C = 16h
This is the basic set up of a cost function which is a direct correlation.
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
Let's calculate for the tablespoons of sugar to tablespoons of milk ratio for Mark, Sharri and Eve.
Mark: 3/2 = 1.5
Sharri: 4/3 = 1.3
Eve: 9/6 = 1.5
From the solution, Eve has an equivalent ratio to that of Mark's.
Answer:
A 9 ⋅ 1019
B 7.8 ⋅ 106
C 1.45 ⋅ 10−7
D 0.33 ⋅ 10−15
Step-by-step explanation:
A 9 ⋅ 1019
B 7.8 ⋅ 106
C 1.45 ⋅ 10−7
D 0.33 ⋅ 10−15
