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3 years ago

7

Sketch these cartesin products on the x-y plane R^2 14. 11,21x1,1.5,2

1 answer:

ale4655 [162]3 years ago

3 0

Answer:

$\left\{11, 21\right\} \times \left\{1, 1.5, 2\right\} = \left\{ (11, 1), (11, 1.5), (11, 2), (21, 1), (21, 1.5), (21, 2)\right\}$

Step-by-step explanation:

The Cartesian product between two discrete sets, is given by all possible ordered pairs originated with the combinations of the elements of the two sets, thus the requested Cartesian product is:

$\left\{11, 21\right\} \times \left\{1, 1.5, 2\right\} = \left\{ (11, 1), (11, 1.5), (11, 2), (21, 1), (21, 1.5), (21, 2)\right\}$

$A = (11, 1)\\B = (11, 1.5)\\C = (11, 2)\\D = (21, 1)\\E = (21, 1.5)\\F = (21, 2)\\$

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Find four consecutive integers with a sum of 106.

grandymaker [24]

4 consecutive integers...
x, x + 1, x + 2, x + 3

x + x + 1 + x + 2 + x + 3 = 106
4x + 6 = 106
4x = 106 - 6
4x = 100
x = 100/4
x = 25

x + 1 = 25 + 1 = 26
x + 2 = 25 + 2 = 27
x + 3 = 25 + 3 = 28

ur 4 integers are : 25,26,27,28

6 0

2 years ago

The sum of two terms of gp is 6 and that of first four terms is 15/2.Find the sum of first six terms.

Gnoma [55]

Given:

The sum of two terms of GP is 6 and that of first four terms is $\dfrac{15}{2}.$

To find:

The sum of first six terms.

Solution:

We have,

$S_2=6$

$S_4=\dfrac{15}{2}$

Sum of first n terms of a GP is

$S_n=\dfrac{a(1-r^n)}{1-r}$ ...(i)

Putting n=2, we get

$S_2=\dfrac{a(1-r^2)}{1-r}$

$6=\dfrac{a(1-r)(1+r)}{1-r}$

$6=a(1+r)$ ...(ii)

Putting n=4, we get

$S_4=\dfrac{a(1-r^4)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1-r^2)(1+r^2)}{1-r}$

$\dfrac{15}{2}=\dfrac{a(1+r)(1-r)(1+r^2)}{1-r}$

$\dfrac{15}{2}=6(1+r^2)$ (Using (ii))

Divide both sides by 6.

$\dfrac{15}{12}=(1+r^2)$

$\dfrac{5}{4}-1=r^2$

$\dfrac{5-4}{4}=r^2$

$\dfrac{1}{4}=r^2$

Taking square root on both sides, we get

$\pm \sqrt{\dfrac{1}{4}}=r$

$\pm \dfrac{1}{2}=r$

$\pm 0.5=r$

Case 1: If r is positive, then using (ii) we get

$6=a(1+0.5)$

$6=a(1.5)$

$\dfrac{6}{1.5}=a$

$4=a$

The sum of first 6 terms is

$S_6=\dfrac{4(1-(0.5)^6)}{(1-0.5)}$

$S_6=\dfrac{4(1-0.015625)}{0.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Case 2: If r is negative, then using (ii) we get

$6=a(1-0.5)$

$6=a(0.5)$

$\dfrac{6}{0.5}=a$

$12=a$

The sum of first 6 terms is

$S_6=\dfrac{12(1-(-0.5)^6)}{(1+0.5)}$

$S_6=\dfrac{12(1-0.015625)}{1.5}$

$S_6=8(0.984375)$

$S_6=7.875$

Therefore, the sum of the first six terms is 7.875.

5 0

2 years ago

[(-6) + 5] ÷ [(-2) + 1]

Ira Lisetskai [31]

Answer:

Answer is 1

Explanation:

(-6 + 5) / (-2 + 1)

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1

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3 years ago

Read 2 more answers

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just olya [345]

Answer:

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Step-by-step explanation:

hope this helps :)

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2 years ago

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Yuri [45]

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3 years ago