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alexandr402 [8]
3 years ago
10

Prove the identity sin(x-y)/cosxsiny=tanxcoty-1

Mathematics
1 answer:
photoshop1234 [79]3 years ago
6 0

Step-by-step explanation:

\frac{sin(x - y)}{cos \: x \: sin \: y}  \\  \\  =  \frac{sin \: x \: cos \: y -cos \: x \: sin \: y }{cos \: x \: sin \: y}  \\  \\  =    \frac{sin \: x \: cos \: y }{cos \: x \: sin \: y}   +   \frac{-cos \: x \: sin \: y }{cos \: x \: sin \: y}  \\  \\ =    \frac{sin \: x \:}{cos \: x }  \times  \frac{cos \: y }{sin \: y}   -    1 \\  \\  = tan \: x \: cot \: y - 1 \\  \\  \therefore \:  \frac{sin(x - y)}{cos \: x \: sin \: y} = tan \: x \: cot \: y - 1  \\  \\ thus \: proved \\

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What is the square root of 150 simplified?
timurjin [86]
\sqrt{150}=\sqrt{25\cdot6}=\sqrt{25}\cdot\sqrt6=\boxed{5\sqrt6}
7 0
3 years ago
Read 2 more answers
Sterre charges $35 to file tax returns, but files for free if she only needs the easiest form. Then she donates $2 to clean wate
Sauron [17]

Charges for filing each tax return not through the easiest form = $35

Charges for the filing each tax return through the easiest form = $0

Donation made to clean water project for each tax return filed = $2

Let total tax returns filed be 'a' and total tax returns filed at $35 be 'b'

⇒ Tax returns filed at $0 = a-b

Total money charged by Sterre = $7, 245

Total donation made by Sterre = $1, 242

Now, first we will determine the total tax returns filed by Sterre

Total donation made by Sterre = Donation made per tax return × Total returns filed by Sterre

⇒ 1,242 = 2 × a

⇒ a = 621

Hence, Sterre filed total of 621 tax returns

Now total money charged by Sterre = Charges for filing each tax return not through the easiest form × Tax returns filed at $35

⇒ 7,245 = 35 * b

⇒ b = 207

Hence, Sterre filed 207 returns at $35.

⇒ Tax returns filed at $0 = 621 - 207

⇒ Tax returns filed at $0 = 414

Hence, at $35, Sterre filed 207 tax returns, and at $0 Sterre filed 414 tax returns.

6 0
4 years ago
What is the value of k? please answer fast
skad [1K]

Answer:

k = 10

Step-by-step explanation:

The external angle of a triangle is equal to the two opposite interior angles.

∠MYZ is an exterior angle of the triangle, thus

4k + 5 + 6k + 10 = 115, that is

10k + 15 = 115 ( subtract 15 from both sides )

10k = 100 ( divide both sides by 10 )

k = 10

6 0
3 years ago
Read 2 more answers
Can someone please help me answer number 6!?! please!!
Fynjy0 [20]

Hello there! Your answers would be:

a. 600 - 75x = y

b. 8 months

Need an Explanation?:


Part a:

Okay, so she has 600 dollars, and she has a monthly bill, but no income. This means she is not earning any money, only loosing some.

This equation will model your situation: 600 - 75x = y

This is because:

  • The 600 remains constant, you are taking away from it. The 75 x represents the amount from the total taken away after each month.
  • Again, she does not earn money, only spends it on her bill.
  • Y represents the total amount of money she has left after each month.

Part b:

This is asking us to see how many months it'll take for her to have $0. The question is telling us to have g(x) = 0. (This is just another way of saying y = 0, which translates to her having no money left)

So, plug 0 into the equation in place of y and solve for x.

600 - 75x = 0

<em>Start by subtracting 600 from both sides to work to isolate x.</em>

-75x = -600

<em>Next, divide -600 by -75 to finish isolating x and get your answer. </em>

X = 8

This means it will be 8 months before her checking account reaches 0.

<em>So, these are your final answers. I hope this helps, and have a great day! Please don't hesitate to ask if you need more help with this specific question! </em>


8 0
3 years ago
The weight of oranges growing in an orchard is normally distributed with a mean weight of 7 oz. and a standard deviation of 1.5
Katena32 [7]

Answer:

2 to 11 ounces would be the interval.

Step-by-step explanation:

Add 3 standard deviations above and below the mean to get the range in which 99.7% of the data in a normal distribution will fall

6.5 + 4.5 = 11

6.5 - 4.5 = 2.

Hope this helped!

3 0
3 years ago
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