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coldgirl [10]
2 years ago
9

Find an equation for y (in terms of β and α). Then find tan y.

Mathematics
2 answers:
dmitriy555 [2]2 years ago
7 0

This can be expanded through the tangent angle addition formula:

tan(α+β)=tanα+tanβ1−tan -α + tanβ

Thus,tan(x+y)=tanx+tany1−tan x tany

Hope it helps you

avanturin [10]2 years ago
5 0

Answer:

  • See below

Step-by-step explanation:

<u>Angle opposite to 6 is complementary of α:</u>

  • 90 - α

<u>Similarly, angle opposite to side 4 of the triangle in the right side is:</u>

  • 90 - β

<u>Sum of the interior angles of the triangle on the bottom:</u>

  • 90 - α + 90 - β + γ = 180
  • γ = α + β
  • tan γ = tan (α + β)

<u>From the smaller triangles we get:</u>

  • tan α = 4/6 = 2/3
  • tan β = 3/4

<u>Use the identity below and find the value of tan γ:</u>

  • tan (α + β) = (tan α + tan β)/(1 - tan α tan β)
  • tan γ =
  • tan (α + β) =
  • (2/3 + 3/4) / (1 - 2/3*3/4) =
  • (17/12) / (1/2) =
  • 17/6 =
  • 2 5/6
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The left and right page numbers of an open book are two consecutive integers whose sum is 385. Find these page numbers.
Alona [7]
Consecutive integers are integers that follow one another. For example, 2,3,4,5,etc.... are consecutive integers

So algebraically, consecutive integers follow the form x, x+1, x+2, etc...

Since the sum of two consecutive integers is 239, this means:

x%2Bx%2B1=239

2x%2B1=239 Combine like terms on the left side

2x=239-1Subtract 1 from both sides

2x=238 Combine like terms on the right side

x=%28238%29%2F%282%29 Divide both sides by 2 to isolate x

x=119 Divide

So our first number is x=119

So to find the next number, simply add 1 to it to get 119%2B1=120

Answer: So our two page numbers are 119 and 120
6 0
3 years ago
Evaluate the Expression<br> When X=2, 3x-1=
Alex777 [14]

Answer:

5

Step-by-step explanation:

If X equals 2, then 3 times X would be 6. This is because if a number and a variable are put together, you have to multiply them. 6-1 is 5.

4 0
2 years ago
Can someone help please
m_a_m_a [10]

Answer:

What do you need help with?

Step-by-step explanation:

4 0
2 years ago
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12. Find the value of x.<br> (11x - 151°<br> (5x - 13°
Step2247 [10]

Answer:

Step-by-step explanation:

I guess the angles are supplementary, which means they have a sum of 180º.

11x - 15 + 5x - 13 = 180

16x -28 = 180

16x = 208

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4 0
2 years ago
The guttering hold up to 20 litre of rain water. Work out the length of guttering in meters if the diameter is 11.5cm.
bazaltina [42]

Answer:

1107.0213 cm

Step-by-step explanation:

Assuming this gutter is half a cylinder,

Volume of half a cylinder = 0.5(πr²l)²

where, Volume = 20l, π = 3.142, r = 0.5(11.5) and l = ?

But, the other units are in cm while the Volume is in liters, so let's convert the liters to cm³

It would be easier to convert the liters to m³ then to cm³ rather than converting directly. So,

1000 L = 1 m³

     1 L = ?

1 ÷ 1000 = 0.001 m³

      1 m³ = 1,000,000cm³

0.001 m³ = ?

0.001 x 1,000,000 = 1000 cm³

So, if 1 L = 1000 cm³

      20 L = ?

20 x 1000 = 20,000 cm³

Thus, 20,000 = 0.5(3.142 x 0.5(11.5) x l)

20,000 = 0.5(3.142 x 5.75 x l)

20,000 = 18.0665l

Make l the subject and divide both sides by 18.0665

length = 1107.0213 cm

6 0
2 years ago
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