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(8x plus 3)(4x plus 7)?
It is equivalent to: 32x^2 +88x +21
How would you work out the possible values of k when the line y equals x -8 is tangent to the curve y equals 4x squared plus kx plus 1?
Since the curves are tangent, they have the same slope at that point and the same x and y value at that point.Set equations equal and set slopes equal and solveTogetslope, you need to know calculus first derivativeslope of one equation is dy/dx = 8x +kand the othereqaution slope is dy/dx = 1so youhave4x^2 + kx + 1 = x -88x + k = 14x^2 +kx -x + 9 = 08x + k -1 = 0solve for kk = -11 or +13Another way but with the same answer:-If: y = 4x2+kx+1 and y = x-8Then: 4x2+kx+1 = x-8So: 4x2+kx-x+9 = 0For the line to be tangent with the curve the discriminant b2-4ac must = 0So if: -4*4*9 = -144 then (k-1)2 must = 144So it follows: (k-1)(k-1) = 144 => k2-2k-143 = 0Solving the quadratic equation: k = -11 or k = 13
A square is cut from each corner of a sheet of metal with dimensions 12cm by 10cm to form an open rectangular container find using calculus the max volume of the container?
If you cut a square of length x cm from each corner of the sheet, you will be able to fold the flaps your form up to create a box that is 12-2x long, 10-2x wide, and x high. Using the formula for the volume of a rectangular prism (length*width*height) we find the volume as a function of x to be Volume(x)=(12-2x)*(10-2x)*x=4x3-44x²+120x In order to maximize this volume, we need to find where its derivative is 0. d/dx(Volume(x))=12x²-88x+120=0 Since this quadratic cannot be factored, we will have to solve it using the quadratic formula, giving us that x=1/3 * (11±√31)~1.81075, 5.52259 While we may have two answers, only one of them is valid. Since we need to cut this amount out of a 10 by 12 box, we can't cut 5.52259 from each corner or else we would be cutting more than 10 inches (since you cut twice per side) on one side, which is more than whats there to cut! Therefore, the only possible solution is the 1.81075. To make sure this is a max and not a min though, we need to make sure the second derivative is negative there. d²/dx²(Volume)=12x-88=6*(1.81075)-44=-44.542 Since it was negative like we wanted, we know that the maximum volume is achieved when we cut out 3.62149 inches. Plugging that value of x into our original equation for volume we get Volume(1.81075)=1.810753-22*1.81075²+120*1.81075=96.7706 cubic centimeters.
(8x plus 3)(4x plus 7)?
It is equivalent to: 32x^2 +88x +21
52x - 7 equals 33 - 36x plus 4?
52x - 7 = 33 - 36x + 4 52x + 36x = 33 + 7 + 4 88x = 44 x = 1/2
What is the greatest common factor of 24y and 88x?
It is 8.
Factor negative x cube plus three x square plus eighty eight x?
-x3+3x2+88x -x(x2-3x-88) -x(x-11)(x+8)
I am taking geometry and our teacher gave us this problem 2X -90x plus 10. What the hell do i do?
If you mean: 2x-90x+10 then it can be simplified to 10-88x by collecting like terms together.
If 5280 feet equal a mile what does 2100 feet equal?
700 yards so you want to subtract the 2 numbers twice then subtract that answer that you got
How would you work out the possible values of k when the line y equals x -8 is tangent to the curve y equals 4x squared plus kx plus 1?
Since the curves are tangent, they have the same slope at that point and the same x and y value at that point.Set equations equal and set slopes equal and solveTogetslope, you need to know calculus first derivativeslope of one equation is dy/dx = 8x +kand the othereqaution slope is dy/dx = 1so youhave4x^2 + kx + 1 = x -88x + k = 14x^2 +kx -x + 9 = 08x + k -1 = 0solve for kk = -11 or +13Another way but with the same answer:-If: y = 4x2+kx+1 and y = x-8Then: 4x2+kx+1 = x-8So: 4x2+kx-x+9 = 0For the line to be tangent with the curve the discriminant b2-4ac must = 0So if: -4*4*9 = -144 then (k-1)2 must = 144So it follows: (k-1)(k-1) = 144 => k2-2k-143 = 0Solving the quadratic equation: k = -11 or k = 13
What is my yearly gross pay at 11.00 an hour 8 hours a week and paid biweekly?
11 x 8 hours = $88 per week. Thatis 88x 2 = 176$ biweekly, and over the year x 26 pay periods =176*26 = $4576. It doesn't depend on how often you're paid.
Is area code 262 a free area code call?
Toll free codes in US and Canada are 800, 855, 866, 877, and 888. Future toll-free codes include 844, 833, 822, and the remaining 88X codes. In UK they use 0800 code for toll free calls. Area code 262 is a regular area code for Racine and Waukesha, Wisconsin, surrounding but not including Milwaukee.
You Want 88 Songs They Each Cost 0.99 What Do you Pay?
87.12 or 87 dollars and 12 cents. ---- Explanation. You pay 88x.99. An easy way to figure this out is to realize that .99 is one cent less than a dollar. So if each cost 1 dollar the amount you pay would be 88 dollars, but you need to subtract 88 cent so you need to pay 88-.88= 87 dollars and 12 cents. You can also just multiply, but the method I mentioned may be quicker.
Is area code 885 toll-free?
In North America (USA, Canada, etc.), there is no area code 886. It is reserved for future toll-free use, but not until we run out of the current 800, 888, 877, 866, 855, and 844 numbers, and then run out of 833 and 822 numbers, and then 880 through 885. That should take at least a couple of decades. 886 is an area code in some other countries: in China, it is the area code of Nujiang province. Also, telephone country code +886 is Taiwan. Neither of those is a toll-free code.
A square is cut from each corner of a sheet of metal with dimensions 12cm by 10cm to form an open rectangular container find using calculus the max volume of the container?
If you cut a square of length x cm from each corner of the sheet, you will be able to fold the flaps your form up to create a box that is 12-2x long, 10-2x wide, and x high. Using the formula for the volume of a rectangular prism (length*width*height) we find the volume as a function of x to be Volume(x)=(12-2x)*(10-2x)*x=4x3-44x²+120x In order to maximize this volume, we need to find where its derivative is 0. d/dx(Volume(x))=12x²-88x+120=0 Since this quadratic cannot be factored, we will have to solve it using the quadratic formula, giving us that x=1/3 * (11±√31)~1.81075, 5.52259 While we may have two answers, only one of them is valid. Since we need to cut this amount out of a 10 by 12 box, we can't cut 5.52259 from each corner or else we would be cutting more than 10 inches (since you cut twice per side) on one side, which is more than whats there to cut! Therefore, the only possible solution is the 1.81075. To make sure this is a max and not a min though, we need to make sure the second derivative is negative there. d²/dx²(Volume)=12x-88=6*(1.81075)-44=-44.542 Since it was negative like we wanted, we know that the maximum volume is achieved when we cut out 3.62149 inches. Plugging that value of x into our original equation for volume we get Volume(1.81075)=1.810753-22*1.81075²+120*1.81075=96.7706 cubic centimeters.
