Answer:
the cyclists rode at 35 mph
Step-by-step explanation:
Assuming that the cyclists stopped, and accelerated instantaneously at the same speed than before but in opposite direction , then
distance= speed*time
since the cyclists and the train reaches the end of the tunnel at the same time and denoting L as the length of the tunnel :
time = distance covered by cyclists / speed of cyclists = distance covered by train / speed of the train
thus denoting v as the speed of the cyclists :
7/8*L / v = L / 40 mph
v = 7/8 * 40 mph = 35 mph
v= 35 mph
thus the cyclists rode at 35 mph
Answer:
the common ratio is either 2 or -2.
the sum of the first 7 terms is then either 765 or 255
Step-by-step explanation:
a geometric sequence or series of progression (these are the most common names for the same thing) means that every new term of the sequence is created by multiplying the previous term by a constant factor which is called the common ratio.
so,
a1
a2 = a1×f
a3 = a2×f = a1×f²
a4 = a3×f = a1×f³
the problem description here tells us
a3 = 4×a1
and from above we know a3 = a1×f².
so, f² = 4
and therefore the common ratio = f = 2 or -2 (we need to keep that in mind).
again, the problem description tells us
a2 + a4 = 30
a1×f + a1×f³ = 30
for f = 2
a1×2 + a1×2³ = 30
2a1 + 8a1 = 30
10a1 = 30
a1 = 3
for f = -2
a1×-2 + a1×(-2)³ = 30
-10a1 = 30
a1 = -3
the sum of the first n terms of a geometric sequence is
sn = a1×(1 - f^(n+1))/(1-f) for f <>1
so, for f = 2
s7 = 3×(1 - 2⁸)/(1-2) = 3×-255/-1 = 3×255 = 765
for f = -2
s7 = -3×(1 - (-2)⁸)/(1 - -2) = -3×(1-256)/3 = -3×-255/3 =
= -1×-255 = 255
Answer:
She has walked <u>7233.6 ft</u>
Step-by-step explanation:
13.7 miles ÷ 10 = 1.37 miles
1 mile = 5280 ft
5280 x 1.37 = 7233.6 ft (or 7234 if rounded to the nearest ft)
Answer:
6 1/6
Step-by-step explanation:
-2 1/2 * 3 1/3
-2 * -3 = 6
1/2 * 1/3 = 1/6
Answer:
-8,-4,6
Step-by-step explanation:
Just answered it
