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1 year ago

Which statements are true about the graphs of all nth degree polynomials?

Mathematics

2 answers:

vova2212 [387]1 year ago

6 0

The statements are true about the graphs of all nth degree polynomials are B and D.

B. It goes up and down at most a total of n times.

D. The number of x-intercepts is at most n.

vagabundo [1.1K]1 year ago

5 0

<h2>Answer:</h2>

The statement that is true about the graphs of all nth degree polynomials is:

B.) It goes up and down at most a total of n times.

D.) The number of x-intercepts is at most n.

<h2>Step-by-step explanation:</h2>

We know that the number of times the graph goes up and down depends on the number of distinct zeros of a polynomial and as we know that a polynomial of nth degree may have repetitive zero.

Hence, the graph of nth degree polynomial goes up and down at most a total of n times.

Also, the number of x-intercept is the x-value of the point where the function is zero i.e. it depends on the number of zeros of polynomial.

Hence, The number of x-intercepts is at most n.

Also, the end behavior of graph depends on degree as well as sign of the leading coefficient.

Hence, correct options are:

Option B and option: D

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Use the binomial theorem to ﬁnd the coeﬃcient of xayb in the expansion of (5x2 + 2y3)6, where a) a = 6, b = 9. b) a = 2, b = 15.

goldfiish [28.3K]

Answer:

Step-by-step explanation:

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

we use these for the expansion of (5x² + 2y³)⁶

1(5x²)⁶(2y³)⁰ + 6(5x²)⁵(2y³)¹ + 15(5x²)⁴(2y³)² + 20(5x²)³(2y³)³+ 15(5x²)²(2y³)⁴+ 6(5x²)¹(2y³)⁵ + 1(5x²)⁰(2y³)⁶

78125ₓ¹²+187500ₓ¹⁰ y³ +37500ₓ⁸y⁶+20000ₓ⁶y⁹+6000x⁴y¹²+960x²y¹⁵+2y¹⁸

a.)a = 6, b = 9. the coeﬃcient of xᵃyᵇ ( 20000ₓ⁶y⁹) = 20000

b) a = 2, b = 15. the coeﬃcient of xᵃyᵇ ( 960x²y¹⁵) = 960

c) a = 3, b = 12. the coeﬃcient of xᵃyᵇ is not present

d) a = 12, b = 0 the coeﬃcient of xᵃyᵇ ( 78125ₓ¹²) = 78125

e) a = 8, b = 9. the coeﬃcient of xᵃyᵇ is not present

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The arc length of AB is 8 m (app.)

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Given that the radius of the circle is 8 m.

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The arc length of AB can be determined using the formula,

$arc \ length=\frac{central \ angle}{360^{\circ}} \times circumference$

Substituting central angle = 60° and circumference = 2πr in the above formula, we get,

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