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Length of an Arc Application
Problem 203: Assume the orbit of Mercury around the sun is a perfect circle. Mercury is approximately 36 million miles from the sun. Solution:
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Trigonometric Ratios Application
Problem 202: Suppose we are looking out a window that is 50 ft from the ground and we look down at a angle (this is called the angle of depression) to spot a fire on the ground. Approximately how far away from us in is the fire? Why is this only an approximation? Solution: The…
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NonLinear System of Equations by Substitution II
Problem 201: Solve the system by using substitution: Solution: Using equation two and plugging it into equation one we have (1) Using this ‘s values we can find the ‘s values. That is, : (2) : (3) Thus the potential solutions are and . However, we need to check that this potential…
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Nonlinear System of Equations by Substitution
Problem 200: Solve the system by using substitution . Solution: Using equation two and plugging it into equation one we have (1) Using this ‘s values we can find the ‘s values. That is, : (2) : (3) Thus the potential solutions are and . However, we need to check that this…
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Linear Equations Application
Problem 198: A class used cars and buses for a field trip. They used 6 vehicles for this trip. Each cars hold 5 students and each bus holds 30 students. If 80 students went to the trip how many of each vehicle did they use? Solution: Let be the amount of cars used and the…
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Obtaining a Line from Two Points
Problem 198: Find the equation of a line that contains the points and . Write the equation in slope-intercept form. Solution: The slope-intercept form of a line is given by (1) Using our two given points we can the slope. That is, (2) Then (1) takes the form (3) We just need…
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Linear Equations
Problem 197: Wilbur sent $142 on shirts. Printed shirts cost $24. Plain shirts cost $11. If he purchased a total of 7 shirts, how many of each kind did he purchase? Solution: Let denotes the amount of printed shirts and the amount of plain shirts. Since it costed Wilbur $142 for the shirts, we have…
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Radicals in Applications
Problem 196: The skid marks of a vehicle involved in an accident were 122 feet long. The speed of the car before the brakes were applied is feet/second. Find the speed of the vehicle before the brakes were applied. Round your answer to the nearest tenth. Solution: Let be the speed of the car. Then…
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Triangles Application
Problem 195: An architect is designing the entryway of a restaurant. She wants to put a triangular window above the doorway. Due to energy restrictions, the window can only have an area of 120 square feet and the architect wants the base to be 4 feet more than twice the height. Find the base and…
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Right Triangle Application
Problem 194: A boat’s sail is in the shape of a right triangles. The hypothenuse will be 17 feet long. The length of one side will be 7 feet less than the length of the other side. Find the lengths of the other sides of the sail. Solution: If we have a right triangle, we…
One Problem at a Time
