Mathematics, 03.01.2020 22:31 sarahelisabeth444

The curve c(t) = (cost, sint, t) lies on which of the following surfaces. enter t or f depending on whether the statement is true or false. (you must enter t or f -- true and false will not 1. a 2. a 3. an 4. a circular cylinder

Answers: 2

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Answer from: arppy

1. Plane False

2. Sphere False

3. Ellipsoid False

4. Circular cylinder True

Step-by-step explanation:

For this case we have the following curve C(t) = (cos t , sin t , t

And we can express like this the terms for the curve or each component:

x= cos t, y= sin t , z =t

1. Plane False

The general equation for a plane is given by:

a ( x − x 1 ) + b ( y − y 1 ) + c ( z − z 1 ) = 0.

For this case we don't satisfy this since have sinusoidal functions and this equation is never satisfied.

2. Sphere False

The general equation for a sphere is given by:

(x - a)² + (y - b)² + (z - c)² = r²

And for this case if we see our parametric equation again that is not satisfied since we have two cosenoidal functions. And another function z=t

3. Ellipsoid False

The general equation for an ellipsoid is given by:

x^2/a2 + y^2/b2 + z^2/c2 = 1

And for this case again that's not satisfied since we have

$\frac{cos^2 t}{a^2} + \frac{sin^2 t}{b^2}+\frac{t^2}{c^2} \neq 1$

4. Circular cylinder True

The general equation for a circular cylinder is given by:

x^2 +y^2 = r^2

And if we replace the equations that we have we got:

cos^2 t + sin^2 t = 1 from the fundamental trigonometry property.

So then we see that our function satisfy the condition and is the most appropiate option.

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

Answer from: Quest

Answer: v= lwhstep by step explanation: length x width x heightl = 12kmw = 6kmh = 6km12 x 6 = 7272 x 6 = 432therefore your answer would be c) 432 km^3

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The curve c(t) = (cost, sint, t) lies on which of the following surfaces. enter t or f depending on...