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3 years ago

6

Anyone nervous about semester exams

1 answer:

Veronika [31]3 years ago

8 0

Answer:

YES

Step-by-step explanation:

I am literally trying to fit in as much studying as possible but I keep getting distracted ;-;

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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

3 years ago

Tickets to a concert are available online for $20 each, plus a one-time handling fee of $1.75. The total cost is a function of t

grin007 [14]

The answer is (c) (sorry adding extra characters so brainly can exept it.)

3 0

3 years ago

Read 2 more answers

Find the Volume. Plz Help

koban [17]

Answer:

B

Step-by-step explanation:

$V = \frac{l*w*h}{2} = \frac{18*12*9}{2} = \frac{1944}{2} = 972$

3 0

3 years ago

Read 2 more answers

What is sin B ?

Neporo4naja [7]

Answer:

The answer to your question is sin B = $\frac{8}{17}$

Step-by-step explanation:

Sine is the trigonometric function that relates the opposite side and the hypotenuse.

In the picture, we have the hypotenuse and the adjacent side, so we must calculate the opposite side using the Pythagorean theorem.

b² = c² - a²

b² = 17² - 15²

b² = 289 - 225

b² = 64

b = 8

Now, we can calculate the sine

sin B = $\frac{opposite side}{hypotenuse}$

sin B = $\frac{8}{17}$

3 0

3 years ago

What’s bigger -4 4/25 or -4.16

Rina8888 [55]

Answer:

they are equal

Step-by-step explanation:

6 0

3 years ago