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Mathematics

1 answer:

Rina8888 [55]3 years ago

6 0

Answer:

Divided into five equal parts

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If one letter is chosen at random from the word refuse what is the probability that the letter chosen will be an e

mrs_skeptik [129]

Answer: 1/3

Step-by-step explanation: The probability is given by the number of times the event could happen (in this case get an "e"), over the number of all the possibilities (in this case, the six letters of the word)

Therefore, probability $\frac{letter_e}{all letter}=\frac{2}{6} =\frac{1}{3}$

5 0

2 years ago

Finding an Equation of a tangent Line in Exercise, find an equation of the tangent line to the graph of the function at the give

frutty [35]

Answer:

$y=\dfrac{3x}{e}+\dfrac{4}{e}$

this is the equation of the tangent at point (-1,1/e)

Step-by-step explanation:

to find the tangent line we need to find the derivative of the function g(x).

$g(x) =e^{x^3}$

we know that $\frac{d}{dx}(e^{f(x)})=e^{f(x)}f'(x)$

$g'(x) =e^{x^{3}}(3 x^{2})$

$g'(x) =3 x^{2} e^{x^{3}}$

this the equation of the slope of the curve at any point x and it also the slope of the tangent at any point x. hence, g'(x) can be denoted as 'm'

to find the slope at (-1,1/e) we'll use the x-coordinate of the point i.e. x = -1

$m =3 (-1)^{2} e^{(-1)^{3}}\\m =3e^{-1}\\m=\dfrac{3}{e}$