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2 years ago

Please help mee!!! Arrange the following numbers from largest to smallest: 1.065, 0.39, 1.29

Mathematics

1 answer:

Marat540 [252]2 years ago

6 0

1.29
1.065
0.39
its pretty easy its a matter of logic

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3 years ago

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Let the curve C be the intersection of the cylinder

$16x^2+y^2=16$

and the plane

$x+y+z=1$

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To see clearly that this is an ellipse, le us divide through by 16, to get

$\frac{x^2}{1}+ \frac{y^2}{16}=1$

$\frac{x^2}{1^2}+ \frac{y^2}{4^2}=1$ ,

We can write the following parametric equations,

$x=cos(t), y=4sin(t)$

for

$0\le t \le 2\pi$

Since C lies on the plane,

$x+y+z=1$

it must satisfy its equation.

Let us make z the subject first,

$z=1-x-y$

This implies that,

$z=1-sin(t)-4cos(t)$

We can now write the vector equation of C, to obtain,

$r(t)=(cos(t),4sin(t),1-cos(t)-4sin(t))$

The length of the curve of the intersection of the cylinder and the plane is now given by,

$\int\limits^{2\pi}_0 {|r'(t)|} \, dt$

But

$r'(t)=(-sin(t),4cos(t),sin(t)-4cos(t))$

$|r'(t)|=\sqrt{(-sin(t))^2+(4cos(t))^2+(sin(t)-4cos(t))}$

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Therefore the length of the curve of the intersection intersection of the cylinder and the plane is 24.0878 units correct to four decimal places.

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3 years ago

Crickets can jump with a vertical velocity of up to 14 ft/s. Which equation models the height of such a jump, in feet, after t s

Natasha_Volkova [10]

Acceleration is simplified by assuming it is the constant -g

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h=(-gt^2)/2 +14t +C we are not given an initial height so C is 0

h(t)=14t-gt^2/2 letting g=32 and neatening up a bit...

h(t)=14t-16t^2

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2 years ago

Read 2 more answers