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Agata [3.3K]
3 years ago
15

Alex, Gil and Meg shared 740 cards. Alex had 20 fewer cards than Gil and 120 fewer cards than Meg. How many cards did Alex have?

Mathematics
2 answers:
oksian1 [2.3K]3 years ago
4 0

Answer:

Step-by-step explanation:

saveliy_v [14]3 years ago
3 0

The answer is 200 , Alex has 200 cards.

If you start at 740 cards total and you subtract the 20 more cards Gil had and the 120 cards more that Meg had you will be left with 600 cards and then you divide that by the 3 of them and each of them would get 200 cards.

To double check your work you would add them all up the 200 cards Alex has plus the 220 that Gil has and the 320 that Meg has and you get a total of 740 cards.

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If f(x)=\sin x, then we have \sin(x+2\pi)=\sin x\cos2\pi+\cos x\sin2\pi=\sin x, and so \sin x is periodic with period 2\pi.

It gets a bit more complicated for a function like yours. We're looking for k such that

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The second two are satisfied whenever k\in\left\{0,\pm\dfrac{10}7,\pm\dfrac{20}7,\ldots\right\}, and more generally when k=\dfrac{10n}7 with n\in\mathbb Z (any multiple of 10/7).

It then follows that all four equations will be satisfied whenever the two sets above intersect. This happens when k is any common multiple of 4 and 10/7. The least positive one would be 20, which means the period for your function is 20.

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f(t)=\displaystyle\sum_{i=1}^n(a_i\sin(b_it)+c_i\cos(d_it))

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