Select from the drop-down menus to correctly complete the proof. To prove that 4π is irrational, assume the product is rational and set it equal to ab, where b is not equal to 0: 4π=ab. Isolating π gives π=a4b. The right side of the equation is
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. Because the left side of the equation is
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, this is a contradiction. Therefore, the assumption is wrong, and the number 4πis
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.

(! ) three cylinders have a height of 8 cm. cylinder 1 has a radius of 1 cm. cylinder 2 has a radius of 2 cm. cylinder 3 has a radius of 3 cm. find the volume of each cylinder

The edge of a cube was found to be 30 cm with a possible error in measurement of 0.4 cm. use differentials to estimate the maximum possible error, relative error, and percentage error in computing the volume of the cube and the surface area of the cube. (round your answers to four decimal places.) (a) the volume of the cube maximum possible error cm3 relative error percentage error % (b) the surface area of the cube maximum possible error cm2 relative error percentage error %

In a two-digit number the units' digit is 7 more than the tens' digit. the number with digits reversed is three times as large as the sum of the original number and the two digits. find the number.