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3 years ago

12

Please do the bottom questions, I provided the rest.

2 answers:

Tresset [83]3 years ago

7 0

jndendudendndjdjndjenjdejdnjnjendjendndndjejdnednedje.Step-by-step explanation:

Aneli [31]3 years ago

4 0

Answer:

6x + 10 ≤ 100

Step-by-step explanation:

<u>For 3.</u>

6x + 10 ≤ 100

6x + 10 - 10 ≤ 100 - 10

6x ≤ 90

(6x)/6 ≤ 90/6

x ≤ 15

<u>For 4.</u>

On the number line, you draw a closed/filled dot on 15. Then you draw a line from 15 all the way to 0. You can't pass 0 because you can't buy a negative amount of food items.

<u>For 5.</u>

The solution, x ≤ 15, means that Aiden can by at least 15 food items and a best gas grill and not go over his budget of $100.

Hope this helps!

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Sav [38]

By the chain rule,

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

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 <em>a</em> and <em>b</em> 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.

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Step-by-step explanation:

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