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2 years ago

Two times what equals twenty-two

Mathematics

2 answers:

forsale [732]2 years ago

8 0

The are is eleven because 2×11= 22

saul85 [17]2 years ago

6 0

2 multiplied by 11 is 22. so the answer is 11

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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

What is the surface area of a cylindrical ring where the diameter of the cross section is 6.3 in and the center line has a lengt

Kruka [31]

The surface area of the cylindrical ring is given by
πdh
where d is the diameter and h is the height:
π•6.3•48 = 950.02
The answer is C. 950.02 in^2

4 0

3 years ago

Read 2 more answers

At Garland School,

ankoles [38]

490 x 2/5 = 980/5 = 196 girls at Garland

945 x 5/7 = 4725/7 = 675 girls at Bowood

Bowood has more girls:

675-196 = 479 more

8 0

1 year ago

Without solving the equations which answer best describes the solutions.

telo118 [61]

ANSWER:
D. The answers will be different because after distributing the 4 in the first equation it will change the values.

Hope it helps u!

6 0

2 years ago

Logarithmic and Exponential Forms of Equations In Exercise,Write the logarithmic equation as an exponential equation,or vice ver

lesantik [10]

Answer:

e^-1.6094 = 0.2

Step-by-step explanation:

The inverse of In is e

If In 0.2 = -1.6094

Then e^-1.6094 = 0.2

4 0

2 years ago