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The curve C has parametric equations x=cos(t)+1/2*sin(2t) and y =-(1+sin(t)) for 0<=t<=2π. Find a Cartesian equation for C. Find the volume of the solid of revolution of C about the y-axis.

Note the simplest relation to eliminate t is the fact cos 2 (t)+sin 2 (t)=1 for all t, so we need only find x and y in terms of cos(t) and sin(t).Note we have sin(t)=-(y+1) from the equation for y already.Fr...
LP
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How do vaccines prevent certain diseases?

Vaccines introduce a dead, inactive or altered form of a pathogen (a microbe that causes an infectious disease) into the body. These pathogens have antigens, which have a shape specific to that pathogen. The...
AM
Answered by Alice M. • Biology tutor
3196 Views

What is a vector?

A vector describes a movement from one point to another.a column vector shows both the direction and the magnitude of this movement.the top number describes the horizontal movement.the bottom number describe...
TH
Answered by Tom H. • Maths tutor
6567 Views

1) What is the area of a rectangle? 2) What is the area of a triangle?

The area is found by doing length x width. (this can be taught by using squared paper and counting the squares in a shape.2) the area of a triangle is found by using the equation 1/2 x base x height
TH
Answered by Tom H. • Maths tutor
2818 Views

Given M = [[-2,6],[1,3]], find P and D such that M = PDP^(-1) where D is a diagonal matrix

We are given M = [[-2,6],[1,3]], with columns [-2,6] and [1,3]. To find P and D, eigenvalues and eigenvectors must be calculated, as D is defined to be the matrix whose diagonal is comprised of the eigenvalu...
HR
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