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4 years ago

10

What is the simple subject of I could feel the rain on my left shoulder.

1 answer:

ahrayia [7]4 years ago

7 0

This a dang easy question. Ask yourself,what is the sentence about?

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Find the equation of the tangent line to the curve (a lemniscate)

olya-2409 [2.1K]

Answer:

$m=\frac{9}{13}$ and $b=\frac{40}{13}$

Step-by-step explanation:

The equation of curve is

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

We need to find the equation of the tangent line to the curve at the point (-3, 1).

Differentiate with respect to x.

$2[2(x^2+y^2)\frac{d}{dx}(x^2+y^2)]=25(2x-2y\frac{dy}{dx})$

$4(x^2+y^2)(2x+2y\frac{dy}{dx})=25(2x-2y\frac{dy}{dx})$

The point of tangency is (-3,1). It means the slope of tangent is $\frac{dy}{dx}_{(-3,1)}$ .

Substitute x=-3 and y=1 in the above equation.

$4((-3)^2+(1)^2)(2(-3)+2(1)\frac{dy}{dx})=25(2(-3)-2(1)\frac{dy}{dx})$

$40(-6+2\frac{dy}{dx})=25(-6-2\frac{dy}{dx})$

$-240+80\frac{dy}{dx})=-150-50\frac{dy}{dx}$

$80\frac{dy}{dx}+50\frac{dy}{dx}=-150+240$

$130\frac{dy}{dx}=90$

Divide both sides by 130.

$\frac{dy}{dx}=\frac{9}{13}$

If a line passes through a points $(x_1,y_1)$ with slope m, then the point slope form of the line is

$y-y_1=m(x-x_1)$

The slope of tangent line is $\frac{9}{13}$ and it passes through the point (-3,1). So, the equation of tangent is

$y-1=\frac{9}{13}(x-(-3))$

$y-1=\frac{9}{13}(x)+\frac{27}{13}$

Add 1 on both sides.

$y=\frac{9}{13}(x)+\frac{27}{13}+1$

$y=\frac{9}{13}(x)+\frac{40}{13}$

Therefore, $m=\frac{9}{13}$ and $b=\frac{40}{13}$ .

5 0

3 years ago

Thepotemich [5.8K]

Answer:

Step-by-step explanation:

D

4 0

3 years ago

If the first term is 5 and the common difference is -3?

Doss [256]

-2 is the answer
----------------------------
You're Welcome.

6 0

3 years ago

Factored form of 16m^4-121

AnnZ [28]

$16m^4-121 =(4m^2-11)(4m^2+11)$

8 0

3 years ago

Haleigh split 4/9 of a gallon of juice into 8 cups. How much juice was in each cup?

Brut [27]

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▹ Answer

<em>1/18 of a gallon of juice in each cup.</em>

▹ Step-by-Step Explanation

Since we have 4/9 of a gallon of juice for 8 cups, we will divide to find the amount of juice in each cup.

$\frac{4}{9} / 8$

Since this operation is division, we have to change 8 to it's reciprocal which is 1/8:

$\frac{4}{9}/ \frac{1}{8} = \frac{4}{72} = \frac{1}{18}$

Our final answer will be 1/18 of a gallon of juice in each cup.

Hope this helps!

CloutAnswers ❁

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5 0

3 years ago