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Snezhnost [94]
3 years ago
9

What are the roots of the polynomial equation 3x^4+12x^2=6x^3

Mathematics
1 answer:
Dominik [7]3 years ago
7 0
Factor the equation to give
3x^4+12x^2=6x^3
3x^4+12x^2-6x^3=0
x^2(3x^2+12-6x)=0
By the zero product property, either x^2=0 or (3x^2+12-6x)=0 or both.
If x^2=0, then x=0
if (3x^2+12-6x)=0, we use the quadratic formula to solve for x
where x=1 ± √ (3) i

Answer: the roots of <span>3x^4+12x^2=6x^3 are {0 (multiplicity 2), 1+&radic;3 i, 1-&radic;3 i}</span>
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Step-by-step explanation:

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4 0
3 years ago
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9. Alicia Martin's savings account has a principle of $1,200. It earns 6% interest compounded quartly
zavuch27 [327]

Answer:

9) \$1236.27\,10)\,\$6451.07\, 11)\,\$10,152.87 \,12)\,\$907.95 \,13)\,\$4957.69

Step-by-step explanation:

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A=P(1+\frac{r}{n})^{nt} ⇒ Amount (A), Principle (P), rate (r) in decimal form, number of compoundings (n) a year and t, in year or its fractions.

A=P(1+\frac{r}{n})^{nt}\Rightarrow A=1200(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A=\$1236.27

10) Aubrey Daniel's case:

A=P(1+\frac{r}{n})^{nt}\Rightarrow A=5725(1+\frac{0.04}{4})^{4*3}\Rightarrow A\approx \$6451.07

11) As for Angelo, similarly to Alicia.

A=P(1+\frac{r}{n})^{nt}\Rightarrow A=9855(1+\frac{0.06}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$10,152.87

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A=P(1+\frac{r}{n})^{nt}\Rightarrow A=860(1+\frac{0.055}{2})^{2*1}\Rightarrow A\approx \$907.95

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A=P(1+\frac{r}{n})^{nt}\Rightarrow A=4860(1+\frac{0.04}{4})^{4*\frac{1}{2}}\Rightarrow A\approx \$4957.69

6 0
3 years ago
A sample of 36 observations is selected from one population with a population standard deviation of 4.2. The sample mean is 101.
Digiron [165]

Answer:

Step-by-step explanation:

Given that :

the null and the alternative hypothesis are computed as :

H_o: \mu_1 = \mu_2

H_a : \mu _1 \neq \mu_2

This is a two tailed test

This is because of the ≠ sign in the alternative hypothesis which signifies that the rejection region in the alternative hypothesis are at the both sides of the hypothesized mean difference .

Decision Rule: at the level of significance ∝ = 0 . 10

The decision rule is to reject the null hypothesis if z < - 1 . 64 and z > 1 . 64

NOTE: DURING THE MOMENT OF TYPING THIS ANSWER THERE IS A TECHNICAL ISSUE WHICH MAKES ME TO BE UNABLE TO SUBMIT THE FULL ANSWER BUT I'VE MADE SCREENSHOTS OF THEM AND THEY CAN BE FOUND IN THE ATTACHED FILE BELOW

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3 years ago
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Radda [10]
The answer to #5 is 33.
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