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2 years ago

According to class 8 please solve

Mathematics

1 answer:

Harrizon [31]2 years ago

7 0

Answer:

i) 4x

ii) Father's age = 3(x + 10)

Son's age = x + 10

iii) 4x + 10 = 3(x + 10)

iv) Present age of the son = x = 20

Present age of the father = 4x = 4(20)

= 80

Step-by-step explanation:

Present age of the son = x

Present age of the father = 4x

Age of the son in 10 years = x + 10

Age of the father in 10 years = 3(x + 10)

4x + 10 = 3(x + 10)

4x + 10 = 3x + 30

4x - 3x = 30 - 10

x = 20

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Step-by-step explanation:

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$\int \frac{dx}{\sqrt{9-x^2}}$

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We have the term in the following format: $a^2 - x^2$ , in which a = 3.

In this case, the substitution is given by:

$x = a\sin{\theta}$

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In this question:

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We have the following trigonometric identity:

$\sin^{2}{\theta} + \cos^{2}{\theta} = 1$

$1 - \sin^{2}{\theta} = \cos^{2}{\theta}$

Replacing into the integral:

$\int \frac{3\cos{\theta}d\theta}{\sqrt{9(1 - \sin^{2}{\theta})}} = \int{\frac{3\cos{\theta}d\theta}{\sqrt{9\cos^{2}{\theta}}} = \int \frac{3\cos{\theta}d\theta}{3\cos{\theta}} = \int d\theta = \theta + C$

Coming back to x:

We have that:

$x = 3\sin{\theta}$

$\sin{\theta} = \frac{x}{3}$

Applying the arcsine(inverse sine) function to both sides, we get that:

$\theta = \arcsin{(\frac{x}{3})}$

The result of the integral is:

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3 years ago