Appearance
question:An endangered orangutan is fighting for life after being shot more than 100 times with an air rifle in a cruel attack. The female ape, called Aan,has been blinded in one eye and has sustained other serious wounds to her body after being struck repeatedly by pellets. She was hit 37 times in the head by the lead slugs, while 67 projectiles penetrated other parts of her body in the shooting, which took place in an oil palm plantation in the Indonesian part of Borneo. Wounded: A veterinarian from the Orangutan Foundation removes the airgun pellets from the orangutan . Sick: 37 pellets were shot into her head, while 67 peppered the rest of her body . 'We're amazed, but truly thankful, that she has managed to cheat death – but it has been touch and go', said a local conservationist. The savage attack is yet another incident in a catalogue of cruelty against the large apes which are being targeted by vigilantes working for oil plantation owners. As their forest habitat has dwindled with trees being chopped down for the forestry industries, orangutans have encroached onto oil plantations and other properties looking for food. Earlier this year the Daily Mail revealed the story of a mother orangutan photographed with her arms around a baby ape as hunters working for their oil plantation boss moved in for the kill. Fortunately conservationists were able to save her before any harm came to her or the infant and they were moved to another location. But Aan has not been so lucky. Conservationists said the only good news to emerge from the incident is that she has survived and has started to eat at a clinic where the pellets are still being removed from her. Aan’s recovery is being aided by volunteers from the British-based Orangutan Foundation, but they are concerned she could die from infections caused by the wounds to her head, as well as those near her heart and lungs. The head of the local conservation agency, Hartono, who like many Indonesians uses only one name, said: 'Even though she is eating, she is still, technically, fighting for her life. 'She has been very seriously injured and she could relapse at any moment. But she’s a true fighter. She’s fighting very hard.' Added to the fears that Aan could still die are concerns that should she survive she might lose the sight in her remaining eye and her hearing could be affected. If she survives, conservationists fear she will never be able to be released back into her slowly diminishing world in the wild. Touch and go: Aan could still die of her horrific injuries, but rescuers called her a 'fighter' She would be an easy target for hunters once again and she would have problems finding food. But keeping her in captivity would also cause her distress as she would want to return to a mate or an extended family still in the jungle. Rangers from the conservation group found Aan struggling through grassland on the outskirts of an oil plantation and managed to catch her and take her to a clinic. 'The next few weeks are touch and go,’ said Hartono. 'We are all praying for her.' Six months ago four men were sent to jail for eight months for shooting and beating to death three orangutans and long-nosed monkeys in East Kalimantan – the Indonesian part of Borneo, the large island that is shared with Malaysia. It was revealed after their arrest that the owners of a Malaysian oil company had paid them to drive the apes away from a plantation. Just 50,000 to 60,000 of the two species of orangutans are left in the wild, 80 per cent of them in Indonesia and the remainder in Malaysia. International conservation groups are worried the animals are faced with extinction from poaching and the rapid destruction of their forest habitat, which is being swallowed up by palm oil plantations.
answer:An endangered female orangutan named Aan is fighting for her life after being shot over 100 times with an air rifle in an Indonesian oil palm plantation on Borneo. Aan, who has been blinded in one eye and suffered multiple serious injuries, was hit 37 times in the head and 67 times in other parts of her body. Conservationists from the Orangutan Foundation are working to save her, but she remains in critical condition and at risk of infection. The attack highlights the ongoing conflict between orangutans and plantation workers, as the apes' habitat shrinks due to deforestation. If Aan survives, she may not be able to return to the wild due to potential permanent disabilities, making her an easy target for hunters and complicating her ability to find food. Conservationists are concerned about the future of orangutans, with only 50,000 to 60,000 left in the wild, primarily in Indonesia and Malaysia, as their habitat continues to be destroyed by palm oil plantations.
question:Given a tetrahedron (A B C D), three spheres are drawn with diameters (AB), (AC), and (AD). Prove that the union of the three spheres contains the entire tetrahedron.
