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denis23 [38]
3 years ago
15

Solve each equation using the quadratic formula. Find the exact solutions. 6n^2 + 4n = -11

Mathematics
2 answers:
masha68 [24]3 years ago
7 0

Answer:

(-2±√62i ) / 12

Step-by-step explanation:

Given equation is :

6n²+4n =-11

Adding 11 to both sides of above equation, we get

6n²+4n+11=-11+11

6n²+4n+11= 0

an²+bn+c = 0 is general quadratic equation.

n =(-b±√b²-4ac) / 2a is solution of general equation.

Comparing  general quadratic equation with given quadratic equation,we get

a = 6, b = 4 and c = 11

Putting above values in quadratic formula,we get

n= (-4±√4²-4(6)(11))/ 2(6)

n = ( -4±√16-264) / 12

n = (-4±√-248) / 12

n = ( -4±√-1√248) / 12

n = (-4±√4×62i) / 12

n = (-4± 2√62i) / 12

n = 2(-2±√62i) / 12

n = (-2±√62i ) / 12 is solution of given equation.


kenny6666 [7]3 years ago
3 0

Answer:

n_1=-\frac{1}{3}+1.31i\\n_2=-\frac{1}{3}-1.31i


Step-by-step explanation:

To solve this problem you  must apply the proccedure shown below:

1. You have that the quadratic formula is:

n=\frac{-b+/-\sqrt{b^{2}-4ac}}{2a}

2. To solve the quadratic equation you must substitute the values, you have that:

a=6\\b=4\\c=11

Then:

 n=\frac{-4+/-\sqrt{4^{2}-4(6)(11)}}{2(6)}

3, Therefore, you obtain the following result:

n_1=-\frac{1}{3}+1.31i\\n_2=-\frac{1}{3}-1.31i


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Read 2 more answers
The probability density function of the time to failure of an electronic component in a copier (in hours) is f(x) for Determine
salantis [7]

The question is incomplete. Here is the complete question.

The probability density function of the time to failure of an electronic component in a copier (in hours) is

                                              f(x)=\frac{e^{\frac{-x}{1000} }}{1000}

for x > 0. Determine the probability that

a. A component lasts more than 3000 hours before failure.

b. A componenet fails in the interval from 1000 to 2000 hours.

c. A component fails before 1000 hours.

d. Determine the number of hours at which 10% of all components have failed.

Answer: a. P(x>3000) = 0.5

              b. P(1000<x<2000) = 0.2325

              c. P(x<1000) = 0.6321

              d. 105.4 hours

Step-by-step explanation: <em>Probability Density Function</em> is a function defining the probability of an outcome for a discrete random variable and is mathematically defined as the derivative of the distribution function.

So, probability function is given by:

P(a<x<b) = \int\limits^b_a {P(x)} \, dx

Then, for the electronic component, probability will be:

P(a<x<b) = \int\limits^b_a {\frac{e^{\frac{-x}{1000} }}{1000} } \, dx

P(a<x<b) = \frac{1000}{1000}.e^{\frac{-x}{1000} }

P(a<x<b) = e^{\frac{-b}{1000} }-e^\frac{-a}{1000}

a. For a component to last more than 3000 hours:

P(3000<x<∞) = e^{\frac{-3000}{1000} }-e^\frac{-a}{1000}

Exponential equation to the infinity tends to zero, so:

P(3000<x<∞) = e^{-3}

P(3000<x<∞) = 0.05

There is a probability of 5% of a component to last more than 3000 hours.

b. Probability between 1000 and 2000 hours:

P(1000<x<2000) = e^{\frac{-2000}{1000} }-e^\frac{-1000}{1000}

P(1000<x<2000) = e^{-2}-e^{-1}

P(1000<x<2000) = 0.2325

There is a probability of 23.25% of failure in that interval.

c. Probability of failing between 0 and 1000 hours:

P(0<x<1000) = e^{\frac{-1000}{1000} }-e^\frac{-0}{1000}

P(0<x<1000) = e^{-1}-1

P(0<x<1000) = 0.6321

There is a probability of 63.21% of failing before 1000 hours.

d. P(x) = e^{\frac{-b}{1000} }-e^\frac{-a}{1000}

0.1 = 1-e^\frac{-x}{1000}

-e^{\frac{-x}{1000} }=-0.9

{\frac{-x}{1000} }=ln0.9

-x = -1000.ln(0.9)

x = 105.4

10% of the components will have failed at 105.4 hours.

5 0
3 years ago
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