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Andrews [41]
3 years ago
5

Prove the identity of tan(pi - x) = - tan x

Mathematics
1 answer:
liq [111]3 years ago
8 0

Two ways:

Step-by-step explanation:

1. First way. Using the trig unit circle.

tan (pi - x) = - tan x

2. Second way. Apply the identity:

tan(a-b)=tan a- tan b/ 1 - tan a×tan b

tan (π - x)= tan π - tanx/1 - tan(π)×tanx

Since tan (pi) = 0, therefor:

tan(π−x)=−tanx

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Multiply by hundreds: 545 times 200
fiasKO [112]

Answer:

109000

Step-by-step explanation:

5 0
3 years ago
A company donates 2,292 gifts to a school. the gifts are diveded evenly among 19 classrooms. The rest of the gifts are given to
BARSIC [14]

Answer:

<em>Each classroom received 120 gifts and the hospital received 12 gifts</em>

Step-by-step explanation:

<u>Division As Evenly Distribution</u>

The first concept we manage when learning about divisions is how to distribute an amount N among m elements such as everyone receives the same amount.

If the nature of the problem allows distributing decimal portions of N, then every receiver gets exactly the same amount N/m.

But things are different when the division must be an integer number. For example, if we wanted to divide gifts, we cannot give partial gifts. So the correct division is a matter of the study of integer numbers.

If N is divisible by m, i.e. there is no remainder in the division, then each element will receive N/m gifts. But what if they are not divisible? We must divide and take the integer part of the division and discard the remainder

We want to divide 2,292 gifts to the school, where there are 19 classrooms. If we divide 2,292/19 we get 120 and a remainder of 12.

Answer. Each classroom received 120 gifts and the hospital received 12 gifts

6 0
3 years ago
Solve for x:
astraxan [27]
The answer for this question is 8
7 0
3 years ago
Read 2 more answers
You have just completed an experiment measuring the length (in mm) of 12 soybean plants after 3 days of sprouting. The measureme
sweet-ann [11.9K]

Answer:

The new IQR is 22.    

Step-by-step explanation:

We are given the following data of  length (in mm) of 12 soybean plants after 3 days of sprouting.

53, 47, 51, 54, 43, 39, 61, 57, 55, 46, 44, 43

Sorted data:

39, 43, 43, 44, 46, 47, 51, 53, 54, 55, 57, 61

Formula:

IQR = Q_3 - Q_1\\Q_3 = \text{upper median},\\Q_1 = \text{ lower median}

Median:\\\text{If n is odd, then}\\\\Median = \displaystyle\frac{n+1}{2}th ~term \\\\\text{If n is even, then}\\\\Median = \displaystyle\frac{\frac{n}{2}th~term + (\frac{n}{2}+1)th~term}{2}  

Median ==\dfrac{6^{th}+7^{th}}{2} \dfrac{47+51}{2} = 49

Q_1 =\dfrac{3^{rd}+4^{th}}{2} = \dfrac{43 + 44}{2} = 43.5\\\\Q_3 =\dfrac{9^{th}+10^{th}}{2}= \frac{54 + 55}{2} = 54.5

IQR = Q_3 -Q_1 =54.5-43.5= 11

If every measurement is doubled, then, the IQR will also double itself.

Thus,

New IQR =

2\times \text{IQR}\\=2\TIMES 11\\=22

Thus, the new IQR is 22.

4 0
3 years ago
If you are presenting very complex and complicated information, it is best to:
nignag [31]
Sometimes complex information all at once can be hard to gather... Simplifying ideas and concepts can help with the amount of cramming you're giving to your audience.

You're answer is B. Simplify ideas and concepts. :)
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3 years ago
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