PLEASE HELP ASAP QUESTION ABOVE

Mathematics

1 answer:

ludmilkaskok [199]3 years ago

5 0

Answer:

13230

Step-by-step explanation:

dk i thank this is it just do 7x7x6x9x5

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Find an equation of the tangent line to the curve 2(x2+y2)2=25(x2−y2) (a lemniscate) at the point (−3,1). An equation of the tan

valina [46]

$2(x^2+y^2)^2=25(x^2-y^2)$

Let $y=y(x)$ , so that differentiating both sides wrt $x$ gives

$4(x^2+y^2)\left(2x+2y\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(2x-2y\dfrac{\mathrm dy}{\mathrm dx}\right)$

If $x=-3$ and $y=1$ , the above reduces to

$40\left(-6+2\dfrac{\mathrm dy}{\mathrm dx}\right)=25\left(-6-2\dfrac{\mathrm dy}{\mathrm dx}\right)\implies\dfrac{\mathrm dy}{\mathrm dx}=\dfrac9{13}$

This is the slope of the tangent line, which has equation

$y-1=\dfrac9{13}(x+3)\implies\boxed{y=\dfrac{9x+40}{13}}$

7 0

2 years ago

Solve for x: -6(x + 4) + 9 > -5(x + 6)

devlian [24]

Answer:

x < 15

Step-by-step explanation:

Let's first expand the parentheses on both sides. Remember that when expanding parentheses, the result will be the sum of the products of the "outside number" with each of the "inside number".

On the left, the parenthetical expression is: -6(x + 4). Here, the outside term is -6 and the inside terms are x and 4. So:

-6(x + 4) = -6 * x + (-6) * 4 = -6x - 24

On the right, the parenthetical expression is: -5(x + 6). Here, the outside term is -5 and the inside terms are x and 6. So:

-5(x + 6) = -5 * x + (-5) * 6 = -5x - 30

Now put these back in:

-6(x + 4) + 9 > -5(x + 6)

-6x - 24 + 9 > -5x - 30

-6x - 15 > -5x - 30

x < 15

Thus the answer is x < 15.

Hope this helps!

3 0