Find the dimensions of the rectangle of largest area?
y will be the height. x will be half the width (mirrored across the y-axis). The formula for the area is: f(x) = 2xy Plug in for y: f(x) = 2x(5 - x²) f(x) = 10x - 2x^3 Take the first derivative: f'(x) = 10 - 6x² Set that to zero: 0 = 10 - 6x² 6x² = 10 x² = 10/6 x² = 5/3 x = √(5/3) x ≈ 1.29 y = 5 - (√(5/3))² y = 5 - 5/3 y = 15/3 - 5/3 y = 10/3 The width (2x) is: 2x ≈ 2.58 The height (y) is: y ≈ 3.33
Calculus math problem need answer?
Find the absolute extrema of the function on the interval [2, 8]. (Round your answers to the nearest hundredth.) g(x)=x/(lnx) absolute min.:____ at x=______ absolute max.:____ at x=______
Solve for x - Do not round any intermediate computations, and round your answer to the nearest hundredth?
2ln(x)=-1 so ln(x)=-0.5 so x=e^(-0.5) =0.6065... ≈0.61
Geometry Help, please... I really need it.?
1. What is the equation of the circle with the given graph? http://i43.tinypic.com/2w5j12v.gif (x + 3)^2 + (y -- 2)^2 = 3^2 = 9 ANSWER Centre is (--3, 2) and radius is 3. 3. What is the measure of arc AR? http://i42.tinypic.com/jt19wo.gif 1/3 of 360 = 120 degrees ANSWER In circle O, which of the following is a diameter? http://i39.tinypic.com/34sfe3o.gif RC ANSWER 5. What is mFAD? http://i39.tinypic.com/2jb79ty.gif 90 -- 42 = 48 degrees ANSWER In circle F, the measure of AFE = 120° and the measure of arc BD = 50°. What is the measure of C? http://i44.tinypic.com/2py9qud.gif 35° ANSWER 7. Which of the following is the equation of a circle with a radius of 2 and its center at (4, -3)? (x - 4)^2 + (y + 3)^2 = 4 Which of the following is an inscribed angle in circle I? http://i40.tinypic.com/25u1v12.gif < GAD ANSWER The circle described by the equation (x - 3)^2 + (y + 4)^2 = 9 is translated 5 units to the left and 1 unit up. At what point is the center of the image circle located? (-2, -3) ANSWER Circle A has a radius of 5 cm, and arcs RC, CS, and SM are congruent. To the nearest hundredth, what is the best approximation of the length of arc RC? http://i43.tinypic.com/513byv.gif 5.24 cm ANSWER If line ET is tangent to circle A at T, and the measure of TNG = 35°, what is the measure of NET? http://i43.tinypic.com/5x3ltz.gif NET = 90 -- TNG = 90 -- 35 = 55 ANSWER55° In circle A, arc CD is congruent to arc BD. What is the measure of CBD? http://i41.tinypic.com/9gavma.gif 45° ANSWER Thank you in advance...
Homework Question: Joe walked 4 miles north, 9 miles east, 8 miles north, and then 7 miles east. If Joe now decides to walk straight back to where he started, how far must he walk?
The answer provided by User-9597828242429937573 is great, but there are couple of omissions that make its precision unacceptable for practical purposes:1. Our planet is not spherical: its height is less than width due to its rotation. We should take it into account;2. Joe is not a point, but rather a material object. We have to make calculations probably for his geometrical center or, maybe, his center of mass. It should be discussed and decided. If agreed upon geometrical center, 1/2 of Joe's height should be added to the radius;3. Since the journey is long, the result depends on the time he starts and his speed - because of thermal expansion of the Earth's surface heated by the Sun. If Joe is walking while the surface is expanding, his trip back may be longer if the temperature is still high;4. Of course, we should consider the Earth deformation due to the Moon's gravity;5. The answer has to be expressed in closest integer number of Plank lengths. Otherwise, it would be absolutely unrealistic.Other than that, it is pretty accurate and will probably satisfy Joe. :)