True, this equation is a quadratic equation,.
        
                    
             
        
        
        
Csc a - sin a = cos a cot a
1/sin a - sin a = cos a (cos a / sin a)
(1 - sin^2 a)/sin a = cos^2 a/sin a
cos^2 a/sin a = cos^2 a/sin a
Therefore, the given equation is an identity.
        
             
        
        
        
37.5 km is equal to 15 cm
        
             
        
        
        
Answer:
Options (1), (2), (3) and (7)
Step-by-step explanation:
Given expression is ![\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D) .
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Now we will solve this expression with the help of law of exponents.
![\frac{\sqrt[3]{8^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}=\frac{\sqrt[3]{(2^3)^{\frac{1}{3}}\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%5B3%5D%7B8%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B%282%5E3%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
            ![=\frac{\sqrt[3]{2\times 3} }{3\times2^{\frac{1}{9}}}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B%5Csqrt%5B3%5D%7B2%5Ctimes%203%7D%20%7D%7B3%5Ctimes2%5E%7B%5Cfrac%7B1%7D%7B9%7D%7D%7D)
            
            
            
            
             [Option 2]
 [Option 2]
![2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B9%7D%7D%5Ctimes%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%3D%28%5Csqrt%5B9%5D%7B2%7D%29%5E2%5Ctimes%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%29%5E2) [Option 1]
 [Option 1]
 ![2^{\frac{2}{9}}\times 3^{-\frac{2}{3} }=(\sqrt[9]{2})^2\times (\sqrt[3]{\frac{1}{3} } )^2](https://tex.z-dn.net/?f=2%5E%7B%5Cfrac%7B2%7D%7B9%7D%7D%5Ctimes%203%5E%7B-%5Cfrac%7B2%7D%7B3%7D%20%7D%3D%28%5Csqrt%5B9%5D%7B2%7D%29%5E2%5Ctimes%20%28%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%20%29%5E2)
                 
                 ![=\sqrt[9]{4}\times \sqrt[3]{\frac{1}{9} }](https://tex.z-dn.net/?f=%3D%5Csqrt%5B9%5D%7B4%7D%5Ctimes%20%5Csqrt%5B3%5D%7B%5Cfrac%7B1%7D%7B9%7D%20%7D) [Option 3]
 [Option 3]

                ![=\sqrt[9]{2^2}\times \sqrt[3]{3^{-2}}](https://tex.z-dn.net/?f=%3D%5Csqrt%5B9%5D%7B2%5E2%7D%5Ctimes%20%5Csqrt%5B3%5D%7B3%5E%7B-2%7D%7D) [Option 7]
 [Option 7]
Therefore, Options (1), (2), (3) and (7) are the correct options. 
 
        
             
        
        
        
The formula for the amount of a monthly payment A on principal amount P at interest rate i loaned for t years is given by
... A = P(i/12)/(1 -(1 +i/12)^(-12t))
Filling in the given values, this is
... A = $204000(.05/12)/(1 -(1 +.05/12)^(-12·20)) ≈ $1346.31