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kupik [55]
1 year ago
7

1. 3x^2-7=31 2. 2x^2+18=0 3. 4x^2-26=-50 4. 2x^2+36=x^2

Mathematics
1 answer:
yan [13]1 year ago
4 0

The quadratic equations are solved and answered below -

<h3>What is a equation?</h3>

An equation is a mathematical statement showing the equivalence of two mathematical expressions. Example -

3x + 5 = 8

Given is -

3x² - 7 = 31

2x² + 18 = 0

4x² - 26 = - 50

2x² + 36 = x²

We have -

3x² - 7 = 31

3x² = 38

x² = 38/3

x² = 12.67

x = ±3.56

2x² + 18 = 0

2x² = - 18

x² = -9

x = ±3i

4x² - 26 = - 50

4x² = - 24

x² = -6

x = ±√6i

2x² + 36 = x²

x² = - 36

x = ±√6 i

Therefore, the quadratic equations are solved above.

To solve more questions on Rectangles and their Dimensions, visit the link below -

brainly.com/question/1041084

#SPJ1

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Answer:

I_{corner} =\frac{\rho _{ab}}{3}(a^2+b^2)

Step-by-step explanation:

By applying the concept of calculus;

the moment of inertia of the lamina about one corner I_{corner} is:

I_{corner} = \int\limits \int\limits_R (x^2+y^2)  \rho d A \\ \\ I_{corner} = \int\limits^a_0\int\limits^b_0 \rho(x^2+y^2) dy dx

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I_{corner} =  \rho \int\limits^a_0 {x^2y}+ \frac{y^3}{3} |^ {^ b}_{_0} \, dx

I_{corner} =  \rho \int\limits^a_0 (bx^2 + \frac{b^3}{3})dx

I_{corner} =  \rho [\frac{bx^3}{3}+ \frac{b^3x}{3}]^ {^ a} _{_0}

I_{corner} =  \rho [\frac{a^3b}{3}+ \frac{ab^3}{3}]

I_{corner} =\frac{\rho _{ab}}{3}(a^2+b^2)

Thus; the moment of inertia of the lamina about one corner is I_{corner} =\frac{\rho _{ab}}{3}(a^2+b^2)

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