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3 years ago

If I say "Everything I tell you is a lie," am I telling you the truth or a lie?

1 answer:

8 0

The answer would be a lie because even if this statement was true, someone would be lying on another lie.
So the answer would be B.

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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

4 years ago

Slope integrals for calculus, having trouble need all the help I can get

Harlamova29_29 [7]

(1) The integral is straightforward; x ranges between two constants, and y ranges between two functions of x that don't intersect.

$\displaystyle\int_{-2}^1\int_{-x}^{x^2+2}\mathrm dy\,\mathrm dx$

(2) First find where the two curves intersect:

y ² - 4 = -3y

y ² + 3y - 4 = 0

(y + 4) (y - 1) = 0

y = -4, y = 1 → x = 12, x = -3

That is, they intersect at the points (-3, 1) and (12, -4). Since x ranges between two explicit functions of y, you can capture the area with one integral if you integrate with respect to x first:

$\displaystyle\int_{-4}^1\int_{y^2-4}^{-3y}\mathrm dx\,\mathrm dy$

(3) No special tricks here, x is again bounded between two constants and y between two explicit functions of x.

$\displaystyle\int_1^5\int_0^{\frac1{x^2}}\mathrm dy\,\mathrm dx$

8 0

3 years ago

Which of the following pollutants, when replaced with natural alternatives, could improve human health?

ipn [44]

The correct answer is iii

3 0

3 years ago

Drought and leaching have contributed to the process of __________, a major environmental challenge in Africa.

anygoal [31]

Answer:

Desertification

Explanation:

Drought and leaching leave some parts of Africa without much water, which leads to some portions of the area to turn into a desert, which can prove disastrous for the plants and animals that now find themselves in a completely different habitat.

6 0

3 years ago

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Which activity can strengthen a diverse family?

butalik [34]

Parents practicing authority over children

5 0

3 years ago

Read 2 more answers