In an arithmetic sequence:
Tn=t₁+(n-1)d
t₄=t₁+(4-1)d=t₁+3d
t₅=t₁+(5-1)d=t₁+4d
t₆=t₁+(6-1)d=t₁+5d
t₄+t₅+t₆=(t₁+3d) +(t₁+4d)+(t₁+5d)=3t₁+12d
Therefore:
3t₁+12d=300 (1)
t₁₅=t₁+(15-1)d=t₁+14d
t₁₆=t₁+(16-1)d=t₁+15d
t₁₇=t₁+(17-1)d=t₁+16d
t₁₅+t₁₆+t₁₇=(t₁+14d)+(t₁+15d)+(t₁+16d)=3t₁+45d
Therefore:
3t₁+45d=201 (2)
With the equations (1) and (2) we make an system of equations:
3t₁+12d=300
3t₁+45d=201
we can solve this system of equations by reduction method.
3t₁+12d=300
-(3t₁+45d=201)
-----------------------------
-33d=99 ⇒d=99/-33=-3
3t₁+12d=300
3t₁+12(-3)=300
3t₁-36=300
3t₁=300+36
3t₁=336
t₁=336/3
t₁=112
Threfore:
Tn=112+(n-1)(-3)
Tn=112-3n+3
Tn=115-3n
Now, we calculate T₁₈:
T₁₈=115-3(18)=115-54=61
Answer: T₁₈=61
Tenth place is the answer!! :))
Time taken for Kristin to catch up with the truck will be found using the formula
time=(distance)/(speed)
distance=20 km
speed=90 km/h
thus
time=20/90=2/9 hours
Answer: 2/9 hours
10 miles per second in feet per second is 14.67 feet per second
Step-by-step explanation:
The average speed of one team in a relay race = 10 miles per hour.
We need to find the speed in feet per second.
1 mile per hour = 1.467 feet per second
So, Speed in feet per second is:
1 mile per hour = 1.467 feet per second
10 miles per hour = 10*1.467 feet per second
= 14.67 feet per second
So, 10 miles per second in feet per second is 14.67 feet per second
Keywords: Conversion of units
Learn more about Conversion of units at:
#learnwithBrainly
Answer:
See the detailed answers below
Step-by-step explanation:
Given data
Ratio= 1:4:7
combined ratio= 1+4+7= 12
Total amount= $636,000
Apply the part to all method
The first person will take
1/12= x/ 636,000
cross multiply
12x= 636,000*1
x= 636,000/12
x= 53000
The second person will take
4/12= x/ 636,000
cross multiply
12x= 636,000*4
x= 2544000/12
x= 212000
The third person will take
7/12= x/ 636,000
cross multiply
12x= 636,000*7
x= 4452000/12
x= 371000