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3 years ago

What is the length of the major axis of the conic section shown below?

Mathematics

1 answer:

sveticcg [70]3 years ago

7 0

$\dfrac{(x-2)^2}{49}+\dfrac{(y+5)^2}{36}=1$

The equation of a elipse:

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

The length of the major axis is equal 2a if a > b or 2b if b > a.

We have

$a^2=49\to a=\sqrt{49}=7\\\\b^2=36\to b=\sqrt{36}=6\\\\a > b$

therefore the length of the major axis is equal 2 · 7 = 14.

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<h2>Explanation:</h2>

Here we need to solve some expressions. Remember the following rules:

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$-(-4)+3=4+3=\boxed{7} \\ \\ -(6)+3=-6+3=\boxed{-3} \\ \\ -(-8)+3=8+3=\boxed{11} \\ \\ -(-5)+3=5+3=\boxed{8} \\ \\ -(2)+3=-2+3=\boxed{1} \\ \\ -(15)+3=-15+3=\boxed{-12} \\ \\ -(-6)+3=6+3=\boxed{9}$

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2 years ago

A deck of 52 cards contains 12 picture cards. If the 52 cards are distributed in a random manner among four players in such a wa

Mkey [24]

Answer:

The probability that each player will receive three picture cards = 0.0324

Step-by-step explanation:

As given,

A deck of 52 cards contains 12 picture cards

Remaining card = 52 - 12 = 40

So,

Total number of ways in which 12 picture card is distributed = $\frac{12!}{3! 3! 3! 3!}$

Now,

The Total number of ways in which Remaining cards are distributed = $\frac{40!}{10! 10! 10! 10!}$

So,

Total number of ways of getting 3 picture card and remaining card = $\frac{12!}{3! 3! 3! 3!}$ × $\frac{40!}{10! 10! 10! 10!}$

= $\frac{12! 40!}{(3!)^{4} (10!)^{4} }$

Now,

Total number of ways to distribute 52 cards so that each people get 13 card = $\frac{52!}{13! 13! 13! 13!} = \frac{52!}{ (13!)^{4} }$

∴ The probability = $\frac{\frac{12! 40!}{(3!)^{4} (10!)^{4} }}{\frac{52!}{(13!)^{4} }}$

= $\frac{12! 40!}{(3!)^{4} (10!)^{4} }$ × $\frac{(13!)^{4} }{ 52! }$

= $\frac{12! 40!}{(3!)^{4} (10!)^{4} }$ × $\frac{(13.12.11.10!)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41.40! }$

= $\frac{12!}{(3!)^{4} }$ × $\frac{(13.12.11)^{4} }{ 52.51.50.49.48.47.46.45.44.43.42.41}$

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= 0.0324

∴ we get

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But because K12 teachers' language may sometimes be sloppy, "equivalent" may also mean "approximate." If that is the case (I let you make the call if the premise is true): the following are definitely not 9/11:

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