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3 years ago

For which k are the roots of k(x2+1)=x2+3x–3 real and distinct?

Mathematics

1 answer:

Ugo [173]3 years ago

7 0

Answer:

The solution for k is the interval (-3.5,1.5)

Step-by-step explanation:

we have

$k(x^{2}+1)=x^{2}+3x-3$

$kx^{2}+k=x^{2}+3x-3$

$x^{2}-kx^{2}+3x-3-k=0$

$}[1-k]x^{2}+3x-(3+k)=0$

we know that

If the discriminant is greater than zero . then the quadratic equation has two real and distinct solutions

The discriminant is equal to

$D=b^{2}-4ac$

In this problem we have

a=(1-k)

b=3

c=-(3+k)

substitute

$D=3^{2}-4(1-k)(-3-k)\\ \\D=9-4(-3-k+3k+k^{2})\\ \\D=9+12+4k-12k-4k^{2}\\ \\D=21-8k-4k^{2}$

$21-8k-4k^{2} > 0$

solve the quadratic equation by graphing

The solution for k is the interval (-3.5,1.5)

see the attached figure

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3 years ago

What is the solution to the equation? <br>1/7g=3/14

Crazy boy [7]

Answer:

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1 year ago

Read 2 more answers

Each month, a shopkeeper spends 7x+19 dollars on rent and electricity. If he spends 5x−2 dollars on rent, how much does he spe

insens350 [35]

The shopkeeper spends 2x + 21 dollars on electricity

The amount the shopkeeper spends on electricity less than $100 is:

x < 39.5

<h3>What is a linear inequality?</h3>

Linear inequality explains the range of values that a variable represents.

Total amount spent by the shopkeeper = 7x + 19

Amount spent on rent = 5x - 2

Total amount spent = Amount spent on rent + Amount spent on electricity

(7x + 19) = (5x - 2 ) + Amount spent on electricity

Amount spent on electricity = (7x + 19) - (5x - 2)

Amount spent on electricity = 7x - 5x + 19 + 2

Amount spent on electricity = 2x + 21

For which value(s) of x is the amount the shopkeeper spends on electricity less than $100?

Amount spent on electricity < 100

2x + 21 < 100

2x < 100 - 21

2x < 79

x < 79/2

x < 39.5

Learn more on linear inequalities here: brainly.com/question/11613554

6 0

2 years ago

The length of time for one individual to be served at a cafeteria is a random variable having an exponential distribution with a

Leya [2.2K]

Answer:

a) 0.25

b) 52.76% probability that a person waits for less than 3 minutes

Step-by-step explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

$f(x) = \lambda e^{-\lambda x}$

In which $\lambda = \frac{1}{m}$ is the decay parameter.

The probability that x is lower or equal to a is given by:

$P(X \leq x) = \int\limits^a_0 {f(x)} \, dx$

Which has the following solution:

$P(X \leq x) = 1 - e^{-\mu x}$

The probability of finding a value higher than x is:

$P(X > x) = 1 - P(X \leq x) = 1 - (1 - e^{-\mu x}) = e^{-\mu x}$

In this question:

$m = 4$

a. Find the value of λ.

$\lambda = \frac{1}{m} = \frac{1}{4} = 0.25$

b. What is the probability that a person waits for less than 3 minutes?

$P(X \leq 3) = 1 - e^{-0.25*3} = 0.5276$

52.76% probability that a person waits for less than 3 minutes

3 0

3 years ago