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ratelena [41]
3 years ago
10

Prove the following identities : i) tan a + cot a = cosec a sec a​

Mathematics
1 answer:
inysia [295]3 years ago
7 0

Step-by-step explanation:

\tan \alpha + \cot\alpha = \dfrac{\sin \alpha}{\cos \alpha} +\dfrac{\cos \alpha}{\sin \alpha}

=\dfrac{\sin^2\alpha + \cos^2\alpha}{\sin\alpha\cos\alpha}=\dfrac{1}{\sin\alpha\cos\alpha}

=\left(\dfrac{1}{\sin\alpha}\right)\!\left(\dfrac{1}{\cos\alpha}\right)=\csc \alpha \sec\alpha

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Fill out the tables for each scenario and answer the question that follows. Use $7.25 as the minimum wage and remember that empl
hichkok12 [17]

Answer:

  • see below for the table values
  • US labor cost: $115275 per year

Step-by-step explanation:

The labor charge is for (6 days/week). In Mongolia, the charge per laborer is then ...

  (6 days/week)($1.10/day) = $6.60/week

The three laborers working 50 weeks/year will have a labor cost of ...

  (3 laborers)($6.60/week/laborer)(50 weeks/year) = $990/year

__

In the US, the labor charge per person per week is ...

  (14 hr/day)(6 day/week) = 84 hr/week

That's 40 hours of straight pay and 44 hours of overtime pay, or ...

  7.25(40 +1.5(44)) = 7.25(106) = 768.50

For 150 person-weeks per year, the total US labor charge is ...

  ($768.50/person/week)(3 persons)(50 weeks/year) = $115,275/year

__

The materials cost for a year is ...

  ($50/rug)(12 rugs/year) = $600/year

__

The revenue is ...

  ($2000/rug)(12 rugs/year) = $24,000/year

Profit is the difference between revenue and the total of costs:

  profit = $24,000 -($990 +600 +10000) = $12410 . . . made in Mongolia

__

So, the table gets filled as follows:

  (labor, material, fixed cost, revenue, profit)

<u>Mongolian-made</u>

  ($990, $600, $10000, $24000, $12410)

<u>US-made</u>

  ($115275, $600, $10000, $24000, -$101,875)

The US labor cost would be $115,275.

_____

<em>Comment</em>

For the given selling price, the break-even labor cost is about $1.06 per hour (on average). At US labor rates, the break-even selling price is about $10,490 per rug.

7 0
3 years ago
Hi :) anyone able to teach this? I don’t understand the question , thanks in advance!
puteri [66]

a) 62.855m

We will need to use the Pythagorean Theorem here, as we know a and c, but not b. I have attached an image of a triangle sketch to set up the problem, which should hopefully help us to visualize this problem a bit better.

Pythagorean Theorem: a^2 + b^2 = c^2

(19.8)^2 + b^2 = (65.9)^2

392.04 + b^2 = 4342.81

b^2 = 3950.77

b = 62.855 (rounded to 3 places)

b) m = 0.315

The gradient is also known as the slope. I've shown what the points would be in the image attached. Now that we know the value of b (x in the points in image), we can use points E and C to find the slope.

Point 1: (0,0)

Point 2: (62.855, 19.8)

m = (19.8 - 0) / (62.855 - 0)

m = 19.8 / 62.855

m = 0.315 (rounded to three places)

c) 17.485 degrees

The angle of inclination would be angle C. To find angle C, we will need to use an inverse trigonometry function. Any can be used since we know all of the side lengths, but I will show Sine here, opposite / hypotenuse.

sin(x) = 19.8 / 65.9

x = sin^-1 (19.8/65.9)

x = 17.485 degrees (rounded to 3 places)

Hope this helps!! :)

7 0
3 years ago
A small concert hall was setting up chairs for the next concert. The graph below shows the
Y_Kistochka [10]

I believe it's A, sorry if it's incorrect. ^-^'

4 0
3 years ago
An electrician earns $110 after his first hour of working for a client. His total pay based on the number of hours worked can be
Sveta_85 [38]
Add the rest of the question
5 0
3 years ago
Uh Expanded form pls? 4.02 x 10^5
Vera_Pavlovna [14]

Answer:

4.02 x 10 x 10 x 10 x 10 x 10

Step-by-step explanation:

The part that needs expanding is the exponent. Since it is to the power of 5 there needs to be 5 written out 10's, all multiplied.

4.02 x 10 x 10 x 10 x 10 x 10

4 0
3 years ago
Read 2 more answers
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