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question:A metal rod is formed into a circular arc with a radius of 4 meters. The angle that the arc subtends at the center is 60 degrees. If the temperature profile along the rod can be modeled using the function T(theta)=100sin(theta)+120, where theta is the angle in radians, find the average temperature of the rod. Round your answer to the nearest hundredth.

answer:To find the average temperature of the rod, we need to integrate the temperature function over the length of the arc and then divide by the length of the arc. First, we need to convert the angle from degrees to radians. 60 degrees = (60 * π) / 180 = π/3 radians Now, we can set up the integral for the average temperature: Average temperature = (1 / length of arc) * ∫[T(θ) * d(arc length)] The differential arc length, d(arc length), can be expressed as: d(arc length) = R * dθ where R is the radius of the circle (4 meters in this case). So, the integral becomes: Average temperature = (1 / length of arc) * ∫[T(θ) * 4 * dθ] The length of the arc can be calculated as: Length of arc = R * θ = 4 * π/3 Now, we can plug this back into the integral: Average temperature = (3 / (4 * π)) * ∫[T(θ) * 4 * dθ] from 0 to π/3 Average temperature = (3 / (4 * π)) * ∫[(100 * sin(θ) + 120) * 4 * dθ] from 0 to π/3 Now, we can integrate: Average temperature = (3 / (4 * π)) * [(-400 * cos(θ) + 480 * θ) | from 0 to π/3] Evaluate the integral at the limits: Average temperature = (3 / (4 * π)) * [(-400 * cos(π/3) + 480 * π/3) - (-400 * cos(0) + 480 * 0)] Average temperature = (3 / (4 * π)) * [(-400 * 1/2 + 480 * π/3) - (-400 * 1)] Average temperature = (3 / (4 * π)) * (-200 + 480 * π/3 + 400) Average temperature = (3 / (4 * π)) * (200 + 480 * π/3) Average temperature ≈ (3 / (4 * π)) * (200 + 480 * 1.047) Average temperature ≈ (3 / (4 * π)) * (200 + 502.56) Average temperature ≈ (3 / (4 * π)) * 702.56 Average temperature ≈ 167.43 The average temperature of the rod is approximately 167.43°C.

question:By . Daniel Mills . An 18-year-old Gold Coast girl has won her bid to have a 680,000-a-year drug subsidised so that she can receive ongoing medical treatments to keep her alive. Bianca Scott, who spent her recent 18th birthday wishing to stay alive, will finally have access to her first government-funded dose of Soliris, which will save her family more than 24,000 a fortnight and help her fight a very rare immune disease which attacks her internal organs. Ms Scott is suffering the life-threatening blood disease called atypical haemolytic uraemic syndrome, or aHUS which can result in blood clots and can destroy internal organs. Bianca has had 11 doses of Soliris since February, costing her family about 250,000, but now she will be given the drug for less after a joint State and Federal Government-funding agreement was reached. Scroll down for video . Bianca Scott was diagnosed with a rare condition called aHUS when she was seven months old, it reappeared late last year . Since her diagnosis, Bianca has spent most of her time in hospital in Brisbane, where she undergoes dialysis and plasma transfusions . Bianca is one of 70 Australians living with aHUS and among 10 who need the treatment urgently. So far she is the only Australian with access to the subsidised drug but it is hoped her case will open the debate up further for Soliris to be accessible to everyone. It is a short-term solution, her mother Tammy Hamawi said, but one that she hopes receives long-term funding. “We have won but we haven’t secured Bianca absolutely to access this medicine long-term,” Ms Hamawi told The Courier Mail. Bianca's mother, who had given up her job running her own mentoring and business consultancy company to care for her daughter, thanked Senator Barry O’Sullivan and Gold Coast MP Karen ­Andrews who told her on Tuesday that Bianca would get the treatment. She had been spending all of the family's money, as well as money borrowed from friends, on the life-saving treatment. She was forced to stop the treatment on June 5, given the ongoing financial demands. She said the government intervention in helping Bianca prolong her life is a big bonus - given Soliris 'is the only treatment' which helps manage her condition. 'Without a doubt Soliris is the most expensive drug in the world,' said Ms Hamawi. 'It is the only treatment in the whole world for aHUS.' Bianca was diagnosed with aHUS, which can strike at any age, when she was seven months old. She then found out then that her uncle had died of the disease as a child. Unusually, the illness lay dormant in Bianca before resurfacing late last year, just a few weeks after she finished high school. Bianca's mother Tammy Hamawi (left) discovered a drug that could treat aHUS, called Soliris, which costs 24,000 per fortnightly dose . Bianca was first diagnosed with the life-threatening illness when she was seven months old (pictured here after her initial diagnosis) So far Ms Hamawi has been able to pay for five courses of the treatment, with help from her family and from donations . Soliris is currently available at a subsidised rate for people suffering with another ultra-rare disease, called paroxysmal nocturnal haemoglobinuria (PNH) through the Life Saving Drugs Program (LSDP). It was being considered by the LSDP as a treatment for aHUS when the LSDP was put under review by the federal government earlier this year. The drug was then moved for consideration to the Pharmaceutical Benefits Advisory Committee (PBAC). The PBAC recommended that Soliris be subsidised under the Pharmaceutical Benefit Scheme for sufferers of aHUS, though there are still several bureaucratic steps to go through before any subsidy will come into effect. Kirsten Bruce, a representative of the aHUS Patient Support Group Australia said that the PBAC recommendation leaves many questions unanswered. Of particular concern, she says, is that under the proposed conditions, patients will only be eligible for the drug is they are currently experiencing a flare-up of the condition, and will only be allowed to take the drug for six months after they have recovered from the attack, even though it is recommended that sufferers remain on the drug for the duration of their lives. 'Sufferers want to know who will qualify for Soliris, whether they'll be able to stay on it long-term, there are so many question marks,' she said. 'The tragedy is there's a drug that's available, that works, and it sits on pharmacy shelves, the doctors want to be able to prescribe it but they can't.' A spokesperson for the Federal Department of Health confirmed that it was currently in negotiations with Alexion, who hold the patent for the drug. Alexion were contacted for comment. 'Mum noticed symptoms and she took me to hospital and they told me the aHUS had come back. Since then I was faced with this terrible battle,' she said. 'I couldn't keep any food down, I was always vomiting, I couldn't stand up, I'd feel very dizzy, I had fevers… sadly I have chronic kidney failure now.' She required an endless run of hospital visits – with Bianca requiring eight-hour stretches of dialysis three to four days a week, as well as plasma infusions – before Ms Hamawi heard of Soliris. 'Thank God for Google!' she said. Ms Hamawi was able to fund five doses of the drug, with the help of her family and friends, and two further doses were bought using donations, including a 19,000 donation from Bianca's school and an anonymous 10,000 donation. 'I am so grateful for that,' said Bianca. 'I thank everyone for that.' Since starting on Soliris on Valentine's Day, Bianca has turned a corner. She still requires dialysis, but the plasma infusions, which she describes as 'weird' and 'scary' have stopped, her hours in hospital have significantly decreased and she is feeling much better. Her blood tests are also showing vastly improved results, with the nephrologist telling Bianca on Monday that if her results continue in the direction they're going she might be able to come off dialysis. But with the cost of Soliris currently so high, it was cost 680,000 a year to keep her on the drug, Bianca and her mother do not have the money to buy their next dose, which Bianca is due to take on Thursday June 19. Without Soliris, Bianca will likely deteriorate, and if left too long, the damage to her kidney will be so severe that she will have to remain on dialysis for the rest of her life. 'She's 17, can you imagine a lifetime of chronic kidney failure? And when I say a lifetime, it's not going to be a long life,' said Ms Hamawi. Ms Hamawi is frustrated at Alexion, the U.S. company that produce Soliris and own the patent for the drug. 'On the one hand 680,000 a year to save your child's life is a big price, it's too high,' she said. However, most of her anger is directed at the Australian government, which she says is 'a system that we thought was there to protect and look after us [and] has in a way let us down'. 'It baffles me how could you justify fuelling aeroplanes to go and look for an aeroplane that’s who knows where. But when someone needs mediciine, and it is the only medicine that is available, you sit there and negotiate and it might take six months,' she said. For more information on Bianca's condition or to donate visit Bianca's Battle. Bianca (pictured right going to her school formal just before the aHUS resurfaced) is Tammy's only child . The 18-year-old is trying to stay positive despite her chronic condition . Soliris costs 24,00 for each dose of the drug .

