What is the y-intercept of this table?

Mathematics

1 answer:

kupik [55]3 years ago

4 0

Answer:

Step-by-step explanation:

The y-intercept exists when x = 0. So where x = 0, from the table we can see that y = 60. The y-intercept for the table is 60.

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A 10 inch diameter pumpkin pie is cut into 6 equal servings. What is the area of the top of each piece of pie?

Ivan

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7 0

3 years ago

In the expansion of ( x^3 - 2/x^2 ) ^10 , find the coefficient of 1/x^5

Lilit [14]

Answer:

240

Step-by-step explanation:

We need to find the coeffeicent of the binomial expansion of

$( {x}^{3} - 2 {x}^{ - 2} ) {}^{10}$

Note that

$- 2 {x}^{ - 2} = - \frac{2}{ {x}^{2} }$

The binomial theorem states that

$(x + y) {}^{n} = x {}^{n} y {}^{0} + \binom{n}{1} x {}^{n - 1} y + \binom{n}{2} x {}^{n - 2} y {}^{2} ....... + x {}^{0} y {}^{n} ( \binom{n}{n} )$

Using this, we let expand our series

$( {x}^{3} - 2 {x}^{ - 2} ) {}^{10} = x {}^{30} + \binom{10}{1} ( {x}^{27} 2 {x}^{ - 2} ) + \binom{10}{2} {x}^{24} 2x {}^{ - 4} + \binom{10}{3} {x}^{21} 2x {}^{ - 6} + \binom{10}{4} {x}^{18} 2x { }^{ - 8} + \binom{10}{5} x {}^{15} 2x {}^{ - 10} + \binom{10}{6} x {}^{12}2 x {}^{ - 12} + \binom{10}{7} x {}^{ 9} 2x {}^{ - 14} + \binom{10}{8} x {}^{ 6} 2x {}^{ - 16} + \binom{10}{9} ( {x}^{3} )2x {}^{ - 18} + 2x {}^{ - 20}$