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2 years ago

I dont understand linear equations,what is the purpose of a linear equation?

Mathematics

2 answers:

Hatshy [7]2 years ago

8 0

Answer:

it's a straight line graph

Step-by-step explanation:

it indicates something is directly proportional

Darina [25.2K]2 years ago

4 0

A linear equation in two variables describes a relationship in which the value of one of the variables depends on the value of the other variable. In a linear equation in x and y, x is called x is the independent variable and y depends on it. We call y the dependent variable.

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Given f(x) = (lnx)^3 find the line tangent to f at x = 3

kirill [66]

Explanation

We must the tangent line at x = 3 of the function:

$f(x)=(\ln x)^3.$

The tangent line is given by:

$y=m*(x-h)+k.$

Where:

• m is the slope of the tangent line of f(x) at x = h,

• k = f(h) is the value of the function at x = h.

In this case, we have h = 3.

1) First, we compute the derivative of f(x):

$f^{\prime}(x)=\frac{d}{dx}((\ln x)^3)=3*(\ln x)^2*\frac{d}{dx}(\ln x)=3*(\ln x)^2*\frac{1}{x}=\frac{3(\ln x)^2}{x}.$

2) By evaluating the result of f'(x) at x = h = 3, we get:

$m=f^{\prime}(3)=\frac{3}{3}*(\ln3)^2=(\ln3)^2.$

3) The value of k is:

$k=f(3)=(\ln3)^3$

4) Replacing the values of m, h and k in the general equation of the tangent line, we get:

$y=(\ln3)^2*(x-3)+(\ln3)^3.$

Plotting the function f(x) and the tangent line we verify that our result is correct:

Answer

The equation of the tangent line to f(x) and x = 3 is:

$y=(\ln3)^2*(x-3)+(\ln3)^3$

6 0

1 year ago

The sum of the squares of 3 consecutive positive integers is 116. What are the numbers?

Elza [17]

You are supposed to use the third option: 3n2 + 6n + 5 = 116.
Take a look at the attachment to see how I got that solution.
Hope it helps! :)

5 0

2 years ago

A number divided by 6 minus -3 equals 12

liberstina [14]

Let the number be x.

Therefore, by the problem

x/6-(-3) = 12

or, x/6+3 = 12

or, x/6 = 12-3

or, x/6 = 9

or, x = 9 × 6

or, x = 54

The number is 54.

4 0

2 years ago

Read 2 more answers

Square root 5 is closest to what real number?

gladu [14]

The square root of 5 is 2.23 so it would be closer to 2

7 0

3 years ago

An airport limousine can accommodate up to four passengers on any one trip. The company will accept a maximum of six reservation

miss Akunina [59]

Answer:

a) 0.109375 = 0.109 to 3 d.p

b) 1.00 to 3 d.p

Step-by-step explanation:

Probability of someone that made a reservation not showing up = 50% = 0.5

Probability of someone that made a reservation showing up = 1 - 0.5 = 0.5

a) If six reservations are made, what is the probability that at least one individual with a reservation cannot be accommodated on the trip?

For this to happen, 5 or 6 people have to show up since the limousine can accommodate a maximum of 4 people

Let P(X=x) represent x people showing up

probability that at least one individual with a reservation cannot be accommodated on the trip = P(X = 5) + P(X = 6)

P(X = x) can be evaluated using binomial distribution formula

Binomial distribution function is represented by

P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ

n = total number of sample spaces = 6

x = Number of successes required = 5 or 6

p = probability of success = 0.5

q = probability of failure = 0.5

P(X = 5) = ⁶C₅ (0.5)⁵ (0.5)⁶⁻⁵ = 6(0.5)⁶ = 0.09375

P(X = 6) = ⁶C₆ (0.5)⁶ (0.5)⁶⁻⁶ = 1(0.5)⁶ = 0.015625

P(X=5) + P(X=6) = 0.09375 + 0.015625 = 0.109375

b) If six reservations are made, what is the expected number of available places when the limousine departs?

Probability of one person not showing up after reservation of a seat = 0.5

Expected number of people that do not show up = E(X) = Σ xᵢpᵢ

where xᵢ = each independent person,

pᵢ = probability of each independent person not showing up.

E(X) = 6(1×0.5) = 3

If 3 people do not show up, it means 3 people show up and the number of unoccupied seats in a 4-seater limousine = 4 - 3 = 1

So, expected number of unoccupied seats = 1

5 0

2 years ago