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<e> Solve the first order linear inhomogeneous differential equation using the constant variation method
y,- (3y/x)=x
[DMe] Define group. Show that the set P3 of all permutations on three symbols 1,2,3 is a finite non-abelian group of order six with respect to permutation multiplication as composition.
A company has learned that by pricing a newly released toy at $7, sales will reach 3000 per day. Raising the price to $9 will cause the sales to fall to 2000 per day. Assume that the ratio of change in price to change in daily sales is constant and let x be the price of the toy and y be the number of sales.
a. Find the linear equation that models the price-sales relationship for this toy. [Hint: The line must pass through (7,3000) and (9,2000).]
b. Use this equation to predict the daily sales of the toy if the price is set at $8.50.
Find the equation of the line.
Through (3,−5); perpendicular to y=−10.
Find an equation of the line. Write the equation using function notation.
Through (−5,−9); parallel to 6x+5y=11
Find an equation of the line. Write the equation using function notation.
Through (3,−6); perpendicular to 4y=x
Find an equation of the line through (3,4) and parallel to y=3x−4. Write the equation using function notation.
Find an equation of the line passing through the given points. Use function notation to write the equation.
(−2,−2) and (−4,−3)
Find an equation of the line passing through the given points. Use function notation to write the equation.
(3,11) and (4,16)
SHOW that every open interval is uncountable
