18. Find the equation of the line x=5t+6 and y=3?5t in the form y=mx+b.19.What is the slope of the line x=?6t+9 and y=4t+2. m= (b) Where does the line cross the x-axis? (c) Where does the line cross the y-axis?20.Find the point of intersection of the line x=2t+10 and y=3t+1 with the line 2x+3y=0. x= y=22.Suppose the points (3,5) and (19,14) are on line L. (a) What point is midway between these points? (b) What points is 1/3 of the way from (3,5) toward (19,14)? (c) If (4,y) is on L, find y. y= (d) If (x,8) is on L, find x. x=15.Two car companies Elvis and Hearts rent cars. The Elvis car costs 30 dollars plus 20 cents per mile. The Hearts car costs 50 dollars with 50 free miles and then costs 15 cents per mile. On scratch paper graph the cost against distance driven for both companies. (a) It is cheaper to rent from Elvis if you are driving less than _______miles.28.The temperature, T, of a gas is jointly proportional to the pressure P of the gas and the volume V occupied by the gas. Use C as your proportionality constant. (a) Express the temperature in terms of the pressure and the volume. T(P,V)= (b) Use your answer to (a) to express the pressure in terms of the volume and the temperature. P(T,V)= 30.The cost C of moving rubble is proportional to the product of the mass M of the rubble and the distance D the rubble must be moved. Use K as your proportionality constant (Note: we don't use C since we are already using it for cost). (a) Find C(M,D). C(M,D)= (b) If it costs 50 dollars to move 1 ton of rubble 1 mile, how much does it cost to move 14 tons 20 miles?. $29.The weight of a sphere is proportional to its radius cubed. If a sphere of diameter 2 cm has a mass of 2 grams, what diameter sphere has a mass of 128 grams?31.The cost of flying a passenger plane consists of fuel cost and hourly pay for the flight crew. The faster a plane flies, the more fuel it uses to fly each mile. Suppose that the cost of fuel to fly one mile is proportional to the speed of the plane. The plane flies a distance of D miles. (a) Express the time T taken to fly D miles in terms of the velocity V of the plane. T(D,V)= hours (b) Express the cost of the fuel F in terms of the velocity V and the distance D. Use K as your proportionality constant. F(V,D)=$ (c) Express the cost of the flight crew f in terms of the velocity V, the distance D, and the hourly pay P. f(V,P,D)=$ (d) Express the total operating costs C in terms of the velocity V, the distance D, and the hourly pay P. C(V,P,D)=$ (e) If the flight crew costs 200 dollars per hour and the fuel costs 100 dollars per hour when the speed is 300mph how much would it cost to fly 1200 miles at 600 mph. $32. The law of gravitation states that there is a force of attraction between any two objects. The strength of this force is proportional to the product of the masses of the two objects and inversely proportional to the square of the distance between them. Use this to express the force in terms of the two masses M and m and the distance between them r. Use G as your proportionality constant. (G is called the universal gravitational constant.)F(M,m,r)=34.The time is takes to build a skyscraper is proportional to its height and inversely proportional to the number of construction workers. If it takes 10 workers 2.5 years to build a 20 story building, how long will it take 100 workers to build a 40 story building? years35.The world population in 1990 was 5.4 billion and in 1995 was 5.8 bilion. Use linear extrapolation to find the population in 2010. ___________billion 36.For the function f(x)=x? we know f(4)=2 and f(9)=3. (a) Use linear interpolation to find 5??? 5???? (b) Use the table of square roots in the back of the text to find the error to 3 decimal places. Error = (c) What is the percentage error? (Recall that percentage error is 100*error/(exact answer).) Percent error = 37.The average sea-level in 1900 at London-bridge was 33 feet. In 1990 it was 33.08 feet. Use linear interpolation or extrapolation to find: (a) What the average sea-level was in 1959. feet (b) In what year the average sea-level will be 40 feet.40.Combine the following into a single logarithm. For example combining log(53)+log(27) into a single log the answer is log(53×27). Don't bother working out what 53×27 actually is. BUT BEWARE, webwork has kindly(!) printed log( ) for you. So all you need to write is what goes INSIDE the (...) bit. So for the example you would actually type 53×27. Typing log(53×27) will lead to much grief and gnashing of teeth.a)log(20)+log(40)= LOG( )b)log(20)?log(40)= LOG( )c)5log(2)= LOG( )d)log(x)+log(x)= LOG( )e)5log(x)+6log(x)= LOG( )f)log(x2)?log(x6)= LOG( )g) log(x)+log(y)= LOG( )h) x×log(y)= LOG( )i) (x+y)log(a)= LOG( )j) (a+4)log(1)= LOG( )k) a×log(8)?b×log(8)= LOG(41.Use logarithms to solve the equation for x. [Hint: take logs of both sides and simplify]10^(x+3)=.544.A population of rabbits doubles every year and there were 1 million rabbits at the start of 1925.a) How many rabbits are there in 1930? [Hint: How many in 1926, 1927?...]_______ millionb) In what year will there be 10 million rabbits? [Hint: use logs] 46.The half-life of element X is 60 years. If there are 80 g initiallya) How much is there after 240 years? [There is an easy way] _________ gb) How much is there after 17 years? ___________ gc) When will 40 g remain? [there is an easy way] ________ yearsd) When will 50 g remain? [use logs] _________ years47.Bacteria are growing exponentially in an environment of unlimited space and food. The doubling time is 1 hour.a) If there are initially x milligrams of bacteria, express the mass of the bacteria as a function of time t. f(t)=b) Use your answer to (a) to write down an equation whose solution is the time at which there are 3x milligrams of bacteria. Enter your answer in the form, eg 3x=5t2. c) Solve your equation from (b) t = hours
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