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Two circles are concentric if they have the same center. On a coordinate plane, a circle has center (4, 6) and has a radius of 2 units. Which equation represents a circle that is concentric with the circle shown but has a radius that is twice as large? (x – 4)2 + (y – 6)2 = 4 (x – 4)2 + (y – 6)2 = 16 (x – 6)2 + (y – 4)2 = 16 (x – 6)2 + (y – 4)2 = 4
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The height in feet of a baseball can be modeled by the function y = −16t2 + 64t, where t is the time in seconds after the ball is hit. Find the baseball's maximum height and the time it takes to reach this height. Then find how long the baseball is in the air.
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A house has an electric heating system that consists of a 300-W fan and an electric resistance heating element placed in a duct. Air flows steadily through the duct at a rate of 0. 66 kg/s and experiences a temperature rise of 7°C. The rate of heat loss from the air in the duct is estimated to be 300 W. Determine the power rating of the electric resistance heating element. The constant pressure specific heat of air at room temperature is cp = 1. 005 kJ/kg·K
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Consider a chocolate manufacturing company that can produces two types of chocolate - A and B. Both the chocolates require Milk and Choco only. To manufacture each unit of A and B, the following quantities are required: • Each unit of A requires 1 unit of Milk and 2 units of Choco Each unit of B requires 2 unit of Milk and 1 units of Choco Currently, the milk price is 1$/unit and the choco price is 1$/unit. We can sell chocolate A for 10$ and Chocolate B for 8$. Assume we are planning for the next two years. The milk prices may go up 20% by probability of 40% and may go down 10% by probability of 60%. The choco prices may go up 30% by probability of 50% and may go down 20% by probability of 50%. The current demand for A is 1000 units per year. The demand is assumed to stay fix. We have limited budget. Lets calculate the profit we may get from producing any of these chocolates to decide about best option for the next two years (decide about to produce A or B?). The discount rate is k=0.1. Hint: assume we have period 0, 1, 2.
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Write the standard equation of the circle with the center ​(-14​,-5​) that passes through the point ​(​-7,​5).
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What is an equation of the the line that passes through the point (-1,4) and is parallel to the line x+y=4
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The sum of two numbers is 22, but the difference is 6. What are the two numbers?
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There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete?
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