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Paul can mow the grass in 50 minutes but it takes Dan three times as long How long will it take them to mow the grass if they work together?
Paul can mow the grass in 50 minutes, while Dan takes 150 minutes (3 times 50 minutes). Their combined work rate is ( \frac{1}{50} + \frac{1}{150} = \frac{3 + 1}{150} = \frac{4}{150} = \frac{2}{75} ) of the lawn per minute. Therefore, together they can complete the job in ( \frac{75}{2} = 37.5 ) minutes.
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
The first number when writing 4 000 000 in scientific notation?
4,000,000 in Scientific Notation = 4 x 106
How do you write 675 million in scientific notation?
675 000 000 in scientific notation is 6.75*108
How is .000 9234 in scientific notation?
.0009234 in Scientific Notation = 9.234 x 10-4
How to express 4 050 000 000 000 in scientific notation?
4.05*1012
What is the sscientific notation for 70 000?
If you mean 70,000 then it is 7.0*10^4 in scientific notation
What is the scientific notation for 000 9234?
9.234 x 10-4
What is the scientific notation of 16 000?
1.6 x 10^4
What is the scientific notation of 14 000?
1.4 x 10^4
How do I write 56 000 in scientific notation?
5.6 x 10^4
What is 22 000 Mg in scientific notation?
2.2 x 10^4 Mg
What is the scientific notation of 4?
4 in Scientific Notation = 4 x 100
What is the scientific notation for 0.0006903?
The scientific notation for 0.0006903 is 6.903 × 10^-4.
