Math Answers

Show that (¬𝑃 ⟶ 𝑅) ∧ (𝑄 ↔ 𝑃) ⟺ (𝑃 ∨ 𝑄 ∨ 𝑅) ∧ (𝑃 ∨ ¬𝑄 ∨ 𝑅) ∧ (𝑃 ∨ ¬𝑄 ∨ ¬𝑅) ∧ (¬𝑃 ∨ 𝑄 ∨ 𝑅) ∧ (¬𝑃 ∨ 𝑄 ∨ ¬𝑅).

Prove that 1·1 ! + 2·2!+· ··+ n · n! = (n+I)!-1

whenever n is a positive integer.

 5. If the function y = y(x) is such that x dy dx + 2y = x cos x, use the integrating-factor method to show that y = sin x + 2 cos x /x − 2 sin x/x^2 + c/x^2 , where c is an arbitrary constant

 4. Find the general solution of the differential equation dy/dx + y cot x = 1, recalling that cot x = cos x / sin x 

 3. Find the particular solution of the linear equation dy/dx + 1/x y = x if y(1) = 0

1. Find the general solution of the differential equation dy/dx = y^2 /1 + x^2

William bought shares 20.3. and sold them 6.6. in the same year. The purchase price was 473 € and the selling price 639 €. What is the annual interest rate for the investment after the 30 % tax is paid from the sales profit?

A buyer and seller agreed following about the price of an excavator: The buyer pays

• 10869 € after 4 months and
• 74244 € after 8 months

Calculate the cash price of an excavator using annual discount interest rate of 7.3 %.

Jennifer deposits 15.3. 6148 € in an account with an annual interest rate of 1.76 %. At the end of that year, Jennifer withdraws her deposit (including the capital and acrrued interest). Her friend Janet wants to withdraw from her own account at the same time exatcly the same amount of money (including the capital and acrrued interest) as Jennifer. Janet makes her deposit 20.7. and the interest rate of her account is 2.1 % annually. The tax at source rate is 30 %. What is the amount of Janet's deposit?

23194 € was deposited on 4.4.2006 in a bank account. The interest rate was 3,5 % (p.a.) and the tax at source rate was 30 %. The bank added the accrued interest to the capital at the end of each year. Calculate the accumulated value of the investment on 4.4.2010 when the account was closed.