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3 years ago

The sum of three consecutive terms of an A.P is 18 and their product is 120. Find the terms?

Mathematics

1 answer:

GarryVolchara [31]3 years ago

6 0

Answer:

2 6 10

Step-by-step explanation:

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Use Stokes' Theorem to evaluate C F · dr F(x, y, z) = xyi + yzj + zxk, C is the boundary of the part of the paraboloid z = 1 − x

Serggg [28]

I assume $C$ has counterclockwise orientation when viewed from above.

By Stokes' theorem,

$\displaystyle\int_C\vec F\cdot\mathrm d\vec r=\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

so we first compute the curl:

$\vec F(x,y,z)=xy\,\vec\imath+yz\,\vec\jmath+xz\,\vec k$

$\implies\nabla\times\vec F(x,y,z)=-y\,\vec\imath-z\,\vec\jmath-x\,\vec k$

Then parameterize $S$ by

$\vec r(u,v)=\cos u\sin v\,\vec\imath+\sin u\sin v\,\vec\jmath+\cos^2v\,\vec k$

where the $z$ -component is obtained from

$1-(\cos u\sin v)^2-(\sin u\sin v)^2=1-\sin^2v=\cos^2v$

with $0\le u\le\dfrac\pi2$ and $0\le v\le\dfrac\pi2$ .

Take the normal vector to $S$ to be

$\vec r_v\times\vec r_u=2\cos u\cos v\sin^2v\,\vec\imath+\sin u\sin v\sin(2v)\,\vec\jmath+\cos v\sin v\,\vec k$

Then the line integral is equal in value to the surface integral,

$\displaystyle\iint_S(\nabla\times\vec F)\cdot\mathrm d\vec S$

$=\displaystyle\int_0^{\pi/2}\int_0^{\pi/2}(-\sin u\sin v\,\vec\imath-\cos^2v\,\vec\jmath-\cos u\sin v\,\vec k)\cdot(\vec r_v\times\vec r_u)\,\mathrm du\,\mathrm dv$

$=\displaystyle-\int_0^{\pi/2}\int_0^{\pi/2}\cos v\sin^2v(\cos u+2\cos^2v\sin u+\sin(2u)\sin v)\,\mathrm du\,\mathrm dv=\boxed{-\frac{17}{20}}$

6 0

3 years ago

The leaning tower of Pisa currently "leans" at a 4 degree angle and has a vertical height of 55.86 meters. How tall was the lean

Marizza181 [45]

Answer:

56 meters.

Step-by-step explanation:

Please find the attachment.

Let the leaning tower's be h meters tall, when it was originally built.

We can see from our attachment that the side with length 55.86 meters is hypotenuse and h is adjacent side for 4 degree angle.

Since we know that cosine relates the adjacent and hypotenuse of a right triangle.

$\text{Cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}$

Upon substituting our given values we will get,

$\text{Cos (4)}=\frac{55.86}{h}$

$h=\frac{55.86}{\text{Cos (4)}}$

$h=\frac{55.86}{0.99756405026}$

$h=55.996\approx 56$

Therefore, the leaning tower was approximately 56 meters, when it was originally built.

6 0

3 years ago

Vertical angles are congruent <br><br> a. never<br> b. sometimes <br> c. always

yarga [219]

Answer:

Step-by-step explanation:

because vertical angles angles that are opposite each other and formed by two intersecting lines are congruent

hope this helps :D

5 0

3 years ago

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Jet001 [13]

Answer:

Step-by-step explanation:

Sorry

5 0

3 years ago

Read 2 more answers

I FREEking need help on this! You will get some POINTS for it ∵

omeli [17]

What do you need help on? All I see is a y axis and x axis grid.

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3 years ago

The sum of three consecutive terms of an A.P is 18 and their product is 120. Find the terms?​

The sum of three consecutive terms of an A.P is 18 and their product is 120. Find the terms?