Can someone please help me with this question 5 star rating + brainly if solved!

Mathematics

1 answer:

ser-zykov [4K]3 years ago

5 0

The pink one
because it actually can be divided by the top numbers by the bottom and you still get the same answer of the first two

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Write a recursive formula for the sequence 10, 6, 2, -2 ..find next term . Make sure to identify first term. Use an&an-1 in

Iteru [2.4K]

hello :
(-2)-(2) =(2)-(6)=(6)-(10)=-4 (common diffrence)of aritmetic sequence
a recursive formula for the sequence is : An+1=An-4
next term is : (-2)+(-4) = -6

4 0

3 years ago

You are given the polar curve r = e^θ

galina1969 [7]

The tangent to $r(\theta)=e^\theta$ has slope $\frac{\mathrm dy}{\mathrm dx}$ , where

$\begin{cases}x(\theta)=r(\theta)\cos\theta\\y(\theta)=r(\theta)=\sin\theta\end{cases}$

By the chain rule, we have

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{\frac{\mathrm dy}{\mathrm d\theta}}{\frac{\mathrm dx}{\mathrm d\theta}}$

and by the product rule,

$\dfrac{\mathrm dx}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\cos\theta-r(\theta)\sin\theta$

$\dfrac{\mathrm dy}{\mathrm d\theta}=\dfrac{\mathrm dr}{\mathrm d\theta}\sin\theta+r(\theta)\cos\theta$

so that with $\frac{\mathrm dr}{\mathrm d\theta}=e^\theta$ , we get

$\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{e^\theta\sin\theta+e^\theta\cos\theta}{e^\theta\cos\theta-e^\theta\sin\theta}=\dfrac{\sin\theta+\cos\theta}{\cos\theta-\sin\theta}=-\dfrac{1+\sin(2\theta)}{\cos(2\theta)}$