$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\mathrm dy}{\mathrm dt}\dfrac{\mathrm dt}{\mathrm dx}\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm dt}}{\frac{\mathrm dx}{\mathrm dt}}$

It looks like we're given

$\begin{cases}x=a\sin(2t)(1+\cos(2t))\\y=b\cos(2t)(1-\cos(2t))\end{cases}$

where a and b are presumably constant.

Recall that

$\cos^2t=\dfrac{1+\cos(2t)}2$

$\sin^2t=\dfrac{1-\cos(2t)}2$

so that

$\begin{cases}x=2a\sin(2t)\cos^2t\\y=2b\cos(2t)\sin^2t\end{cases}$

Then we have

$\dfrac{\mathrm dx}{\mathrm dt}=4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t$

$\dfrac{\mathrm dy}{\mathrm dt}=-4b\sin(2t)\sin^2t+4b\cos(2t)\sin t\cos t$

$\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{4b\cos(2t)\sin t\cos t-4b\sin(2t)\sin^2}{4a\cos(2t)\cos^2t-4a\sin(2t)\cos t\sin t}$

$\implies\boxed{\dfrac{\mathrm dy}{\mathrm dx}=\dfrac ba\tan t}$

where the last reduction follows from dividing through everything by $\cos(2t)\cos^2t$ and simplifying.

I'm not sure at which point you're supposed to evaluate the derivative (22/7*4, as in 88/7? or something else?), so I'll leave that to you.

8 0

3 years ago

I need a little help

user100 [1]

Answer:

A) x = 8 $\sqrt{2}$

Step-by-step explanation:

in a 45-45-90 triangle, the legs to hypotenuse ratio is 1 : $\sqrt{2}$

so in this problem the leg is 8 and the hypotenuse is 8 $\sqrt{2}$

3 0

2 years ago

Write and test a conjecture about the quotient of a negative number and a positive number. Give at least two examples when testi

4vir4ik [10]

Answer:A negative number divided by a positive number is always negative

Step-by-step explanation:

5 0

3 years ago

Given m/n, find the value of x.

pickupchik [31]

Answer:

x = 152 degrees.

Step-by-step explanation:

The way the 2 angles are positioned indicates that they are corresponding angles.

Corresponding angles are equal.

x = 152 degrees.

Make you know what corresponding angles are and when they can be used. Make sure you also know what parallel lines are (2 or more lines whose distance is a constant). Make sure you also know what a transversal is (a line that crosses the parallel lines).

8 0

1 year ago