Math Answers

convert 67.5% into simple fraction

(1) Using an identity from this section, write sin 7x − sin 3x as a product.
(2) Using an identity from this section, find the exact value of sin 105◦
sin 15◦
(3) Using an identity from this section, find the exact value of sin 195◦
cos 75◦
(4) Using identities from this section, verify the identity cos t−cos 3t over sin t+sin 3t = tan t.
(5) Using an identity from this section, write sin 7x sin 3x as a sum or a difference.

8/49 × 7/24 ÷ − 2/14

The annual bonus given to the employees of a company is 5% of their taxable incomes . after the state and central taxes are deducted.The state tax 10% of taxable income. The central tax is 20% of taxable income after deducting the state tax. Formulate this situation for determining the bonus.as a linear system.

Show that d : Q [x] / { 0 } --> N Union {0} : d{f} = 2^(deg f) is a Euclidean valuation on Q [x] .

Consider the ring Homomorphism phi : Z [x] --> Z/(3) : phi [summation (n) (i=0) of a_i x^i ]= a_0 bar .Show that Ker phi = (x,3) . What does the Fundamental Theorem of Homomorphism say in this case ?

Check whether f :( 4Z, +) --> ( Z_4 , +) : f(4m) = bar m is a group Homomorphism or not. If it is , what does the Fundamental Theorem of Homomorphism gives us in this case? If is not a Homomorphism , obtain the range of f

How many Sylow 5 - subgroups, Sylow 3 - subgroups and Sylow 2 - subgroups can a group of order 200 have ? Give reasons for your answer .

Let G be a group , H ∆= G and beta <= (G/H) . Let A = { x belongs to G | H x belongs to beta } . Show that (1) A <= G ,
(2) H∆= A , (3) beta =( A/H ) .