Mindset separates the best from the rest: the right mindset drives the right habits, which drive the right performance. Skills focus has three traps for the unwary manager: Skills are in plentiful supply and becoming a commodity.

Explanation:

6 0

2 years ago

Explain in detail, how you solved the following problem: The first two terms of a sequence are 10 and 20. If each term after the

KIM [24]

Answer:

$T_{2020} = 15$

Explanation:

Given

$T_1 = 10$

$T_2 = 20$

Each term after the second term is the average of all of the preceding terms

Required:

Explain how to solve the 2020th term

Solve the 2020th term

Solving the 2020th term of a sequence using conventional method may be a little bit difficult but in questions like this, it's not.

The very first thing to do is to solve for the third term;

The value of the third term is the value of every other term after the second term of the sequence; So, what I'll do is that I'll assign the value of the third term to the 2020th term

This is proved as follows;

From the question, we have that "..... each term after the second term is the average of all of the preceding terms", in other words the MEAN

$T_{n} = \frac{\sum T{k}}{n-1} ; where: k = 1 .... n -1$

Assume n = 3

$T_{3} = \frac{T_1 + T_2}{2}$

Multiply both sides by 2

$2 * T_{3} = \frac{T_1 + T_2}{2} * 2$

$2T_{3} = T_1 + T_2$

Assume n = 4

$T_{4} = \frac{T_1 + T_2 + T_3}{3}$

$T_{4} = \frac{(T_1 + T_2) + T_3}{3}$

Substitute $2T_{3} = T_1 + T_2$

$T_{4} = \frac{2T_3 + T_3}{3}$

$T_{4} = \frac{3T_3}{3}$

$T_{4} = T_3$

Assume n = 5

$T_{5} = \frac{T_1 + T_2 + T_3 +T_4}{4}$

$T_{5} = \frac{(T_1 + T_2) + T_3 +(T_4)}{4}$

Substitute $2T_{3} = T_1 + T_2$ and $T_{4} = T_3$

$T_{5} = \frac{2T_3 + T_3 +T_3}{4}$

$T_{5} = \frac{4T_3}{4}$

$T_{5} = \frac{(5-1)T_3}{5-1}$

Replace 5 with n

$T_{n} = \frac{(n-1)T_3}{n-1}$

(n-1) will definitely cancel out (n-1); So, we're left with

$T_{n} = T_3$

Hence,

$T_{2020} = T_3$

Calculating $T_3$

$T_{3} = \frac{10 + 20}{2}$

$T_{3} = \frac{30}{2}$

$T_{3} = 15$

Recall that $T_{2020} = T_3$

$T_{2020} = 15$

3 0

3 years ago

Air pollution from a power plant is being monitored for levels of nitrogen dioxide and ground-level ozone. The levels are measur

zysi [14]

Answer:

There will be an increase in the level of nitrogen dioxide and a decrease in the level of ground-level ozone.

Explanation:

Ozone is a gas normally found in stratosphere, where it protects us from solar radiation. However, under certain circumstances, it can be formed on the ground level.

Conditions that have to be met in order for this to happen are existing of nitrogen oxides and volatile organic compounds (VOC) (both formed from the factories, industry and transport) and their reaction catalyzed by heat and light.

During dark, cold and cloudy days, due to the lack of heat and light from the Sun, formation of ozone will be decreased.

Also, this will enable building up of nitrogen dioxide, due to the same reason, leading to increased concentration.

7 0

3 years ago

Read 2 more answers