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2 years ago

What is the slope between the points (0, 0) and (3, -9)

Mathematics

1 answer:

Vlad1618 [11]2 years ago

3 0

9
—
3

I hope that helps

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Find, correct to four decimal places, the length of the curve of intersection of the cylinder 16x2 + y2 = 16 and the plane x + y

Yuri [45]

Let the curve C be the intersection of the cylinder

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

and the plane

$x+y+z=1$

The projection of C on to the x-y plane is the ellipse

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

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

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

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

$\int\limits^{2\pi}_0 {\sqrt{2sin^2(t)+32cos(t)-8sin(t)cos(t)} }\, dt=24.08778184$

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.

6 0

3 years ago

A bicycle tire has a diameter of 62 cm

anzhelika [568]

Answer

1946.8 cm

Step-by-step explanation:

you first need to find the circumference of the tire. to do this you use the formula C=d(3.14)

you plug in the 62 to the d

62 times 3.14 = 194.68

and multiply that by 10 because it is 10 revolutions to get 1946.8 cm

5 0

3 years ago

A bag contains 12 beads 2 blue 1 green 3 purple the rest red

Anestetic [448]

Answer : 6 red beads

explanation: 2+1+3 = 6

12-6 = 6

hope this helps :)

3 0

3 years ago

What is the 17th term in the geometric sequence?<br> 4,8,16,32,64

Ksivusya [100]

You just multiply by 2 as you can see
4×2=8
8×2=16 and so on
64×2=128 therefore 128 is the answer

7 0

3 years ago

Help Please!!!!!!!!

VladimirAG [237]

Answer:

$14.50 I'm positive.

Step-by-step explanation:

Rented one time shoes: $2.75

One game of bowling: $2.50*4 games of bowling

4 games of bowling is $10

$2.75+$10

One nachos: $1.75*2 orders of nachos

2 orders of nachos is $3.50

Half price of nachos, so 3.50/2 which is 1.75.

$2.75+$10+$1.75= <u>$14.50</u>

HOPE THIS HELPED :)

3 0

3 years ago