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Posted: September 8th, 2022
Task 1
a) Write the following number as a fraction: 0.702702702…
b) Write as simply as possible:
(Hint: Change the root expressions to powers)
c) Solve the following equation:
Task 2
a) Determine the definition quantity and the value quantity of the functions below
b) Explain why the function f(x) above has an inverse. Find the inverse function, and state the definition quantity and the value quantity of the inverse function.
Task 3
Hans buys himself a Rolex. After a few years, he checks the value of the watch, and the value has then increased by 30%. In 2022, he checks the value again, and by then it has decreased by 25%. Hans thinks -Yes, yes, since the value increased by 30% and only decreased by 25%, I have gained 5% anyway-.
a) Is he right? Show by calculation how you arrived at your answer. (Hint: Use growth factor)
b) If the watch was worth NOK 70,000 when he bought it, how much is it worth in 2022?
Task 4
Hans has grown tired of being a professor, and has decided to get rich growing and selling instead -golden- flowers in his garden. Now he wonders how he can make the most money possible from his new floral business idea. He decides to grow and sell tulips and roses. The flower bed for Hans is a total of 20 (m2). Each tulip needs 0.6 (m2) to grow, and each rose needs 0.4 (m2). Since there are no natural gold flowers, Hans has to paint them with gold paint. He will set aside a maximum of 30 hours for this. Each tulip takes 0.5t to paint, while each rose takes 1t to paint. When the flowers are to be sold, Hans expects to earn 50 per tulip, and 75 per rose, not including the cost of gold painting.
a) Forklar hvorfor dette problemet gir følgende sett med ulikheter:
Also explain why the mathematical problem becomes maximizing the function
P(x, y) = 50x + 75y under these conditions.
b) What is the most Hans can earn from selling flowers, when you ignore the cost of gold paint?
c) Hans must pay 65 for gold paint per flower he paints. Is this a good one business idea, given that he grows the flowers that bring the most profit in b)?
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