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Elena L [17]
3 years ago
8

Determine the equation of the following polyromial that passes through point (0,6).

Mathematics
1 answer:
Ostrovityanka [42]3 years ago
3 0

Answer:

Cubic polynomial has zeros at x=−1x=−1 and 22, is tangent to x−x−axis at x=−1x=−1, and passes through the point (0,−6)(0,−6).

So cubic polynomial has double zero at x=−1x=−1, and single zero at x=2x=2

f(x)=a(x+1)2(x−2)f(x)=a(x+1)2(x−2)

f(0)=−6f(0)=−6

a(1)(−2)=−6a(1)(−2)=−6

a=3a=3

f(x)=3(x+1)2(x−2)f(x)=3(x+1)2(x−2)

f(x)=3x3−9x−6

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Answer:

1. \sqrt{100} \sqrt{100}

2. 13.5 + \sqrt{81}

3. \sqrt{9} + \sqrt{729}

6. \frac{3}{5} + 2.5\\\frac{3+12.5}{5}\\\frac{15.5}{5}\\= 3.1

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Step-by-step explanation:

1. \sqrt{100} \sqrt{100} equals to 10 * 10 = 100 which is rational

2. 13.5 + \sqrt{81} equals 13.5 + 9 = 22.5

3. \sqrt{9} + \sqrt{729} -- 3+27 = 30

6. \frac{3}{5} + 2.5\\\frac{3+12.5}{5}\\\frac{15.5}{5}\\= 3.1

Option 4 and 5 are irrational because they include  \sqrt{353}  and \sqrt{216} which are not a perfect square and their answers will be non recurring and non terminating decimal fraction.

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With a 10-units package of batteries with 3 dead batteries, the sampling can be modeled as a binomial random variable with:

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The probability of having k dead batteries in the sample is:

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Then, the probability of having one or more dead batteries in the sample (k≥1) is:

P(x\geq1)=1-P(x=0)\\\\\\P(x=0) = \dbinom{4}{0} p^{0}q^{4}=1*1*0.7^4=0.2401\\\\\\P(x\geq1)=1-0.2401=0.7599\approx0.76

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