answer:Bianca Scott, an 18-year-old from the Gold Coast, has won her battle to have the life-saving drug Soliris subsidized by the Australian government. Diagnosed with atypical haemolytic uraemic syndrome (aHUS) at seven months old, Bianca's condition resurfaced late last year, leading to chronic kidney failure and frequent hospital visits. Soliris, costing 24,000 per fortnightly dose, is the only known treatment for aHUS, but the high cost had been a significant burden for her family. After spending over 250,000 on 11 doses since February, Bianca and her mother, Tammy Hamawi, secured a joint State and Federal Government funding agreement, reducing the financial strain. This short-term solution, however, has not guaranteed long-term access to the drug. Bianca's case has sparked discussions about broader access to Soliris for other aHUS patients, with concerns over eligibility criteria and the duration of treatment. Despite the challenges, Bianca's condition has improved since starting Soliris, and she hopes to eventually come off dialysis. Her mother remains critical of the government's handling of the situation, emphasizing the need for a more efficient

question:What is the average of some numbers: 12, 13, 14, 520, 530, 1115, 1120, 1, 1252140, and 2345 if the average of all these numbers is 858.5454545454545?

answer:The average of a set of numbers is found by adding all the numbers together and then dividing by the count of the numbers. However, the average you provided, 858.5454545454545, does not seem to be correct for the set of numbers you've given. Let's calculate the correct average. First, we add all the numbers together: 12 + 13 + 14 + 520 + 530 + 1115 + 1120 + 1 + 1252140 + 2345 = 1257810 Now, we count the number of values: There are 10 numbers in total. Finally, we divide the sum by the count to find the average: 1257810 / 10 = 125781 So, the correct average of the numbers you provided is boxed{125781,} not 858.5454545454545.

question:Write a Python function that parses a number string and returns a float. The number string may contain spaces, plus/minus signs, and scientific notation. Ensure that the function correctly parses the number string and handles errors. Your code should pass the following assertions: ```python assert parse_number_string('8e3') == 8000.0 assert parse_number_string('123') == 123.0 assert parse_number_string('-45.67') == -45.67 assert parse_number_string('-9.87e-10') == -9.87e-10 ```

answer:You can use regular expressions to parse the number string. The pattern should match an optional sign, followed by one or more digits, an optional decimal point and fraction, and an optional scientific notation. You can use the `re` library to perform the matching and parsing. Here's how you can write the function: ```python import re def parse_number_string(s): pattern = r^([+-]?[0-9]+(.[0-9]*)?([eE][+-]?[0-9]+)?) match = re.search(pattern, s) if match: return float(match.group()) else: raise ValueError(Invalid number string) ``` The regular expression pattern (explained below) matches the following formats: - Positive or negative integer: `+123` or `-456` - Positive or negative decimal number: `+123.45` or `-67.89` - Positive or negative scientific notation: `+1e10` or `-2e-5` - Combination of the above: `+123.45e6` or `-78.9e-12`

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