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A rectangular swimming pool is to be build with an area of 150 square meters The owner wants 2-meter wide decks along either side 3m wide decks at the two ends Whats the smallest property?
Supposing that the actual pool is (a)m long and (b)m wide, then the total property will be (a+6)m long and (b+4)m wide.The next step is to find a relationship between a and b.ab = 150Therefore a = 150/bTherefore, total property area will be:(150/b + 6)(b+4)= 150 + 600/b + 6b + 24= 6b + 600/b + 174= 6b + 600b-1 + 174Taking the derivative and setting it to zero:0 = (6b + 600b-1 + 174)'= 6 + -1*600*b-2= 6 - 600/b2Therefore:6 = 600/b21 = 100/b2b2 = 100b = 10a = 150/10= 15To check whether we have the minimum for area, take the second derivative:(6 - 600/b2)' = (6 - 600b-2)'= 0 - -2*600b-3= 1200b-3= 1200/b3If b is positive, the second derivative will also be positive, so we do have a minimum.Therefore total area of the property:(a+6)m * (b+4)m = (15+6)m * (10+4)m= 21m * 14m= 294m2
How do you find d antilog of a negative term?
The antilog? a log is an exponent, so as an antilog just means you reapply that exponent to the correct base. Log implies base 10, so antilog means use that number as an exponent of 10. If you are using log tables, first separate the whole number part and the decimal part of the log ( they are both negative) then add -1 to the whole number part and +1 to the decimal part. (one is called the characteristic and the other is called the mantissa, but I don't remember which is which now) This creates a positive decimal that you can look up in the log table. The negative integer part becomes an exponent of 10. Put them together and you get an answer in scientific notation. Ex: find antilog of -3.5 (-3 -1) + (-.5 + 1) ==> (-4) + (+.5) look up .5 in the log tables and you get 3.1623 and the -4 becomes 10-4 Put them together by multiplying (adding logs means multiplication of antilogs) to get the final answer 3.1623 x 10-4
What is 3x plus 2 x-1 plus 2x-4 x plus 2 equals 5?
Your notation is hard to read. Did you mean 3x+2x-1+2x-4x+2=5? You have a lot of weird spaces that make your x's look like multiplication or something. The first step is to get variables on one side of the equation and numbers on the other. Add 1 and subtract 2 from 5, giving 3x+2x+2x-4x=4 Now, simply do the math on the variables. 3x+2x+2x-4x giving you 7x-4x which equals 3x, so that means 3x=4(from our earlier work) divide both sides by 3, 3x/3=4/3 gives us x=4/3 or x=1 1/3 or x=1.3333333 however you like.
What is 4 x 4 x 4 x 4 x 4 as a power of 4?
4 x 4 x 4 x 4 x 4 = 45
What is the solution to 4(2x - 2) 4 - 4(x - 3)?
If you mean: 4(2x-2) = 4-4(x-3) then the value of x works out as 2
