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Lady_Fox [76]
3 years ago
15

Prove that: sin8A/1-cos8A=cot4A​

Mathematics
1 answer:
nikitadnepr [17]3 years ago
8 0

Step-by-step explanation:

Recall the identity

\tan \frac{A}{2}= \dfrac{1 - \cos A}{\sin A}

We can see that

\dfrac{\sin 8A}{1 - \cos 8A} = \dfrac{1}{\tan 4A}= \cot 4A

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When Justin goes to work, he drives at an average speed of 60 miles per hour. It takes about 1 hour and 30
dexar [7]

Answer:

$13.14

Step-by-step explanation:

60 mi/1 hour = x mi/1.5 hours

x = 90 mi to drive to work

25 mi/1 gallon = 90 mi/y gallons

y = 3.6 gallons to get to work

$3.65/1 gallon = $z/3.6 gallons

z = $13.14

6 0
3 years ago
Pleas help you'll git 30 points
Mandarinka [93]

Answer:

the answer would be A.

Step-by-step explanation:

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4 0
3 years ago
School a has 18 staff and 225 students.
Pavel [41]

Answer:

School A

Step-by-step explanation:

School A has a ratio of 18/225 = 2/25 staff to students
School B has a ratio of 23/322 = 2/28 = 1/14 staff to students
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6 0
3 years ago
The function f(x) = x2 + 22x + 58 is translated 4 units to the right and 16 units up. What is the vertex form of the new functio
kap26 [50]

Answer:

The new function is (x + 7)² - 47 ⇒ the 3rd answer

Step-by-step explanation:

* Lets put the function f(x) in the vertex form at first and then make

 the translation

∵ The general form of the quadratic function is

  f(x) = ax² + bx + c

∵ The x-coordinate of the vertex of the function is -b/2a

∵ The y-coordinate of the vertex of the function is f(-b/2a)

- Lets find a , b from the function two find the vertex point

∵ f(x) = x² + 22x + 58

∴ a = 1 , b = 22 , c = 58

∵ x-coordinate of the vertex = -b/2a

∴ x-coordinate of the vertex = -22/2(1) = -11

∵ y-coordinate of the vertex = f(-11)

∴ f(-11) = (-11)² + 22(-11) + 58 = 121 - 242 + 58 = -63

∴ The vertex point is (-11 , -63)

- The vertex form of the quadratic function is f(x) = (x - h)² + k , where

  (h , k) are the coordinates of the vertex point

∵ The vertex point is (-11 , -63)

∴ h = -11 , k = -63

∴ f(x) = (x - -11)² + -63

∴ f(x) = (x + 11)² - 63

* lets revise the rules of the translation

- If the function f(x) translated horizontally to the right  

 by m units, then the new function g(x) = f(x - m)

- If the function f(x) translated horizontally to the left  

 by m units, then the new function g(x) = f(x + m)

- If the function f(x) translated vertically up  

 by n units, then the new function g(x) = f(x) + n

- If the function f(x) translated vertically down  

 by n units, then the new function g(x) = f(x) – n

∵ f(x) will translate 4 units to the right

∴ m = 4

∵ f(x) ⇒ f(x - m)

∴ (x + 11)²  ⇒ (x + 11 - 4)² = (x + 7)²

∵f(x) will translate 16 units up

∴ -63 will add by 16

∴ n = 16

∴ f(x) ⇒ f(x) + n

∵ -63 + 16 = -47

∴ The new function is (x + 7)² - 47

5 0
3 years ago
Read 2 more answers
Explain why the statement t > 13 is an inequality
Lelu [443]
Because it has ">" in it.
4 0
3 years ago
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