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3 years ago

15

find the volume of the solid whose base is the region bounded by the x-axis, the curves y=5x, y=3x^2, x=0 and x=1.66667 and whic

h has the property that each cross section perpendicular to the x-axis is an equilateral triangle. VOLUME=???

1 answer:

Gekata [30.6K]3 years ago

4 0

Answer:

$\frac{1250\pi}{81}$

Step-by-step explanation:

Volume of solid of revolution between the curves y=5x and y=3x^2 around x-axis on interval [0, 5/3] can be found by using integral as follows:

$Volume = \int\limits^{\frac{5}{3}}_0 \pi ((5x)^2-(3x^2)^2)dx=\pi\int\limits^{\frac{5}{3}}_0(25x^2-9x^4)dx=\\\\=\pi(\frac{25}{3}x^3-\frac{9}{5}x^5)|^{\frac{5}{3}}_0=\frac{1250\pi}{81}$

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Is 12, 13 or 14 a solution of the inequality 4x>52?

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3 years ago

Find the value of k and x2<br> x^2+ 13x + k = 0, x1=-9

Anarel [89]

Given:

The quadratic equation is:

$x^2+13x+k=0$

$x_1=-9$

To find:

The value of k and $x_1$ .

Solution:

We have,

$x^2+13x+k=0$ ...(i)

Putting $x=-9$ , we get

$(-9)^2+13(-9)+k=0$

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Putting $k=36$ in (i), we get

$x^2+13x+36=0$

Splitting the middle term, we get

$x^2+9x+4x+36=0$

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3 years ago

Usimov [2.4K]

Question:

What is the common denominator of $y+\frac{y-3}{3}$ in the complex fraction $\frac{y+\frac{y-3}{3}}{\frac{5}{y}+\frac{2}{3 y}}$

A) $3 y(y-3)$

B) $y(y-3)$

C) $3y$

D) $3$

Answer:

Option D : 3 is the common denominator

Explanation:

It is given that the complex fraction $\frac{y+\frac{y-3}{3}}{\frac{5}{y}+\frac{2}{3 y}}$

We need to determine the common denominator of $y+\frac{y-3}{3}$ from the complex fraction.

Let us consider the fraction $y+\frac{y-3}{3}$

To find the common denominator, let us take LCM.

Thus, rewriting the above fraction as,

$\frac{y}{1} +\frac{y-3}{3}$$

The LCM can be determined by multiplying the denominators.

Thus, we get,

$1\times3=3$

Thus, the common denominator is 3.

Hence, Option D is the correct answer.

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3 years ago