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An easy way to do this one is to use a graphical calculator (e.g. TI-84) to plot the function inside the square root. The calculator will show that   2 x/(x2 - 324) is defined and non negative  in two intervals:   x > 18   and  -18 < x ≤0 The...

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The equation of a plane in 3d space can be written as    α x +  β y + γ z = 1        for some value of the parameters α, β, γ   The fact that point A is in this plane means that   α - 2 β + 6 γ =1      ...

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My first observation about this problem is that a tire diameter of 8.0m is unrealistically large.   Perhaps on a giant mining machine - but not on a car.   Another issue is the non SI unit of km/hr.  This must be changed to m/s. 80 km/hr = 22.2 m/s  and 30 km/hr...

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Since you have the diagram, you will have noticed that the triangle formed by the the two walks is a right triangle with legs of 7 and 10 km.   This means that the hypotenuse of the triangle is h = sqrt(49 +100).   The next step is to notice that the angle formed by the...

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There are two possible answers to this question.   If the dice are considered distinguishable (that is a 2 on the red die and a 5 on the green die is considered a different outcome than a 5 on the red die and a 2 on the green one) then there are 36 (= 6 x 6) possible outcomes.   However,...

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From the information given, one may conclude that four of the seven numbers are 2,3,3,20.     (the number 3 is the only number appearing twice.  It can appear only twice if the median is 6)     The only way that the median can be 6 is if the number...

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Since  C1 and C2 are in parallel they add to result in C1 + C2.  This combination ins in series with C3 so     1/Ceq =  1/(C1 + C2) +  1/C3.      The values can be plugged in to get   1/Ceq =  .2165 x 10^6  ...

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maths help (answer)

This problem can be solved by writing  S20 / S10  =   2 a2 / a1  =   2( a1  + d )/ a1 Use the formula for the sum of the first n terms of an arithmetic series:     Sn = n (2 a1 +(n-1) d )/2     where a1 is the first...

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maths help (answer)

The set of integers is a countable infinite set.  That is, the integers can be arrange in ordinal number (first, second, third, ...) order.  For example {0, 1, -1, 2, -2, 3 , -3, 4, ...}.   The real numbers cannot be so arranged.  In set theory this means that the set...

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power series (answer)

The ratio test shows that this series will converge for abs(x/4) <1.    The boundary cases x = 4  and x = -4 need to be checked.   For x = 4, the series is the harmonic series which does not converge.  For x = -4, the series is an alternating sign series...

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