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arlik [135]
3 years ago
9

Raju's father is 26 years younger than raju's grandfather and 29 years older than raju. The sum of the ages of all the three is

135 years. also raju's grandmother is 4 times raju's age and his sister is 7 times younger than him.
a) If Raju’s age is ‘x’, then what will be the age of his grandfather.

b)The age of Raju is___

c)The age of Raju’s grandmother is___

d) If Raju’s age is ‘x’, then express Raju’s sister age in terms of Raju’s age
Mathematics
1 answer:
Musya8 [376]3 years ago
8 0

b 7

c 135

d jsjbsbdhejeujsvevevdvvdhdhdhdvevvevdvdvevvevegehhehehebevevvehdhrhevd

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Use the Divergence Theorem to evaluate the following integral S F · N dS and find the outward flux of F through the surface of t
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Answer:

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Step-by-step explanation:

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z = 4 - x² - y²

div F        

For S: z = 0, z = 4 -x² - y²

We have the equation of a parabola

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We have for the surface S₁ the outward normal is N₁ = -k and the outward normal for surface S₂ is N₂ given by

N_2 = \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} }

Solving we have;

\int\limits\int\limits_S { \textbf{F}} \, \cdot \textbf{N} d {S} = \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{N}_1 d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot \textbf{N}_2 d {S}

Plugging the values for N₁ and N₂, we have

= \int\limits\int\limits_{S1} { \textbf{F}} \, \cdot \textbf{(-k)}d {S} + \int\limits\int\limits_{S2} { \textbf{F}} \, \cdot  \frac{2x \textbf{i} +2y \textbf{j} + \textbf{k}}{\sqrt{4x^2+4y^2+1} } d {S}

Where:

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= -\int\limits\int\limits_{S1} 2z \ dA + \int\limits\int\limits_{S2} 4x^2+4y^2+2z \ dA

= -\int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 2z \ dA + \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2+2z \ dA

= \int\limits^2_{-2} \int\limits^{\sqrt{4-y^2}} _{-\sqrt{4-y^2}} 4x^2+4y^2 \ dxdy

= \int\limits^2_{-2} \frac{(16y^2 +32)\sqrt{-(y^2-4)} }{3} dy

= 32π.

6 0
4 years ago
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