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saul85 [17]
3 years ago
11

Verify the identity cos quantity x plus pi divided by two = -sin x

Mathematics
1 answer:
In-s [12.5K]3 years ago
6 0

Answer:

Identity is verified.

Step-by-step explanation:

We have to verify the identity cos(x+\frac{\pi }{2}) = (- sinx)

To prove any identity we always prove one side(either left hand side or right hand side) of the equation equal to the other side.

In this identity we take the left hand side first

cos(x+\frac{\pi}{2})

=cosx\times cos(\pi/2)-sinx\times sin(\pi/2))  (as we know cos(a+b) = cosa×cosb-sina×sinb)

= cosx\times0-sinx\times1

= 0-sinx

= - sinx ( Right hand side)

Hence identity is proved.

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It is desired to pile some logs in layers so that the top layer contains one log, the next layer contains two logs, the next lay
Hitman42 [59]

Answer:

Yes all of the logs can be used in such a grouping.

We'll have <u>19 logs</u> in the bottom row (and have 19 rows)

========================================================

Explanation:

Let n be the number of layers. Let T(n) represent how many logs there are total.

  • If you have 1 layer, then you have 1 log. So we can say that T(1) = 1.
  • If there are n = 2 layers, then we have 1 log on top of two other logs, which leads to 1+2 = 3 logs total. This shows that T(2) = 3.
  • If there are n = 3 layers, then we have 1 log on top of 2 which are on top of 3 at the very bottom. We have 1+2+3 = 6 logs total. So T(3) = 6.
  • Having n = 4 layers gives 1+2+3+4 = 10 logs. So T(4) = 10
  • Having n = 5 layers gives 1+2+3+4+5 = 15 logs. So T(5) = 15

This process continues for however long you like. The sequence 1,3,6,10,15 is the set of triangular numbers, since the logs form a triangular or pyramid shape when stacked this way. To get the nth value in the triangular number sequence, use this formula

T(n) = 0.5*n*(n+1)

---------------

For example, let's say we wanted to find how many logs there were in the fifth layer

T(n) = 0.5*n*(n+1)

T(5) = 0.5*5*(5+1)

T(5) = 15

This matches from earlier.

The purpose of bringing in a formula is to see if we can get T(n) = 190 for some integer n.

-------------------

T(n) = 0.5*n*(n+1)

190 = 0.5*n*(n+1)

190*2 = n(n+1)

380 = n^2+n

0 = n^2+n-380

n^2+n-180 = 0

Applying the quadratic formula will lead to the two solutions: n = -20 and n = 19. We ignore the negative value of n as we can't have a negative number of rows. Therefore, n = 19 is the only valid solution here.

If we wanted to stack 190 logs in this triangular pyramid fashion, then we'll need to have 19 rows. The bottom row will have 19 logs.

----------

Check:

1+2+3+4+5+6+7+8+9+10 = 55

11+12+13+14+15+16+17+18+19 = 135

55+135 = 190

Or you could say,

T(n) = 0.5*n*(n+1)

T(19) = 0.5*19*(19+1)

T(19) = 190

Either way, the answer is confirmed.

8 0
2 years ago
What is the mode for the data set? <br> 59,57,56,50,58,51,54,59,55,52,53 (multiple choice)
jok3333 [9.3K]
The mode for this is 59

Other stuff you may need:
<span><span>Range - 9
</span><span>Median - 55</span><span>
</span><span>Mean - 54.909</span></span>
4 0
3 years ago
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Bacteria are the most common example of exponential growth. Select a number between 2 and 10 to represent the hourly growth rate
shusha [124]

Answer:

bh

Step-by-step explanation:

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Express in terms i root of -40
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Answer:

6.32455532i

Step-by-step explanation:

Use the square root calculator too find it

5 0
2 years ago
Solve each equation mentally.
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16. 4 (9*4=36) 
17. 6 (6*11=66)
18. 8 (10*8=80)
19. 9 (9*5=45)
20. 48 (4*12=48)
21. 13 (13*2=26)



7 0
3 years ago
Read 2 more answers
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