The number of kilometers Tony travels in a canoe, d, varies directly with the amount of time spent in the canoe, t. When Tony ca
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To solve the equation for x, first divide both sides of the equation by 4 to get . Then, take the natural logarithm of both sides (base e) to get
. The left hand side of this equation if equal to 2.7x, so we get
. The final step is to divide both sides of the equation by 2.7, to get that
. This is approximately equal to 0.782.
Answer:
see explanation
Step-by-step explanation:
The secant- secant angle PRS is half the measure of the difference of the intercepted arcs, that is
(PD - QS) = 50 ( multiply both sides by 2 )
PD - QS = 100, that is
12x + 8 - (4x + 4) = 100
12x + 8 - 4x - 4 = 100
8x + 4 = 100 ( subtract 4 from both sides )
8x = 96 ( divide both sides by 8 )
x = 12
Thus
arc PD = 12(12) + 8 = 144 + 8 = 152°
arc QS = 4(12) + 4 = 48 + 4 = 52°
You're considering a sequence of in which consecutive terms differ by 1, meaning
<em>a(n)</em> = <em>a</em> (<em>n</em> - 1) + 1
so <em>a(n)</em> is an arithmetic sequence. (I'm guessing 20102010 should actually be 2010, and 53075307 should be 5307, so 11 should probably be just 1.)
The sum of the first 2010 terms is 5307, or
Find the value of the first term in the sequence, <em>a</em>(1).
We can write <em>a(n)</em> in terms of <em>a</em>(1) by iterative substitution:
<em>a(n)</em> = <em>a</em>(<em>n</em> - 1) + 1
<em>a(n)</em> = (<em>a</em>(<em>n</em> - 2) + 1) + 1 = <em>a</em>(<em>n</em> - 2) + 2
<em>a(n)</em> = (<em>a</em>(<em>n</em> - 3) + 1) + 2 = <em>a</em>(<em>n</em> - 3) + 3
and so on, down to
<em>a(n)</em> = <em>a</em>(1) + <em>n</em> - 1
So the sum of the first 2010 terms is
Recall that
and
So we have
Solve for <em>a</em>(1) :
2010 (<em>a</em>(1) - 1) + 2,021,055 = 5307
2010 (<em>a</em>(1) - 1) = -2,015,748
<em>a</em>(1) - 1 = - 335,958/335
<em>a</em>(1) = - 335,623/335
Now, every second term, starting with <em>a</em>(1), differs by 2, so they form another arithmetic sequence <em>b(n)</em> given by
<em>b(n)</em> = <em>b</em>(<em>n</em> - 1) + 2
or, using the same method as before,
<em>b(n)</em> = <em>b</em>(1) + 2 (<em>n</em> - 1) = <em>a</em>(1) + 2<em>n</em> - 2
The sum of the 1005 terms in this sequence is
= (- 335,623/335 - 2)•1005 + 2•1005•1006/2
= 1146