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Stolb23 [73]
3 years ago
10

Part A: Find a rational number that is between 5.2 and 5.5. Explain why it is rational. (2 points) Part B: Find an irrational nu

mber that is between 5.2 and 5.5. Explain why it is irrational. Include the decimal approximation of the irrational number to the nearest hundredth.
Mathematics
1 answer:
alina1380 [7]3 years ago
6 0

Answer: part A: 5.4 because its a terminating deciaml Part B: 5.67854... and to the nearest hundereth is 5.68  

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}.

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2 years ago
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Answer:

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Step-by-step explanation:

you dont know what x is, so you would just do 22-x

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Given the definitions of
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Answer:

i dont know the question what does it mean

Step-by-step explanation:

8 0
1 year ago
You are one of 55 people whose name will be drawn for a prize. What is the probability that your name will be drawn first?
suter [353]

  Your answer will be 1/55 or A because, at the beginning of the problem it states "you are one of 55 people" ((:

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2)) There are 32 1/5 calories in<br> a candy bar. How many calories<br> are there in 33 candy bars?
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If 1 candy bar is 32 1/5 then you would multiply 32 1/5 x 33 =1062.6
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