If no number can be used more than once, how many different 2-digit numbers can be formed from the digits 4, 6, and 8?

Find II 2e-3f II^2 assuming that e & f are unit vectors such that II e +f II=sqrt(3/2).

sergey [27]

We are given that ||e|| = 1, ||f|| = 1. 

Since ||e + f|| = sqrt(3/2), we have 
3/2 = (e + f) dot (e + f) 
= (e dot e) + 2(e dot f) + (f dot f) 
= ||e||^2 + 2(e dot f) + ||f||^2 
= 1^2 + 2(e dot f) + 1^2 
= 2 + 2(e dot f). 

So e dot f = -1/4. 

Therefore, 
||2e - 3f||^2 = (2e - 3f) dot (2e - 3f) 
= 4(e dot e) - 12(e dot f) + 9(f dot f) 
= 4||e||^2 - 12(e dot f) + 9||f||^2 
= 4(1)^2 - 12(-1/4) + 9(1)^2 
= 4 + 3 + 9 
= 16.

6 0

3 years ago

A paper company needs to ship paper to a large printing business. The a paper will be

eimsori [14]

Given :

A paper company needs to ship paper to a large printing business.

The paper will be shipped in small boxes and large boxes.

Each small box of paper weighs 50 pounds and each large box of paper weighs 80 pounds. A total of 19 boxes of paper were shipped weighing 1280 pounds altogether.

Find :

Determine the number of small boxes shipped and the number of large boxes shipped.

Calculations :

Let "S" be small boxes and "L" be large boxes.

Small box + Large box = 19

50S + 80L = 1280

→ 5S + 8L = 128

→ 5 (19 - L) + 8L = 128

→ 3L = 128 - 95

→ L = 33/3

→ L = 11ㅤㅤ

Finding the small box:

→ S = 19 - L

→ S = 19 - 11

→ S = 8

Therefore ,

Large boxes = 11.

Small boxes = 8.

orrrrrr

The number of small boxes is 8 and that of the large boxes is 11.

Step-by-step explanation:

Each small box of paper weighs 50 pounds and each large box of paper

weighs 80 pounds. A total of 19 boxes of paper were shipped weighing 1280 pounds altogether.

Let there are x small boxes and y large boxes.

Then,

x + y = 19 ............ (1) and

50x + 80y = 1280

⇒ 5x + 8y = 128 ............... (2)

Now, solving equations (1) and (2) we get,

5( 19 - y) + 8y = 128

⇒ 3y = 128 - 95 = 33

⇒ y = 11

Now, from equation (1) we get, x = 19 - y = 19 - 11 = 8

Therefore, the number of small boxes is 8 and that of the large boxes is 11. (Answer)

8 0

2 years ago

Which number is between 0.6 7/9

irakobra [83]

First we make the fractions homonym ( they must have the same denomitator)

0.6 = 6 / 10 7/9

6/10 = 6 * 9 / 10 * 9 = 54 / 90 7/9 = 7 * 10 / 9 * 10 = 70 / 90

The numbers which are between these numbers are ;

55 / 90 , 56 / 90 , 57 / 90 , 58 / 90 , 59 / 90, 60 / 90 , 61 / 90 , 62 / 90 , 63 / 90 , 64 / 90, 67 / 90 , 68 / 90 , 69 / 90

62 / 90 = 62 / 2 / 90 /2 = 31 / 45

So the right answer is B.

Hope that helps :)

8 0

3 years ago

Please help me !!!!!! I need help

kvv77 [185]

Answer:

y +8 = -4(x -8)

Step-by-step explanation:

You recognize that the given equation is in slope-intercept form:

y = mx + b

with m = 1/4 and b = 5.

A perpendicular line will have a slope that is the negative reciprocal of this value of m, so the desired slope is ...

-1/m = -1/(1/4) = -4

The point-slope form of the equation for a line is ...

y -k = m(x -h) . . . . . for slope m through point (h, k)

Using m=-4 and (h, k) = (8, -8), the point-slope form of the equation for the line you want is ...

y +8 = -4(x -8)

3 0

3 years ago

Find the next term in the sequence 3, 6, 9, 15, 24,

leonid [27]

39, it is like the fibonacci sequence you take the 2 previous numbers and add them together to get the next number.

8 0

3 years ago