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
Answer:
6x - 15y = -63
15x -15y = -90
Step-by-step explanation:
We need to multiply the two equations by a constant that will eliminate the y terms.
The two equations are:
2x - 5y = -21
3x - 3y = -18
Let us multiply the first by 3 and the second by 6. The resulting equations will be:
6x - 15y = -63
15x -15y = -90
Note: To solve the system of equations we can simply subtract the first from the second.
9514 1404 393
Answer:
C. parallelogram, then rectangle
Step-by-step explanation:
The attached image shows how the shape evolves as the number of segments of the circle increases. The smaller the central angle, the closer the shape becomes to a rectangle.
Answer:
18
Step-by-step explanation:
to be 18 7 bitween one is the complet the neme of soit and can be instracttion
Answer: the trip (one-way) that Alan made on Saturday was 63 miles.
Step-by-step explanation:
Let x represent the distance of the trip that Alan made on Saturday.
Let t represent the time that it took Alan to make the trip on Saturday.
On Saturday, Alan traveled North along minor roads averaging 36 mph to visit a friend.
Distance = speed × time.
Therefore, distance travelled on Saturday would be
x = 36 × t = 36t
On Sunday, he traveled East along main roads averaging 60 mph to visit his mother. The trip to visit his mother was 24 miles longer and took 18 minutes(18/60 = 0.3 hours) less. This means that the distance travelled would be
x + 24 and the time spent would be t - 0.3 hours.
Distance travelled on Sunday would be
x + 24 = 60(t - 0.3)
x + 24 = 60t - 18 - - - - - - -- - - 1
Substituting x = 36t into equation 1, it becomes
36t + 24 = 60t - 18
60t - 36t = 24 + 18
24t = 42
t = 42/24 = 1.75
x = 36t = 36 × 1.75
x = 63 miles
