially pulling the number apart into its different values places. in this case, it would be five hundred plus forty plus three plus two tenths plus four hundredths, which is 500 + 40 + 3 + .2 + .4. hope this helps!
Answer:
a). 59.049°C
b). 2.1179 seconds
Step-by-step explanation:
Expression representing the final temperature after decrease in temperature of the metal from 100°C to T°C is,
T = 
where x = duration of cooling
a). Temperature when x = 5 seconds
T = 100(0.9)⁵
= 59.049
≈ 59.049°C
b). If the temperature of the metal decreases from 100°C to 80°C
Which means for T = 80°C we have to calculate the duration of cooling 'x' seconds
80 =
0.8 = 
By taking log on both the sides
log(0.8) =log[]
-0.09691 = x[log(0.9)]
-0.09691 = -0.045757x
x = 
x = 2.1179
x ≈ 2.1179 seconds
