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3 years ago

6

1. A kitchen is shaped like a rectangle with dimensions of 4 ft by 7 ft. The

1 answer:

coldgirl [10]3 years ago

8 0

Answer:

112 tiles

Step-by-step explanation:

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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

2 years ago

Which equation represents a parabola?

Evgesh-ka [11]

Answer:

(B)

Step-by-step explanation:

we know that standard equation of parabola y²= 4x or x² = 4y .

So option (B) is correct .

Hope it's helpful

5 0

3 years ago

The table represents a linear function.

Alona [7]

Answer: -6

See attached picture

6 0

2 years ago

How is 1/10 written as a whole number

valina [46]

It is just 10 isn't it?

6 0

3 years ago

Please help me! Please don't get it wrong ;-;

polet [3.4K]

Answer:

Its 40 degrees

Step-by-step explanation:

60+80=140

180-140=40 (a straight line is always 180 degrees)

Hope it helped

3 0

3 years ago