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a_sh-v [17]
2 years ago
12

Which expression is equivalent to cot t sec t?

Mathematics
1 answer:
Solnce55 [7]2 years ago
8 0

Answer: csc(t)

Step-by-step explanation:

Alright, lets get started.

The given expression is given as :

cot( t) \times sec (t)

We know quotient identity as :

cot(t)=\frac{cos(t)}{sin(t)}

Similarly, we know reciprocal identity as :

sec(t)=\frac{1}{cos(t)}

lets plug the value of cot and sec in given expression

\frac{cos(t)}{sin(t)}  \times \frac{1}{cos(t)}

cos will be cancelled, remaining will be

\frac{1}{sin(t)}

Using reciprocal identity again, that will equal to :

csc(t)  ................... Answer (A)

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Two mechanics worked on a car. The first mechanic charged S95 per hour, and the second mechanic charged S115 per hour.
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The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.

Step-by-step explanation:

Given,

Charges of first mechanic = $95 per hour

Charges of second mechanic = $115 per hour

Total hours = 25

Total amount charged = $2675

Let,

The number of hours worked by first mechanic = x

The number of hours worked by second mechanic = y

According to given statement;

x+y=25    Eqn 1

95x+115y=2675     Eqn 2

Multiplying Eqn 1 by 95

95(x+y=25)\\95x+95y=2375\ \ \ \ Eqn\ 3

Subtracting Eqn 3 from Eqn 2

(95x+115y)-(95x+95y)=2675-2375\\95x+115y-95x-95y=300\\20y=300

Dividing both sides by 20

\frac{20y}{20}=\frac{300}{20}\\y=15

Putting y=15 in Eqn 1

x+15=25\\x=25-15\\x=10

The first mechanic worked for 10 hours and the second mechanic worked for 15 hours.

Keywords: linear equation, elimination method

Learn more about elimination method at:

  • brainly.com/question/12700460
  • brainly.com/question/12773544

#LearnwithBrainly

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Which of the following numbers is rational? <br><br> -9<br> 5/8<br> 0<br> all of above
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Step-by-step explanation:

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A sector with a radius of 6 cm has a central angle measure of 4pi/9 (in radians). What is the area of the sector?
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Step-by-step explanation:

The area of a sector of circunference delimited by an angle in radians can be calculated by using the formula below:

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area = [(4*pi/9)*(6)²]/2

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