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mina [271]
3 years ago
7

A baseball team played 130 games in a season. If it won sixteen more games

Mathematics
1 answer:
egoroff_w [7]3 years ago
4 0

Answer:

The team has 92 wins and 38 losses.

Step-by-step explanation:

In a season 130 games are played by a baseball team.

Let us assume that the team wins x games and losses y games.

Therefore, we can write, x + y=130....... (1)

It is given that if the team won sixteen more games twice as many games as it lost.

So, we can conclude that x =2y+16 ......(2)

Hence, solving equations (1) and (2) we get, (2y+16) + y =130

⇒ 3y = 114

⇒ y =38

And from equation (2), x = 2×38 + 16 = 92

Therefore, the team has 92 wins and 38 losses. (Answer)

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The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

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b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

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\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

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\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

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\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

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