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A surveyor in a helicopter looks and sees that his instruments are broken. Knowing that a lake is 1000m wide, the piolet ovserves that the angle of depression to 2 points on the opposite shores of a lake are 32 degress and 45 degrees. What is the height of the helicopter to the nearest metre?

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Pace University MAT 100 Prof. \( \qquad \) Fall 2024 Practice Exam 3 Name 18. The product of two consecutive even numbers is 288 . Find the numbers. 19. A caterer estimates that 6 gallons of punch will serve 40 people. How much additional punch would be required to serve 60 people? 20. A water tank can be filled in 6 minutes and emptied in 8 minutes. If the drain is accidentally left open when the tank is being filled, how long does it take to fill the tank? Label your variable with appropriate units. Page 2 of 2

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2.05 mol of O2 gas is held at 500 K in a 2 L container. Use the van der Waals equation, [P+a(nV)2](V−nb)=nRT to calculate the pressure of the gas. Constants needed for the problem include R=0.08206 L⋅atmmol⋅K and constants of a=1.363 atm⋅L2mol2 and b=0.0319 Lmol for O2. 42.452 atm 42.526 atm 42.056 atm 42.045 atm

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Example 4. A cylindrical propane tank has a radius of 2 ft and a volume of \( 50.24 \mathrm{ft}^{3} \). What is the height of the tank?

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6. What type of mutation affects only a single nucleotide base on a gene? O Mutation caused by UV radiation Back mutation O Mutation caused by a nucleoside analog O Frameshift mutation O Point mutation

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A patient is prescribed 0.260 mg of a drug that is available in 65-µg tablets. How many tablets are needed? Round your answer to the nearest whole tablet. Note: Reference the SI prefixes table for additional information. tablets are needed.

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Problem 13. For each case, decide whether or not S is a subring of R. (1) S is the set of all rational numbers of the form (a)/(b), where b is not divisible by 3 , and R=Q. (2) S is the set of all functions which are linear combinations of the functions {1,cosnt,sinnt|ninZ}, and R is the set of all functions that map R->R. (3) S is the set of real matrices of the form ([a,b],[-b,a]), and R is the set of all real 2 imes 2 matrices. Problem 13. For each case, decide whether or not S is a subring of R. (1) S is the set of all rational numbers of the form a/b; where b is not divisible by 3, and R=Q. (2) S is the set of all functions which are linear combinations of the functions {1,cos nt,sin nt |n E Z}, and R is the set of all functions that map R - R. (3) S is the set of real matrices of the form and R is the set of all real 2 x 2 matrices.

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Write a linear equation for the following table. \(x = \text{time}\) \(y = \text{distance}\) \begin{tabular}{|c|c|} \hline 1 & 54 \\ 2 & 73 \\ 3 & 92 \\ 4 & 111 \\ 5 & 130 \\ \hline \end{tabular} y = \underline{\qquad}x + \underline{\qquad}

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\lim_{x \to -\infty} (x^2 - x^3)e^{2x}

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Listen A wheat farmer sells wheat in a perfectly competitive market and hires labour in a perfectly competitive market. The market price of wheat is $2 a bushel, the wage rate is $10, the farmer employs five workers and the marginal product of the fifth worker is 3 bushels. What would you advise this farmer to do? A) Do nothing because the wage rate and the marginal product of the last worker hired are equal. B) Reduce employment because the wage paid is more than the marginal revenue product. C) Reduce the product price so that the wage and marginal revenue product will be equal. D) Increase employment because the wage paid is less than the marginal revenue product.

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