Pls help me complete this

Mathematics

1 answer:

san4es73 [151]3 years ago

6 0

Answer: 1/10, 3/20, 1/4, 1/5, 3/10

Step-by-step explanation: So first, you need to find the total number of times Leon spins the spinner, which is 20. You get 20 by counting the total number of x's there are.

Then you need to find the number of times each number got landed on. In order, it would be 2/20, 3/20, 5/20, 4/20, and 6/20.

Next, you have to simplify them. 2/20 simplified is 1/10, then 3/20 can't be simplified, so leave it like that, 5/20 would be 1/4, 4/20 would be 1/5, and finally, 6/20 would be 3/10.

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∫∫x²(y-x)dxdy ,d là miền giới hạn bởi các đường y=x² và x=y²

Valentin [98]

It looks like the integral is

$\displaystyle \iint_D x^2 (y-x) \,\mathrm dx\,\mathrm dy$

where D is the set

D = {(x, y) : 0 ≤ x ≤ 1 and x ² ≤ y ≤ √x}

So we have

$\displaystyle \iint_D x^2(y-x)\,\mathrm dx\,\mathrm dy = \int_0^1 \int_{x^2}^{\sqrt x} x^2(y-x)\,\mathrm dy\,\mathrm dx \\\\ = \int_0^1 \left(\frac{x^2y^2}2-x^3y\right)\bigg|_{y=x^2}^{y=\sqrt x} \\\\ = \int_0^1 \left(\frac{x^3}2-x^{7/2}+x^5-\frac{x^6}2\right)\,\mathrm dx \\\\ = \left(\frac{x^4}8 - \frac{2x^{9/2}}9 + \frac{x^6}6 - \frac{x^7}{14}\right)\bigg|_{x=0}^{x=1} = \frac18-\frac29+\frac16-\frac1{14} = \boxed{-\frac{1}{504}}$