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levacccp [35]
3 years ago
5

Solve for x 2cos(x + 40 ^ 0) = 1/2 for r 0<= x<=360^ Worth 6 marks

Mathematics
1 answer:
gregori [183]3 years ago
6 0

Answer: x = 115.5°

Step-by-step explanation:

I suppose that we have the equation:

2*cos(x + 40°) = 1/2 for 0° < x < 360°

Let's solve this.

First, we isolate the cosine function:

cos(x + 40°) = (1/2)/2 = 1/4

cos(x + 40°) = 1/4

Now we can use the Acos(x) function, remember that:

Acos(cos(x)) = x

cos(Acos(x)) = x

Then if we use this function in both sides, we get:

Acos( cos(x + 40°)) = Acos(1/4)

x + 40° = Acos(1/4) = 75.5°

x = 75.5° + 40° = 115.5°

x = 115.5°

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Answer:

1100 field-side tickets and 4500 end-zone tickets.

Step-by-step explanation:

Let x represent number of field side tickets and y represent number of end-zone tickets.

We have been given that the total number of people at a football game was 5600. We can represent this information in an equation as:

x+y=5600...(1)

y=5600-x...(1)    

We are also told that Field-side tickets were 40 dollars and end-zone tickets were 20 dollars.

Cost of x field side tickets would be 40x and cost of y end-zone tickets would be 20y.

The total amount of money received for the tickets was $134000. We can represent this information in an equation as:

40x+20y=134000...(2)

Upon substituting equation (1) in equation (2), we will get:

40x+20(5600-x)=134000

40x+112000-20x=134000

20x+112000=134000

20x+112000-112000=134000-112000

20x=22000

\frac{20x}{20}=\frac{22000}{20}

x=1100

Therefore, 1100 field side tickets were sold.

Upon substituting x=1100 in equation (1), we will get:

y=5600-1100

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