Prove that a parametric equation's range is subset of a cartesian equation r(t)=t(t−2)^3i+t(t−2)^2j where r:RR to RR^2 C={(x,y) in RR^2∣y^4=x^3+2x^2y} I have difficulty with this question. This is where I am up to. 1) Find dy/dx of the cartesian curve dy/dx=(3x^2+4xy)/(4y^3−2x^2); 2) (4y^3−2x^2)=0,y=(2x^(2/3))/2; 3) Substitute y into cartesian equation and find x=-27/16,0.

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to the given matrix
$$\left[\begin{array}{cccc}1& 3& 0& -4\\ 2& 6& 0& -8\end{array}\right]$$

Find, correct to the nearest degree, the three angles of the triangle with the given vertices
A(1, 0, -1), B(3, -2, 0), C(1, 3, 3)

Whether f is a function from Z to R if 
a) ${\displaystyle f\left(n\right)=\pm n}$. 
b) ${\displaystyle f\left(n\right)=\sqrt{n^2+1}}$. 
c) ${\displaystyle f\left(n\right)=\frac{1}{n^2-4}}$.

How to write the expression $6^{\frac{3}{2}}$ in radical form?

How to evaluate ${\displaystyle \sin \left(\frac{-5\pi }{4}\right)}$?

What is the derivative of ${\cot }^{2}x$ ?

How to verify the identity: $\frac{\cos \left(x\right)-\cos \left(y\right)}{\sin \left(x\right)+\sin \left(y\right)}+\frac{\sin \left(x\right)-\sin \left(y\right)}{\cos \left(x\right)+\cos \left(y\right)}=0$?

Find $\tan \left(22.5^{\circ }\right)$ using the half-angle formula.

How to find the exact values of $\cos 22.5°$ using the half-angle formula?

How to express the complex number in trigonometric form: 5-5i?

The solution set of $\tan <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}=3\cot <!--\; \; -->\mathrm{\theta <!--\; \theta \; -->}$ is

How to find the angle between the vector and $x-$axis?

Find the probability of getting 5 Mondays in the month of february in a leap year.

How to find the inflection points for the given function ${\displaystyle f\left(x\right)=x^3-3x^2+6x}$?

How do I find the value of sec(3pi/4)?