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Answers by Michael F.

Compounding (answer)

both of these exercises seem to be translating the expressions into the form aert and solving for r. a. y=3000(1.36)t=3000ert tln(1.36)=tr  r=ln(1.36)  y=3000etln(1.36) The other is similar as y=15etln(.29)  with r=ln(.29)

Let r=length of light beam from lighthouse to spot  on shore.      θ=angle from perpendicular to shore from lighthouse to beam.     100/r = =cosθ  or r=100secθ dr/dt = 100 secθ tanθ dθ/dt, which for θ=π/4, the right triangle is formed by 100...

∫xdx/(x2-5x+25) The derivative of the denominator is 2x-5, alas the numerator is not that.  ∫xdx/(x2-5x+25)=(1/2)∫2xdx/(x2-5x+25) and now comes one of the neat secrets, add 0, as -5+5 ∫xdx/(x2-5x+25)=(1/2)∫(2x-5+5)dx/(x2-5x+25)=(1/2)∫(2x-5)dx/(x2-5x+25)+(1/2)∫5dx/(x2-5x+25) The...

Word problem (answer)

Let D= number of ducks 2 legs per duck C=number of cows 4 legs per cow   D+  C=50 2D+4C=154 now solve

The saying is "don't look a gift horse in the teeth"  - don't carefully evaluate a gift, it's a sign of ingratitude. a house of cards - a scheme or a plan which is highly unstable. a flash in the pan - not untold riches, but a few grains of gold  

x - y + z = -7 x + y + z =1 x + y - z = 9 Second equation minus first equation 0+2y+0=8       y=4 Second equation minus third equation 0+0+2z=-8      z=-4 First equation plus third...

y = x - 1 and the parabola y^2  = 2x + 6   x=y+1 x=(y2-6)/2 equating the two expressions for x 2y+2=y2-6 y2-2y-8=0 (y-4)(y+2)=0 y=4, y=-2 substituting in the first equation 4=x-1  x=5   (5,4) -2=x-1   x=-1  ...

The equation is of a straight line.  The two points are (8,3) and (13,7).  The double point form of the straight line is (y-3)=[(7-3)/(13-8)](x-8) or y-3=[4/5](x-8) or y-3=4x/5-32/5 and so 4x/5-y=32/5-3 or 4x-5y=32-15=17 4x-5y=17 is the Ax+By=C form. 

calculus proof (answer)

f(x)=Σx4n/(4n)!  One assumes the question is based on f(x)=Σn=0∞x4n/(4n)! fiv(x)=Σn=0∞ (4n)(4n-1)(4n-2)(4n-3)x4n-4/(4n)!=Σn=4∞ x4n-4/(4n-4)! the terms with n<4 become zero. This sum is exactly f(x), as the same terms are summed in both cases.  In an expanded illustration we have f(x)=1+x4/4...

ABt  for A=[a] and B= [c]                 [b]             [d] ABt=[a][c d]  = [ac   ad]        [b]           ...

The fact that the arc length is 3 and he radius is 7 is a complete specification of the size of the angle which is length of arc/length of circle =angle in radians /2π angle in radians=2π×3/(2π×7)=3/7 radians = (180/π)×3/7 degrees=24.55533408 Either start at the x-axis and go up 3/7...

Let E=set of even numbered cards E=(E∩A)∪(E∩B) a disjoint union P(E)=P(E∩A)+P(E∩B)=5/10+2/5=5/10+4/10=9/10!!! P(A|E)=P(A∩E)/P(E)=(5/10)/(9/10)=5/9 Sorry for the arithmetic error. Same theorem, different statement.