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2 years ago

10. Create an example of an irrational value between 2 and 3.

Mathematics

1 answer:

Alik [6]2 years ago

8 0

Answer:

$\sqrt{5$ = 2.23606797...

$\sqrt{6}$ = 2.44948974...

$\sqrt{7}$ = 2.64575131...

$\sqrt{8}$ = 2.82842712...

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x

= $64 + 192 \times x^{1} + 240 \times x^{2}$ + terms involving higher powers of x

so, the first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

Again,

$(2+x - x^{2})^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})$

Now, by inspection,

the term $x^{2}$ comes from k =5 and k = 6

for k = 5, the coefficient of $x^{2}$ is , $(-32) \times 6$ = -192

for k = 6 , the coefficient of $x^{2}$ is, $6_{C_{2}} \times 2^{4}$ = 240

so, coefficient of $x^{2}$ in the final expression = (240 - 192) = 48

3 0

2 years ago

Write in slope intercept form the equation of a line that has the slope of 1/3 and the y- intercept of 5.

ludmilkaskok [199]

Answer:

y = 1/3x + 5

Step-by-step explanation:

Slope intercept form is y = mx + b

m is the slope

b is the y intercept

plug your number in

y = 1/3x + 5

5 0

3 years ago

Please help, if you do not know do not answer please!

Paul [167]

Answer:

1,3 are functions

2,4 are not

6 0

2 years ago

Read 2 more answers

5 less than a number is equivalent to 1 more than three times the number. the number is

lutik1710 [3]

Answer:

x = -1

Step-by-step explanation:

5 less than a number is equivalent to 1 more than three times the number

number = x

x - 5 = 3x + 1

now im going to get the numbers and variable on different sides

x - 5 + 5 = x

3x + 1 - 3x = 1

x + 3x = 4x

1 - 5 = -4

4x = -4

lastly im going to divide each side by 4

4x / 4 = x

-4 / 4 = -1

x = -1

3 0

3 years ago

A bag contains 2 white marbles and 7 purple marbles. Two marbles are drawn at random. One marble is drawn and not replaced. Then

Masja [62]

A.
$\frac{7purple}{9total} * \frac{2white}{8total} \\ \frac{14}{72} \\ =0.194$
The denominator of the second number goes down one because you aren't replacing the initial marble pulled, making the amount of marbles in the bag go down, but not affecting the white count because you pulled a purple marble.
b.
$\frac{2white}{9total} * \frac{1white}{8total} \\ \frac{2}{72} \\ =0.278$
The same can be said about the denominator for this problem, but not the numerator. The numerator must go down one number as well, because you already chose one white marble, taking one of the white marbles out of the bag, leaving you with one solitary, white marble.
c.
Chance of selecting two purple marbles:
 $\frac{7purple}{9total} * \frac{6purple}{8total} \\ \frac{42}{72} \\ =0.583$
Chance of selecting two white marbles:
$\frac{2white}{9total} * \frac{1white}{8total} \\ \frac{2}{72} \\ =0.278$
Chance of selecting two purple vs. Chance of Selecting 2 white:
0.583>0.278.
It is more likely to select 2 purple marbles.

Hope this helps!

6 0

3 years ago

Read 2 more answers