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Vlad1618 [11]
2 years ago
9

Is -2 + √3 rational or irrational?explain why.

Mathematics
1 answer:
andrey2020 [161]2 years ago
3 0

Answer:

It is irrational

Step-by-step explanation:

Let us assume that 2+√3 is a rational number.

A rational number can be written in the form of p/q.

2+√3=p/q

√3=p/q-2

√3=(p-2q)/q  

p,q are integers then (p-2q)/q is a rational number.

But this contradicts the fact that √3 is an irrational number.

So, our assumption is false.

Therefore,2+√3 is an irrational number.

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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
.
KIM [24]

Answer:

x=-1 is the answers for the question

Step-by-step explanation:

please mark me as brainlest

3 0
2 years ago
Which of the following could explain the changes in growth between the 15th month and the 24th month ?
noname [10]

Answer:  The Answer is A

Step-by-step explanation:

i think it's right

6 0
3 years ago
Let g(x) = |x + 1|, solve the equation g(x) = 2x + 4
hammer [34]

Answer:

Step-by-step explanation:

g(x)= -x-1 or g(x) = x+1

if g(x) = -x-1

-x-1=2x+4

-x=2x+5

-x/2=x+5

-x/2 -x=5

-x/2-2x/2=5

-x-2x=5

-3x=5

x=5/-3

if g(x) = x+1

x+1=2x+4

x=2x+3

x/2=x+3

x/2-x=3

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3 years ago
What is the vertical clearance 2 m from the edge of the tunnel?
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When x=0 y=50 when y=0 x=+\-5. -x^2 makes the parabola open downward y(x)=2x^2+50;y(3)=2*9+50=32
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3 years ago
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