Heights and Distances Questions and Answers

Two search teams spot a stranded climber between them on a mountain. The first team is 0.6 miles from the second team, and both teams are at an altitude of 0.2 miles. The angle of elevation from the first team to the stranded climber is 16 °. The angle of elevation from the second team to the climber is 24°. What is the altitude of the climber? Round to the nearest hundredth of a mile. miles

The infield of a baseball field is a square with sides measuring 90 feet. A ball thrown from third to first base is caught in 1.2 seconds. Find the speed of the ball in feet per second. Round to the nearest tenth.

A plane rises from take-off and flies at an angle of 15° with the horizontal runway. When it has gained 450 feet, find the distance the plane has flown. The plane has flown

A wheelchair ramp is to be built beside the steps to the campus library. Find the angle of elevation of the 34-foot ramp, to the nearest tenth of a degree, if its final height is 5 feet.

An object is thrown upward at a speed of 115 feet per second by a machine from a height of 4 feet off the ground. The height h of the object after t seconds can be found using the equation h = 16t² + 115t +4 When will the height be 172 feet? Hint: Set h to 172. When will the object reach the ground? 7.22

A plane flew for 5 hours heading west and for 4 hours heading south. If the total distance traveled was 3,444 miles, and the plane traveled 39 miles per hour faster heading west, at what speed was the plane traveling west? (Do not include the units in your response.)

Lily and William are both driving along the same highway in two different cars to a stadium in a distant city. At noon, Lily is 313 miles away from the stadium and William is 334 miles away from the stadium. Lily is driving along the highway at a speed of 44 miles per hour and William is driving at speed of 51 miles per hour. Let L represent Lily's distance, in miles, away from the stadium t hours after noon. Let W represent William's distance, in miles, away from the stadium t hours after noon. Write an equation for each situation, in terms of t, and determine the interval of hours, t, for which Lily is closer to the stadium than William.

The New York Knicks play in Madison Square Garden, the Los Angeles Lakers play in the Staples Center, and the Miami Heat play in American Airlines Arena. Madison Square Garden is about 2.8 x 10³ miles from the Staples Center and Madison Square Garden is about 1.4 x 10³ miles from American Airlines Arena. A. How many times of the distance the Knicks travel to play the Heat is the distance the Knicks travel to play the Lakers? B. How much further is the Staples Center than American Airlines Arena from Madison Square Garden?

Samantha goes on a road trip; she has to drive 1,311 miles and 20 hours to get to her destination but she can only drive 10 hours and 500 per day. Her rental car charges $98 per day and the car goes 22 miles and requires 1 gallon to travel 22 miles. The car can hold 16 gallon of gas and gas costs $4.60 per gallon. Now write an equation for the amount you will spend on the vehicle Rental and Gas. If C is the cost, x is the amount of days, and g is the number of gallons needed for your trip. Now include the cost of the gas in your equation - replace g.

Find the distance between the pair of points. (2,3) and (-7, -24) The distance is (Type an integer or a decimal rounded to three decimal places as needed.)

The surface areas of two similar solids are 441 cm² and 225 cm². If the approximate volume of the smaller solid is 250 cm³, what is the volume of the larger solid? A. 466 cm³ B. 932 cm³ C. 686 cm³ D. 500 cm³

Sumalee wants to make a 23% saline solution. She has already poured 9 qt. of a 18% saline solution into a beaker. How many qt. of a 32% saline solution must she add to this to create the desired mixture? 5 qt. 6qt. 1 qt. 2 qt. 9 qt.

The radius of a cylindrical construction pipe is 2 ft, and its length is 18 ft. Answer the parts below. Make sure that you use the correct units in your answers. If necessary, refer to the list of geometry formulas. (a) Find the exact volume of the pipe. Write your answer in terms of . Exact volume: (b) Using the ALEKS calculator, approximate the volume of the pipe. To do the approximation, use your answer to part (a) and the button on the calculator. Round your answer to the nearest hundredth. Approximate volume:

A homeowner is going to build the raised bed garden shown in the plan, against an existing garden wall. The homeowner will build the new wall by stacking concrete blocks without mortar, and then fill in the walled space with garden soil. The concrete blocks have dimensions 8 inches x 8 inches x 16 inches. The wall will be capped by capstones that have dimensions 8 inches x 2 inches x 16 inches. Concrete blocks cost $1.50 each, capstones cost $1.00 each, and garden soil costs $36 per cubic yard. The homeowner will do all the work and will buy materials. How much will they cost?

A jet and a passenger plane left Nairobi at the same time. The planes flew in opposite directions. The passenger plane flew 255 km/h faster than the jet. After seven hours they were 5005 km apart. Find the jet's speed. 340 km/h 240 km/h 230 km/h 80 km/h 210 km/h

A ball is thrown from an initial height of 5 feet with an initial upward velocity of 24 ft/s. The ball's height / (in feet) after / seconds is given by the following. h=5+24t-16t2 Find all values of 1 for which the ball's height is 9 feet. Round your answer(s) to the nearest hundredth. (If there is more than one answer, use the "or" button.)