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3 years ago

9

Solve the equation `x^{4}+13x^{2}+36=0` for all values of `x`.

1 answer:

Zolol [24]3 years ago

7 0

Answer: x4+13x2+36=0

Step-by-step explanation:

Let's solve your equation step-by-step.

x4+13x2+36=0

Step 1: Factor left side of equation.

(x2+4)(x2+9)=0

Step 2: Set factors equal to 0.

x2+4=0 or x2+9=0

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What is the atomic number of an atom?

mariarad [96]

Answer:

The number of protons

Step-by-step explanation:

Its the correct answer

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3 years ago

Megan has a piece of fabric which is a right triangular shape. The length of leg 1 is 4 m. The length of the other leg is twice

Bess [88]

Answer:

8.94 m

Step-by-step explanation:

Use the Pythagorean Theorum - $a^2 + b^2 = c^2$ . Use leg 1 as <em>a</em>, leg 2 as <em>b</em>, and the third side as <em>c</em>.

We know leg 1 is 4, and that leg 2 is twice as long as leg 1...

$(4)^2 + (4*2)^2 = c^2$

Now, we use the Order of Operations to find $c^2$ ...

$4^2+8^2=c^2\\16+64=c^2\\80=c^2$

Now, we find the square root of $c^2$ to find c...

$\sqrt{80} =8.94$

So, the length of the third side is 8.94 m.

8 0

3 years ago

Suppose that y = k * (x - 1/3) ^ 2 is a parabola in the xy -plane that passes through the point (2/3, 1) :Find k and the length

Dennis_Churaev [7]

Answer:

k = 9

length of chord = 2/3

Step-by-step explanation:

Equation of parabola: $y=k (x-\frac13)^2$

<u />

<u>Part 1</u>

If the curve passes through point $(\frac23 ,1)$ , this means that when $x=\dfrac23$ , $y = 1$

Substitute these values into the equation and solve for $k$ :

$\implies 1=k \left(\dfrac23-\dfrac13\right)^2$

$\implies 1=k \left(\dfrac13 \right)^2$

Apply the exponent rule $\left(\dfrac{a}{b} \right)^c=\dfrac{a^c}{b^c}$ :

$\implies 1=k \left(\dfrac{1^2}{3^2} \right)$

$\implies 1=\dfrac{1}{9}k$

$\implies k=9$

<u>Part 2</u>

The chord of a parabola is a line segment whose endpoints are points on the parabola.

We are told that one end of the chord is at $(\frac23 ,1)$ and that the chord is horizontal. Therefore, the y-coordinate of the other end of the chord will also be 1. Substitute y = 1 into the equation for the parabola and solve for x:

$\implies 1=9 \left(x-\dfrac13 \right)^2$

$\implies \dfrac19 = \left(x-\dfrac13 \right)^2$

$\implies \sqrt{\dfrac19} = x-\dfrac13$

$\implies \pm \dfrac13 = x-\dfrac13$

$\implies x=\dfrac23, x=0$

Therefore, the endpoints of the horizontal chord are: (0, 1) and (2/3, 1)

To calculate the length of the chord, find the difference between the x-coordinates:

$\implies \dfrac23-0=\dfrac23$

**Please see attached diagram for drawn graph. Chord is in red**

6 0

2 years ago

Answer number 10 please thank you

galina1969 [7]

Answer:

35%

Step-by-step explanation:

3 0

2 years ago

63.92 divided by 4.7

FinnZ [79.3K]

The answer would be 13.6

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3 years ago