Math Questions
1. Find the angular size of a circular object with a 1-inch diameter viewed from a distance of 2
The angular size of the object is?
2. A mountain peak rises from sea level to a summit elevation of 3399 ft over a horizontal distance of 15,847 ft. Find the grade of the peak. The grade of the peak is___%
3. Given that the pair of triangles is similar, find the length of the side labeled n.
4. To get to a cabin, Dana can ride a bicycle west from a parking lot along the edge of a rectangular reservoir for 1.5 miles, and then south along the edge for 0.8 miles. Or she can row a boat directly from the parking lot. If Dana can ride 1.3 times as fast as she can row, which is the faster route? Choose the faster route below.
__Riding a bicycle
__Rowing a boat
5. A King in ancient times agreed to reward the inventor of chess with one grain of wheat on the first of the 64 squares of a chess board. On the second square the King would place two grains of wheat, on the third square, four grains of wheat, and on the fourth square eight grains of wheat. If the amount of wheat is doubled in this way on each of the remaining squares, how many grains of wheat should be placed on square 18? Also find the total number of grains of wheat on the board at this time and their total weight in pounds. (Assume that each grain of wheat weighs 1/7000 pound.) How many grains of wheat should be placed on square 18?
6. A leprechaun places a magic penny under a girl’s pillow. The next night there are 2 magic pennies under her pillow. Each night the number of magic pennies doubles. How much money will the girl have after 25 nights?
7. The initial population of a town is 4000, and it grows with a doubling time of 10 years. What will the population be in 8 years?
8. Use a growth rate of 0.9% to predict the population in 2053 of a country that in the year 2006 had a population of 100 million. Use the approximate doubling time formula. What is the predicted population of the country in 2053?
9. How many times greater is the intensity of sound from a concert speaker at a distance of 1 meter than the intensity at a distance of 6 meters? The intensity of sound is __ times as strong at 1 m as at 6 m.
10. A $1170 washing machine in a laundromat is depreciated for tax purposes at a rate of $ 90 per year. Find a function for the depreciated value of the washing machine as it varies with time. When does the depreciated value reach $0? The equation of the line in slope-intercept form is V=___.
11. Answer the questions for the problem given below.
The average price of a home in a town was $179 comma 000 in 2007 but home prices are rising by 4% per year. a. Find an exponential function of the form for growth to model the situation described.
12. The drug Valium is eliminated from the bloodstream exponentially with a half-life of 36 hours. Suppose that a patient receives an initial dose of 10 milligrams of Valium at midnight.
a. How much Valium is in the patient’s blood at noon on the first day?
b. Estimate when the Valium concentration will reach 25% of its initial level.
13. A toxic radioactive substance with a density of 7 milligrams per square centimeter is detected in the ventilating ducts of a nuclear processing building that was used 35 years ago. If the half- life of the substance is 20 years, what was the density of the substance when it was deposited 35 years ago?
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