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4 years ago

How can you tell it if linear or non-linear

1 answer:

6 0

In linear equations, the graph will always be a straight line. In non linear equations, the graph may look like a parabola (curvy instead of straight).

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The point P(1,1/2) lies on the curve y=x/(1+x). (a) If Q is the point (x,x/(1+x)), find the slope of the secant line PQ correct

lukranit [14]

Answer:

See explanation

Step-by-step explanation:

You are given the equation of the curve

$y=\dfrac{x}{1+x}$

Point $P\left(1,\dfrac{1}{2}\right)$ lies on the curve.

Point $Q\left(x,\dfrac{x}{1+x}\right)$ is an arbitrary point on the curve.

The slope of the secant line PQ is

$\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{\frac{x}{1+x}-\frac{1}{2}}{x-1}=\dfrac{\frac{2x-(1+x)}{2(x+1)}}{x-1}=\dfrac{\frac{2x-1-x}{2(x+1)}}{x-1}=\\ \\=\dfrac{\frac{x-1}{2(x+1)}}{x-1}=\dfrac{x-1}{2(x+1)}\cdot \dfrac{1}{x-1}=\dfrac{1}{2(x+1)}\ [\text{When}\ x\neq 1]$

1. If x=0.5, then the slope is

$\dfrac{1}{2(0.5+1)}=\dfrac{1}{3}\approx 0.3333$

2. If x=0.9, then the slope is

$\dfrac{1}{2(0.9+1)}=\dfrac{1}{3.8}\approx 0.2632$

3. If x=0.99, then the slope is

$\dfrac{1}{2(0.99+1)}=\dfrac{1}{3.98}\approx 0.2513$

4. If x=0.999, then the slope is

$\dfrac{1}{2(0.999+1)}=\dfrac{1}{3.998}\approx 0.2501$

5. If x=1.5, then the slope is

$\dfrac{1}{2(1.5+1)}=\dfrac{1}{5}\approx 0.2$

6. If x=1.1, then the slope is

$\dfrac{1}{2(1.1+1)}=\dfrac{1}{4.2}\approx 0.2381$

7. If x=1.01, then the slope is

$\dfrac{1}{2(1.01+1)}=\dfrac{1}{4.02}\approx 0.2488$

8. If x=1.001, then the slope is

$\dfrac{1}{2(1.001+1)}=\dfrac{1}{4.002}\approx 0.2499$

7 0

3 years ago

Given the formula for the perimeter of a rectangle where I represents the length and w represents the width 2(l+w)

s344n2d4d5 [400]

2 represents area Becuase of the area formula

8 0

3 years ago

3x(23c+2x)-3x(23c-2x)

Alekssandra [29.7K]

69cx+6x-69cx+6x=12x I hope I was helping you.

3 0

3 years ago

A fair die is rolled 12 times. Consider the following four possible outcomes: (i) 5 2 6 3 2 1 4 1 6 5 3 4 (ii) 1 1 2 2 3 3 4 4 5

wolverine [178]

Answer: Hello mate!

A fair die has the possible results of 1, 2, 3, 4, 5 and 6, where all have the same probability ( that is 1/6).

then when you throw the dice 12 times, all the possible arrays of 12 numbers between 1 and 6 have the same probability of showing up, that is equal to

(1/6)^12

this means that the distribution (iii) 6 6 6 6 6 6 6 6 6 6 6 6 (where each 6 has a 1/6 probability) has the same probabilities that (iv) 1 5 4 3 5 1 2 4 4 6 4 5 (where each number has the same probability; 1/6) and we here are imposing order, so the first number must be a 1, which has a 1/6, the second must be a 5, which also has a 1/6; this is the same for every number (doesn't matter if they are different or equal)

then the correct answer is: with a fair die. They are all equally likely.

6 0

4 years ago

If rain is falling at 0.5 inches per hour and 1.5 inches have already accumulated, how many hours must have passed if there are

zavuch27 [327]

Given :

Rain is falling at 0.5 inches per hour and 1.5 inches have already accumulated.

To Find :

How many hours must have passed if there are 5 inches of rain .

Solution :

Let , after x hours rain accumulated is 5 inches .

We know , general equation of line :

y = mx +c

Here , m = 0.5 and c = 1 .

So , equation of rain accumulated is :

$y=0.5x+1$

Now , putting value of x = 5 hours .

We get :

$y=0.5\times 5+1\\\\y=2.5+1=3.5\ inches$

Hence , this is the required solution .

7 0

4 years ago

How can you tell it if linear or non-linear​

How can you tell it if linear or non-linear