Identify the surface with the given vector equation. r(s, t) = s sin 4t, s2, s cos 4t

a. plane
b. hyperbolic paraboloid
c circular paraboloid
d. circular cylinder
e. elliptic cylinder

Circular paraboloid

Step-by-step explanation:

Given ,

Here, these are the respective axes components.

We see that , from the parameterised equation ,

This can also be written as :

This is similar to an equation of a parabola in 1 Dimension.

By fixing the value of z=0,

We get which is equation of a parabola curving towards the positive infinity of y-axis and in the x-y plane.

By fixing the value of x=0,

We get which is equation of a parabola curving towards positive infinity of y-axis and in the y-z plane.

Thus by fixing the values of x and z alternatively ,  we get a CIRCULAR PARABOLOID.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !