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Leto [7]
3 years ago
5

F(x) = 4√(2x³-1) F'(x) =.....?

Mathematics
1 answer:
goldfiish [28.3K]3 years ago
6 0

Answer:

\large\boxed{f'(x)=\dfrac{12x^2}{\sqrt{2x^3-1}}}

Step-by-step explanation:

f(x)=4\sqrt{2x^3-1}=4\left(2x^3-1\right)^\frac{1}{2}\\\\f'(x)=4\cdot\dfrac{1}{2}(2x^3-1)^{-\frac{1}{2}}\cdot3\cdot2x^2=\dfrac{12x^2}{(2x^3-1)^\frac{1}{2}}=\dfrac{12x^2}{\sqrt{2x^3-1}}\\\\\text{used}\\\\\sqrt{a}=a^\frac{1}{2}\\\\\bigg[f\left(g(x)\right)\bigg]'=f'(g(x))\cdot g'(x)\\\\\bigg[nf(x)\bigg]'=nf'(x)\\\\(x^n)'=nx^{n-1}

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F(x)= 2x-6

Y=Mx+b

B= y intercept= -6

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3 years ago
Rabies is a viral disease of mammals transmitted through the bite of a rabid animal. The virus infects the central nervous syste
lisabon 2012 [21]

Answer:

(a) The value of <em>x</em> is 0.30.

(b) The probability that a reported case of rabies is not a raccoon is 0.45.

(c) The probability that a reported case of rabies is either a bat or a fox is 0.15.

Step-by-step explanation:

Denote the events as follows:

<em>R</em> = reported case of rabies is a raccoon

<em>F</em> = reported case of rabies is a fox

<em>B</em> = reported case of rabies is a bat

<em>O</em> = reported case of rabies is a some other animal.

The data provided is:

P (R) = 0.55

P (F) = 0.11

P (B) = 0.04

P (O) = <em>x</em>.

(a)

A property of a probability distribution is that the sum of all individual properties is 1.

That is, \sum P(X)=1

Compute the value of <em>x</em> as follows:

\sum P(X)=1\\P(R)+P(F)+P(B)+P(O)=1\\0.55+0.11+0.04+x=1\\0.70+x=1\\x=1-0.70\\x=0.30

Thus, the value of <em>x</em> is 0.30.

(b)

The probability of the complement of an event is the probability of its not happening.

P(A^{c})=1-P(A)

Compute the probability that a reported case of rabies is not a raccoon as follows:

P(R^{c})=1-P(R)\\=1-0.55\\=0.45

Thus, the probability that a reported case of rabies is not a raccoon is 0.45.

(c)

Compute the probability that a reported case of rabies is either a bat or a fox as follows:

P(B\cup F)=P(B)+P(F)\\=0.11+0.04\\=0.15

Thus, the probability that a reported case of rabies is either a bat or a fox is 0.15.

4 0
3 years ago
You spin the spinner and flip a coin. Find the probability of the compound event.
zimovet [89]

Answer:

the compound probability is 1/8.

Step-by-step explanation:

1/4 for the spinner x 1/2 for the coin

4 0
3 years ago
Which of the following is not true? ​
Lisa [10]

Answer:

The last one.

Step-by-step explanation: Because 1/2 divided by 4 = 1/8 and 1/2 x 4/1 = 2

3 0
3 years ago
the depth D, in inches, od wsnow in my yard t hours after it started snowing this morning is given by D=1.5t + 4. if the depth o
Blababa [14]

Answer:

8.5 inches

Step-by-step explanation:

First let's find the time t when the depth of the snow is 7 inches.

To do this, we just need to use the value of D = 7 then find the value of t:

7 = 1.5t + 4

1.5t = 3

t = 2\ hours

We want to find the depth of snow one hour from now, so we just need to use the value of t = 3 to calculate D:

D = 1.5*3 + 4

D = 4.5 + 4 = 8.5\ inches

The depth of snow one hour from now will be 8.5 inches.

7 0
3 years ago
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