A computer can perform 4.66 x 10³ calculations per second. How many calculations can this computer perform in one minute?
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- A sphere of radius r has surface area A = 4πr2 and volume V = 4/3πr3. The radius of sphere 2 is triple the radius of sphere 1. What is the ratio of the areas, A2/A1?As an architect, you are designing a new house. A window has a height between 130 cm and 140 cm and a width between 64 cm and 60 cm. What is the largest area that the window could be?Each of the following equations was given by a student during an examination 1/2 mv^2=1/2 mv_0^2+√mgh v=v_0+at^2 ma=v^2 Do a dimensional analysis of each equation and explain why the equation can’t be correct. (Hint: Determine the dimensions on each side of the equation and compare them.)
- The length and width of a rectangular room are measured to be 3.885 ± 0.0065 m and 3.2 ± 0.0045 m. In this problem you can approximate the error on a product or quotient of quantities by the sum of the percent error on each quantity.Calculate the floor area of the room in square meters.The radius of an atom of gold (Au) is about 1.35 Å. How many gold atoms would have to be lined up to span 4.0 mm? Express your answer using two significant figures.Physical units in mechanics are usually some combination of the dimensions time T, mass M, and length L. Consider the physical quantities m, r, u, a, and t with dimensions [m] = M, [r] = L, [u] = LT-, [a] = LT-2, and [1] = T. Enter the dimensional expression of the quantity on the right-hand side of each equation. Your answers may contain only M, L, T, and exponents. Assume that each of the following equations is dimensionally consistent. Lo = mur [Lo] = W = mar [W] = T
- 3 sig figsBacteria and other prokaryotes are found deep underground, in water, and in the air. One micron (10-6 m) is a typical length scale associated with these microbes. (a) Estimate the total number of bacteria and other prokaryotes onthe Earth. (b) Estimate the total mass of all such microbes.The dot product of vectors A and B is 6 sq. meters. If B = 3.5i + 5.1j – 3k meters and the angle between A and B is 63 degrees, what is the magnitude of vector A? Express your answers in meters and in two decimal places.
- U.S. football field is 120 yards long (including the end zones). How long is the field in the following units of measurement? (a) meters (b) millimeters mm (c) feet ft (d) inches inThe extraterrestrials in an exoplanet in a distant galaxy have the following units to measure distances.1 dray = 12 elim; 1 toof = 24 dray; 1 chin = 1250 toof. a. Convert 2.4 chin to elim. __________________ elim b. The alien grows vegetables in 16.0 square dray (i.e., dray2) patch. Calculate the area of the patch insquare elim (i.e., elim2).____________ clim2the average density of an atom is approximately 103 kg/m3. The nucleus of an atom has a radius about 10-5 times that of the entire atom, and contains nearly all the mass of the atom. What is the approximate density, in kilograms per cubic meter, of a nucleus?