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#1: A city park is rectangular in shape. The longer side of the park is 500 feet. A walkway runs diagonally through the park. The angle formed by the walkway and the shorter side of the park is 65°.

What is the perimeter of the park?

The  shorter   side  is given by

500/tan 65   ≈ 233ft

So.....the perimeter ≈  2 [ 500 + 233  ]  = 2 [ 733 ]  ≈  1466 ft

#2: The initial balance of a mutual fund is $1800. The fund is expected to grow in value at an annual rate of 5%.

Let x represent the number of years since the fund was started. Let y represent the value of the fund x years later.

What equation models the value of the mutual fund x years after it was started?

y =  1800  (1.05)^x

#3: What type of exponential function is f(x)=0.75(2.1)^x
What is the function's percent rate of change?

Select from the drop-down menus to correctly complete each statement.

The function is an exponential (growth) function.

The percent rate of change of the function is  (210) %.

#4: Let cos(−θ)=4/5 and tanθ> 0.

What is the value of sin(−θ)?

Note  sin(-θ)  =  -sin(θ)      and cos (-θ)  =  cos (θ)

So......

cos (θ)  =  4/5      and  sin (θ) =  3/5      so.....-sin(θ)  =  -3/5 

#5: 

Let tan(x)=2/5.

What is the value of tan(π+x)

Note.....tan ( pi + x)   =  tan (x)     =     2/5