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2 years ago

14

What is 1487.9286 rounded to the nearest penny

1 answer:

tester [92]2 years ago

3 0

1487.93 should be the correct answer I believe.

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Find an m > 0 such that the the equation x^4−(3m+2)x^2+m^2=0 has four real solutions that form an arithmetic sequence.

Aleonysh [2.5K]

Answer:

The value of m is 6.

Step-by-step explanation:

Here, the given equation,

$x^4-(3m+2)x^2+m^2=0$

$x^4+0x^3-(3m+2)x^2+0x+m^2=0$

Let the roots of the equation are a-3b, a-b, a+b and a + 3b, ( they must be form an AP )

Thus, we can write,

$a-3b+a-b+a+b+a+3b=\frac{\text{coefficient of }x^3}{\text{coefficient of }x^4}$

$=\frac{0}{1}=0$

$\implies a=0----(1)$

$(-3b)(-b)+(-b)(b)+(b)(3b)+(3b)(-3b)+(-b)(3b)+(-3b)(b)=\frac{\text{coefficient of }x^2}{\text{coefficient of }x^4}}$

$=\frac{-3m-2}{1}$

$3b^2-b^2+3b^2-9b^2-3b^2-3b^2=-3m-2$

$-10b^2=-3m-2$

$\implies b^2=\frac{3m+2}{10}-----(2)$

$(-3b)(-b)(b)(3b)=\frac{\text{Constant term}}{\text{coefficient of}x^4}= m^2$

$9b^4=m^2$

$9(\frac{3m+2}{10})^2=m^2$

$9(\frac{9m^2+4+12m}{100})=m^2$

$81m^2+36+108m=100m^2$

$-19m^2+108m+36=0$

$19m^2-108m-36=0$

$19m^2-114m+6m-36=0$

$19m(m-6)+6(m-6)=0$

$(19m+6)(m-6)=0$

$\implies m=-\frac{6}{19}\text{ or }m=6$

But m > 0,

Hence, the value of m is 6.

4 0

2 years ago

Evaluate 9 ÷ 3[(18 − 6) − 22].<br><br> 0.188<br> 0.375<br> 24<br> 48

Natasha2012 [34]

Answer:

Step-by-step explanation:

0.375

6 0

2 years ago

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Olivia received a $700 signing bonus when she accepted a job as a nurse. If she makes $24 an hour, which equation models Olivia'

yan [13]

<span> y = 24x + 700 would be an accurate answer

Hope this helps!</span>

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2 years ago

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What is 2 5/6 + 7/4 <br> A. 2 2/5<br> B. 3 1/5<br> C. 3 4/5<br> D. 4 7/12

Mazyrski [523]

Answer:

D

Step-by-step explanation:

2 5/6=2 10/12

7/4=1 3/4= 1 9/12

2 10/12+1 9/12= 4 7/12

you can just change the denominators to the same which is 12. Hope you appreciate it!

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2 years ago

What Is 40 percent of 95

Stels [109]

Answer:

38

Step-by-step explanation:

95 x 0.40 = 38

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2 years ago

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