w + 2x + 3w - 2xw = 2x + 4w - 2xw, in simplest form
Perimeter: (length: 5 inches; width: 5 inches) P= (2xL) + (2xW) P= (2x5) + (2x5) P= 10 + 10 P= 20 Area (length: 5 inches; width: 5 inches) A= LxW A= 5 x 5 A= 25
Oh, dude, you're hitting me with some math now? Okay, so when you multiply 2w by 7w, you basically just multiply the numbers (2 and 7) and then multiply the variables (w and w). So, 2 times 7 is 14, and w times w is w^2. Put it all together, and you get 14w^2. Easy peasy lemon squeezy.
The Answer To This Question Is : p = 2xl + 2xw p = 2x2+ 2x5 p = 4 + 10 p = 14 !
Perimeter: (length: 5 inches; width: 5 inches) P= (2xL) + (2xW) P= (2x5) + (2x5) P= 10 + 10 P= 20 Area (length: 5 inches; width: 5 inches) A= LxW A= 5 x 5 A= 25
Oh, dude, you're hitting me with some math now? Okay, so when you multiply 2w by 7w, you basically just multiply the numbers (2 and 7) and then multiply the variables (w and w). So, 2 times 7 is 14, and w times w is w^2. Put it all together, and you get 14w^2. Easy peasy lemon squeezy.
Oh, what a happy little rectangle we have here! To find the perimeter, you simply add up all the sides. So, for this rectangle with sides of 9cm and 5cm, the perimeter would be 2(9cm) + 2(5cm) = 18cm + 10cm = 28cm. Just a few simple brushstrokes and you've got your answer!
First we need to find the side length of the square we cut in order to maximize the volume of the box. Let the side of the square be x.Volume = lwhl = 24 - 2xw = 9 - 2xh = xV = (24 - 2x)(9 - 2x)(x)V = [(24)(9)(x) - (24)(2x)(x) - (2x)(9)(x) - (2x)(-2x)(x)]V = 216x - 48x^2 - 18x^2 + 4x^3V = 216x - 60 x^2 + 4x^3 Take the derivativeV' = 216 - 120x + 12x^2 Make the derivative equal to 00 = 216 - 120x + 12x^20 = 12(18 - 10x + x^2)0 = 18 - 10x + x^2x = [10 ± √[(10^2 - 4(1)(18)]]/2x = (10 ± √28)/2x = (10 ± 2√7)/2x = 5 ± √7 = x = 5 ± 2.6x = 7.6 or x = 2.4 this are critical values, which we substitute into volume equationV = 216(2.4) - 60(2.4^2) + 4(2.4^3) = 228 in^3Thus, the side length of the square we cut is 2.4 in, which also is the height of the box. So,l = 12 - 2(2.4) = 12 - 4.8 = 7.2w = 9 - 2(2.4) = 9 - 4.8 = 4.2Or we can estimate and say that the box will be 7 inches long, 4 inches wide, and 2 inches high.