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lys-0071 [83]
3 years ago
7

On a shelf there are 60 novels and 20 poetry books. What is the probability that person A chooses a novel and walks away with it

and then person B walks up shortly after and picks another novel?
Mathematics
1 answer:
butalik [34]3 years ago
4 0
On a shelf there are 60 novels and 20 poetry books. Person A chooses a book at random off the shelf and leaves with it. Shortly after, Person B chooses another book at random. Calculate: 1)The probability that the book selected by Person B is a novel? = A picks a novel and B picks a novel OR A picks poetry and B picks novel =( 60/80*59/79) + ( 20/80* 60/59) = 0.75 2)
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Consider the curve defined by the equation y=6x2+14x. Set up an integral that represents the length of curve from the point (−2,
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Answer:

32.66 units

Step-by-step explanation:

We are given that

y=6x^2+14x

Point A=(-2,-4) and point B=(1,20)

Differentiate w.r. t x

\frac{dy}{dx}=12x+14

We know that length of curve

s=\int_{a}^{b}\sqrt{1+(\frac{dy}{dx})^2}dx

We have a=-2 and b=1

Using the formula

Length of curve=s=\int_{-2}^{1}\sqrt{1+(12x+14)^2}dx

Using substitution method

Substitute t=12x+14

Differentiate w.r t. x

dt=12dx

dx=\frac{1}{12}dt

Length of curve=s=\frac{1}{12}\int_{-2}^{1}\sqrt{1+t^2}dt

We know that

\sqrt{x^2+a^2}dx=\frac{x\sqrt {x^2+a^2}}{2}+\frac{1}{2}\ln(x+\sqrt {x^2+a^2})+C

By using the formula

Length of curve=s=\frac{1}{12}[\frac{t}{2}\sqrt{1+t^2}+\frac{1}{2}ln(t+\sqrt{1+t^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}[\frac{12x+14}{2}\sqrt{1+(12x+14)^2}+\frac{1}{2}ln(12x+14+\sqrt{1+(12x+14)^2})]^{1}_{-2}

Length of curve=s=\frac{1}{12}(\frac{(12+14)\sqrt{1+(26)^2}}{2}+\frac{1}{2}ln(26+\sqrt{1+(26)^2})-\frac{12(-2)+14}{2}\sqrt{1+(-10)^2}-\frac{1}{2}ln(-10+\sqrt{1+(-10)^2})

Length of curve=s=\frac{1}{12}(13\sqrt{677}+\frac{1}{2}ln(26+\sqrt{677})+5\sqrt{101}-\frac{1}{2}ln(-10+\sqrt{101})

Length of curve=s=32.66

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Answer:

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Step-by-step explanation:

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Vedmedyk [2.9K]

Answer:

x/100 x 8 = 6

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x100    x100

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