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yan [13]
3 years ago
14

Lexi made 14 sandwiches for a group picnic. The number of ham sandwiches she made was 4 less than the twice the number of turkey

sandwiches she made.
Mathematics
1 answer:
shutvik [7]3 years ago
6 0

x = # of ham sandwiches

14-x = # of turkey sandwiches ( as Lexi made 14 sandwiches)


as the question said that the number of ha sandwiches are 4 less than twice number of turkey sandwiches,

x = 2 * (14-x) - 4 = 24 - 2x

3x=24

x = 8


the number of ham sandwiches is 8, and the number of turkey sandwiches is 14-8=6

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\displaystyle\int\frac{(\sqrt3\sec t-2)(6\sec^2t-2\sqrt3\sec t-3)}{\sqrt{(\sqrt3\sec t)^2-3}}(\sqrt3\sec t)\,\mathrm dt
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Note that by letting x+2=\sqrt3\sec t, we are enforcing an invertible substitution which would make it so that t=\mathrm{arcsec}\dfrac{x+2}{\sqrt3} requires 0\le t or \dfrac\pi2. However, \tan t is positive over this first interval and negative over the second, so we can't ignore the absolute value.

So let's just assume the integral is being taken over a domain on which \tan t>0 so that |\tan t|=\tan t. This allows us to write

=\displaystyle\int\frac{(6\sqrt3\sec^3t-18\sec^2t+\sqrt3\sec t+6)\sec t}{\tan t}\,\mathrm dt
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