answer:To prove the assertion, we use two observations that are straightforward to verify: 1. **Observation (i):** If point ( P ) lies outside the sphere whose diameter is ( XY ), then the angle ( XPY ) is less than ( 90^circ ).  2. **Observation (ii):** If ( XPY < 90^circ ), then points ( X ) and ( Y ) lie on the same side of the plane through ( P ) that is perpendicular to segment ( XP ).  Using these observations, we can prove the assertion as follows: 1. **Assume** that there exists a point ( P ) in the tetrahedron ( ABCD ) that lies outside all three spheres centered at points ( A, B ), and ( C ) with radii ( frac{AB}{2}, frac{AC}{2} ), and ( frac{AD}{2} ) respectively. 2. **Due to Observation (i):** Since ( P ) is outside all three spheres, the angles ( APB, APC,) and ( APD ) are all less than ( 90^circ ): [ angle APB < 90^circ, quad angle APC < 90^circ, quad angle APD < 90^circ ] 3. **Construct a Plane:** Now, construct a plane through ( P ) that is perpendicular to segment ( AP ). 4. **Application of Observation (ii):** By Observation (ii), points ( A, B, C, ) and ( D ) all lie on the same side of this plane (plane passing through ( P ) perpendicular to ( AP )). 5. **Contradiction:** However, since points ( A, B, C, ) and ( D ) all lie on the same side of this plane, ( P ) cannot be an internal point of the tetrahedron ( ABCD ). 6. **Conclusion:** Hence, the point ( P ) cannot be outside all three spheres simultaneously. Therefore, the union of these three spheres must contain the entire tetrahedron. [ boxed{text{The union of the three spheres contains the tetrahedron.}} ]
question:two employees x and y are paid a total of rs . 770 per week by their employer . if x is paid 120 percent of the sum paid to y , how much is y paid per week ?
answer:Let's denote the amount paid to employee Y per week as Y in rupees. According to the problem, employee X is paid 120 percent of the sum paid to Y. This can be written as: X = 120% of Y X = 1.2 * Y The total amount paid to both employees per week is Rs. 770. Therefore, we can write the equation: X + Y = 770 Now, substitute the value of X from the first equation into the second equation: 1.2 * Y + Y = 770 Combine like terms: 2.2 * Y = 770 Now, divide both sides of the equation by 2.2 to solve for Y: Y = 770 / 2.2 Y = 350 Therefore, employee Y is paid Rs. boxed{350} per week.
question:Discuss 3 asymptotes in hyperbolic geometry - use paragraph-based approach for explanations emphasizing logical progression & key insights.
answer:In hyperbolic geometry, asymptotes play a crucial role in understanding the behavior of curves and lines. Unlike Euclidean geometry, where parallel lines never intersect, hyperbolic geometry allows for multiple parallel lines to diverge from a common point, leading to the concept of asymptotes. Let's explore three types of asymptotes in hyperbolic geometry, highlighting their unique properties and relationships. Firstly, consider a hyperbola in the hyperbolic plane, which consists of two branches that diverge from a common point. The asymptotes of a hyperbola in hyperbolic geometry are the two lines that the branches approach as they tend towards infinity. These asymptotes are also known as the arms of the hyperbola. Intuitively, as you move further away from the center of the hyperbola, the branches become increasingly parallel to the asymptotes, eventually converging to them at infinity. Secondly, we have the asymptotes of a parabolic line, which is a line that is tangent to a circle at a single point. In hyperbolic geometry, a parabolic line has a unique asymptote, which is the line that the parabolic line approaches as it tends towards infinity. This asymptote is also known as the axis of the parabolic line. Interestingly, the axis is also the line that passes through the point of tangency and is perpendicular to the circle. Lastly, consider the asymptotes of a horocycle, which is a curve that is tangent to a line at a single point and has constant curvature. In hyperbolic geometry, a horocycle has a single asymptote, which is the line that the horocycle approaches as it tends towards infinity. This asymptote is also known as the base line of the horocycle. Notably, the base line is also the line that passes through the point of tangency and is parallel to the line that the horocycle is tangent to. A key insight is that these asymptotes are not just abstract concepts, but rather they have a profound impact on the geometry of the hyperbolic plane. For example, the asymptotes of a hyperbola can be used to construct new hyperbolas, while the asymptotes of a parabolic line can be used to construct new parabolic lines. Moreover, the asymptotes of a horocycle can be used to study the properties of horocycles and their relationships with other curves in the hyperbolic plane. The connections between these asymptotes and other areas of mathematics are also worth noting. For instance, the asymptotes of a hyperbola are closely related to the concept of projective geometry, where they play a crucial role in understanding the properties of projective transformations. Similarly, the asymptotes of a parabolic line and a horocycle have connections to the study of differential equations and the theory of curves in mathematics. By understanding these asymptotes, we can gain a deeper appreciation for the intricate relationships between different areas of mathematics and the beautiful structure of the hyperbolic plane.