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2 years ago

What is the expression in radical form? (5x^3 y^2) 2/8

Mathematics

1 answer:

Gre4nikov [31]2 years ago

8 0

Answer: (y^{2}x^{3}⋅5)/4

Step-by-step explanation:

Convert to Radical Form

$(5x^3y^2)\frac{2}{8}$

Reduce the expression $\frac{2}{8}$ by cancelling the common factors.

Factor 2 out of 2.

$5x^3y^2\frac{2(1)}{8}$

Factor 2 out of 8.

$5x^3y^2 \frac{2(1)}{2(4)}$

Cancel the common factor.

$5x^3y^2 \frac{1}{4}$

Combine 5 and $\frac{1}{4}$ .

$x^3y^2\frac{5}{4}$

Combine $x^{3}$ and $\frac{5}{4}$ .

$y^2\frac{x^3(5)}{4}$

Combine $y^{2}$ and $\frac{x^3*5}{4}$

$\frac{y^2x^3*5}{4}$

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Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .

The equation for a sphere of radius $r$ and center $\left(x_0,\, y_0,\, z_0\right)$ would be:

$\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2$ .

In this case, the equation would be:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2$ .

Simplify to obtain:

$\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56$ .

Expand the squares and simplify to obtain:

$x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ .

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2 years ago

URGENT NOW: Use the graph below to fill in the blank with the correct number: f(−2) = _______ X, Y graph. Plotted points negativ

navik [9.2K]

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3 years ago

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mariarad [96]

Answer:

4 week ago question free epoint yasss

Step-by-step explanation:

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2 years ago

I walk each day to school. By what percentage would I need to increase my usual average speed in order for the journey to take 2

lesya692 [45]

Answer:

25%

Step-by-step explanation:

Let v, t be the current average speed and the time taken to reach the school respectively.

As distance = speed x time, so,

distance, d=vt...(i)

Let V be the new average speed in order to to take 20% less time than t.

So, time taken with speed V = t-20% of t = t- 0.2t= 0.8t

As distance is constant, so

d= V(0.8t)= 0.8Vt

hBy using equation (i), we have

0.8Vt = vt

0.8 V = v

V= v/0.8=1.25v

Therefore, the percentage increase in the average speed = $\frac{V-v}{v}\times 100$

$=\frac{1.25v-v}{v}\times 100$

=25%

Hence, the percentage increase in the average speed is 25%.

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2 years ago

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Monica [59]

The answer is 0.12. Hope I helped! please mark as the brainliest!

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2 years ago

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