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2 years ago

Write the equation of the line that’s tangent to the given function at x=1 f(x)= two x to the third power minus four x

Mathematics

1 answer:

Aliun [14]2 years ago

4 0

$f(x)=2x^3-4x$

take the derivitive to find the slope

$f'(x)=3*(2x^2)-2*(4x^0)$

$f'(x)=6x^2-4$

so at x=1, the slope is f'(1)=6(1)^2-4=6-4=2

y=mx+b

y=2x+b

find b

at x=1, f(1)=2(1)^3-4(1)=2-4=-2=y

-2=2(1)+b

-2=2+b

-4=b

equation is y=2x-4

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There is a bag filled with 3 blue and 4 red marbles.

tresset_1 [31]

Using the hypergeometric distribution, it is found that there is a 0.4286 = 42.86% probability of getting 2 of the same colour.

The marbles are chosen without replacement, hence the <em>hypergeometric </em>distribution is used to solve this question.

<h3>What is the hypergeometric distribution formula?</h3>

The formula is:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

x is the number of successes.

N is the size of the population.

n is the size of the sample.

k is the total number of desired outcomes.

In this problem:

There is a total of 3 + 4 = 7 marbles, hence N = 7.

Of those, 3 are blue, hence k = 3.

2 marbles will be taken, hence n = 2.

The probability of getting 2 of the same colour is the sum of P(X = 0), which is both red, with P(X = 2), which is both blue, then:

$P(X = x) = h(x,N,n,k) = \frac{C_{k,x}C_{N-k,n-x}}{C_{N,n}}$

$P(X = 0) = h(0,7,2,3) = \frac{C_{3,0}C_{4,2}}{C_{7,2}} = 0.2857$

$P(X = 2) = h(2,7,2,3) = \frac{C_{3,2}C_{4,0}}{C_{7,2}} = 0.1429$

Hence:

$p = P(X = 0) + P(X = 2) = 0.2857 + 0.1429 = 0.4286$

0.4286 = 42.86% probability of getting 2 of the same colour.

You can learn more about the hypergeometric distribution at brainly.com/question/4818951

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2 years ago

Evaluate the following.<br> (iii) sin 30° + tan 40° - cosec 60° / cot 45° + cos 60° - sec 30°

bearhunter [10]

Sin 30 = 1/2

tan 45 = 1

Cosec 60 = 2 / √3 = 2√3 / 3

cot 45 = 1

Cos 60 = 1/2

sec 30 = 2 / √3 = 2√3 / 3

_______________________________

[ 1/2 + 1 - 2√3/3 ] ÷ [ 1 + 1/2 - 2√3/3 ] = <em>1</em>

The face and denominator of the fraction are exactly the same thus the answer is 1 .

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2 years ago

N+3/4=1/4 solve for n

Hitman42 [59]

Answer:

N = -1/2

Step-by-step explanation:

We are adding in this, so we need to do the opposite to both sides, to get N by itself.

N + 3/4 - 3/4 = 1/4 - 3/4

N = -2/4 or, simplified, -1/2

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2 years ago

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Triss [41]

Answer:

The answer in the simplest form would be 28/9 or 3 1/9

Step-by-step explanation:

Very simple you would divide the 56 and the 18 by 2 and you get 28/9.

or you could change it to a improper fraction in that case it would be 3 1/9

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Step-by-step explanation:

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