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3 years ago

PLEASE HELP!!!

Mathematics

2 answers:

kvasek [131]3 years ago

8 0

Answer:B,C,D

Step-by-step explanation:

Tanzania [10]3 years ago

7 0

Step-by-step explanation:

the dividend divided by the divisor equals the quotient

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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

A photograph measuring 4 inches wide and 5 inches long is enlarged to make a wall mural. If the mural is 82 inches wide, how lon

Aliun [14]

I say it around 150 inches that what I think

6 0

3 years ago

PLEASE HELP GIVING 20 PTS!!!!!! For circle H, JN = 3, NK = x, LN = 2, and NM = 6. Solve for x. PLEASE HEEELLLLPPPPPPP!!!!!!!

Marina CMI [18]

Answer:

x=9

Step-by-step explanation:

when two chords intersects each other, then the product of their segments is equal.

JNxNK = LN x NM

3 *x = 2 * 6

x = (3*6)/2 = 18/2 = 9

5 0

3 years ago

HELP ME PLEASEEEEEEEEEE

natta225 [31]

Answer: it would be (2, -4) because if you flip it it will still be the same just at a different angle.

Step-by-step explanation:

8 0

3 years ago

1. What is the volume, in cubic centimeters, of the sphere shown below? Use 3.14<br> for Pi

prohojiy [21]

Answer:

113.04 cm³

Step-by-step explanation:

diameter = 6cm

so radius = 3cm

Volume of sphere = $\frac{4}3}$ $\pi r^3$

= 4 * 3.14 * 3 * 3 *3 / 3

= 4 * 28.26

= 113.04 cm³

6 0

3 years ago