Answer: rate of train A = 120 km/h
rate of train B = 101 km/h
Step-by-step explanation:
Let x = the speed of train A
Let y = the speed of train B
One train travels 19 km/h slower than the other. Let train B be the slower train. Therefore,
x = y + 19 - - - - - - - - - -1
Recall
Speed = distance/time
Distance = speed × time
If they meet in 3 hours, it means that train A has travelled a distance of
x × 3 = 3x km
And train B has travelled a distance of y × 3 = 3y km
Train A and Train B were 663 kilometers apart when they left their respective destinations. They left at the same time and travelled towards each other. This means that if they meet in 3hours time, they must have covered a total of 663 km. Therefore,
3x + 3y = 663 - - - - - - - - - 2
Substituting x = y + 19 into equation 2, it becomes
3(y + 19) + 3y = 663
3y + 57 + 3y = 663
6y + 57 = 663
6y = 663 - 57 = 606
y = 606/6 = 101 km/h
x = y + 19 = 101 + 19
x = 120 km/h
Answer:
t=11.9
Step-by-step explanation:
960=420(2)^t/10
2.28571429=2^t/10
add log to both sides
log(2.28571429)=10
t log(2)
divide by log 2
1.19264508= 10
/t
10(1.19264508)
11.926450779=t
Answer:
III
Step-by-step explanation:
- 14 tell you that you should be moving left of (0,0) That makes the answer either in quad 2 or quad 3.
- 5i tells you that you are moving down. That tells you that you are moving down.
You are in quad III. It the question was -14 + 5i, you would be moving left and up. That would put you in quad II.
Answer: 11.46
Step-by-step explanation:
Formula for calculating the length of an arc is theta/360 ×2Πr. Where;
length of the arc (L) = 9
Theta= 45°
L = theta/360 × 2Πr
9 = 45/360× 2Πr
9 = 1/8 × 2Πr
9 = Πr/4
Πr = 36
r = 36/Π
r = 11.46
Substituting we have,
9 = r × 45°
r = 9/45
Answer:
a). f(0) = 4
b). f(6) = 8
Step-by-step explanation:
a). When x < 5, piecewise function to be considered,
f(x) = x + 4
Since, x = 0 is less than x = 5
f(0) = 0 + 4
f(0) = 4
b). When 5 ≤ x < 7,
Piecewise function to be considered,
f(x) = 8
Therefore, for x = 6,
f(6) = 8
