
Let

denote the

th partial sum of the series, i.e.

Then

and subtracting from

we get


As

, the exponential term vanishes, leaving us with

and so
Answer:
S varies partly directly as M and Q.
S=C.
S=KMQ+C.
For the first one...
speed=80,m=220,Q=30.
80=K20×30+C.
80=600K+C......(I).equation one.
For the second one....
speed=60,m=300,Q=40.
60=K300×40+C.
60=12000K+C.....(ii). equation two.
Minus eqtn(I) from eqtn(ii).
80=600K+C.
- 60=12000K+C.
K=0.01754~0.018.
Substitute K=0.018 into eqtn(I).
80=600K+C
80=600×0.018+C.
80=10.8+C.
C=80-10.8=69.2.
The relation is S=0.018MQ+69.2
when speed is 100 and mass is 250 find the volume.
100=0.018×250×Q+69.2.
100=4.5Q+69.2.
4.5Q=100-69.2
4.5Q=30.8.
Q=30.8/4.5.
Q=6.8~7litres.
Given:
The equation for the area of the first option is:

Where x is the side length of the current square park.
To find:
The side length of the current square park.
Solution:
We have,

It can be written as:

Splitting the middle term, we get




We know that the side length of a park cannot be negative. So, the only possible value of x is 320.
Therefore, the most direct method to solve the given equation is splitting the middle term and the side length of the current square park is 320 meters.
Let the distance to his office be x, then
On monday, speed = x/20 miles per minutes = 3x miles per hour
On tuesday, speed = (3x + 15) miles per hour
Time = distance / speed
(20 - 6)/60 hours = x/(3x + 15) hours
7/30 = x/(3x + 15)
7(3x + 15) = 30x
21x + 105 = 30x
30x - 21x = 105
9x = 105
x = 105/9 = 11.7 miles
Therfore he travels an average of 11.7 miles to work.