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IgorLugansk [536]
3 years ago
14

Last week, Wendy pell earned $440 for regular-time work by working 40 regular-time hours at $11 an hour. For the week, she was a

lso paid time-and-a-half pay for 7 overtime hour and double-time pay for another 6 1/2 hours. What were her total earnings for the week?
Mathematics
1 answer:
ki77a [65]3 years ago
6 0

Answer:

698.5

Step-by-step explanation:

Time-and-a-half. Time-and-a-half is payment to a worker (or workers) at 1.5 times their usual hourly rate.

11×1.5=16.5 $ per hour

16.5 ×7 =115.5 $ - total for overtime

11×2 = 22$ per hour

22×6.5= 143$ - total for double time payment

440+143+115.5 = 698.5 $ - total earnings

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Prove that: [1 + 1/tan²theta] [1 + 1/cot² thata] = 1/(sin²theta - sin⁴theta]
Stels [109]

Step-by-step explanation:

<h3><u>Given :-</u></h3>

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

<h3><u>Required To Prove :-</u></h3>

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

<h3><u>Proof :-</u></h3>

On taking LHS

[1+(1/Tan²θ)] + [ 1+(1/Cot²θ)]

We know that

Tan θ = 1/ Cot θ

and

Cot θ = 1/Tan θ

=> (1+Cot²θ)(1+Tan²θ)

=> (Cosec² θ) (Sec²θ)

Since Cosec²θ - Cot²θ = 1 and

Sec²θ - Tan²θ = 1

=> (1/Sin² θ)(1/Cos² θ)

Since , Cosec θ = 1/Sinθ

and Sec θ = 1/Cosθ

=> 1/(Sin²θ Cos²θ)

We know that Sin²θ+Cos²θ = 1

=> 1/[(Sin²θ)(1-Sin²θ)]

=> 1/(Sin²θ-Sin²θ Sin²θ)

=> 1/(Sin²θ - Sin⁴θ)

=> RHS

=> LHS = RHS

<u>Hence, Proved.</u>

<h3><u>Answer:-</u></h3>

[1+(1/Tan²θ)]+[1+(1/Cot²θ)] = 1/(Sin²θ-Sin⁴θ)

<h3><u>Used formulae:-</u></h3>

→ Tan θ = 1/ Cot θ

→ Cot θ = 1/Tan θ

→ Cosec θ = 1/Sinθ

→ Sec θ = 1/Cosθ

<h3><u>Used Identities :-</u></h3>

→ Cosec²θ - Cot²θ = 1

→ Sec²θ - Tan²θ = 1

→ Sin²θ+Cos²θ = 1

Hope this helps!!

7 0
2 years ago
How would you solve this problem?
vfiekz [6]

Answer:

x = 47

Step-by-step explanation:

The exterior angle is the sum of the opposite interior angles for a triangle

2x-2   = x + 45

Subtract x from each side

2x-2 -x = x+45-x

x-2 = 45

Add 2 to each side

x-2 +2 = 45+2

x = 47

4 0
2 years ago
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Add 7/10 + (-17/20)....
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7/10 + (-17/20)

Make the denominators equal:

14/20 + (-17/20)

Add:

-3/20

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3 years ago
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40-15=g so they scored 25 this year and 25+15=40
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