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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

Please help no links

kap26 [50]

Answer: B or C

Step-by-step explanation:

if u can compare the triangles u u can use ur math and get the answer

3 0

3 years ago

Read 2 more answers

Adam plans to choose a video game from a section of the store where everything is 75%

Minchanka [31]

Answer:

Look below

Step-by-step explanation:

In Adam's expression, d represents the original price of the game. 0.75d represents 75% of the original price; this is the amount of the discount, since everything is 75% off. Taking the difference of the original price and the discount, d-0.75d, gives us the total price of the game. In Rena's expression, 0.25 represents 25%. This is because taking 75% off of the price means we still pay 100-75 = 25% of the original price. Multiplying the original price, d, by the 0.25, gives us 25% of the original price; this is the total price.

6 0

3 years ago

How do you prove that angles are parallel?

3241004551 [841]

Answer:#1

if corresponding angles are congruent

#2

if alternate interior angles are congruent

#3

if consecutive, or same side, interior angles are supplementary

#4

if two lines are parallel to the same line

#5

if two lines are perpendicular to the same line

#6

if alternate exterior angles are congruent

7 0

3 years ago

Read 2 more answers

Solve the problem.When exposed to ethylene gas, green bananas will ripen at an accelerated rate. The number of days for ripening

Alex Ar [27]

The table and the plotted data are in the attachment.

Answer and Step-by-step explanation: A line of best fit is the best approximation of the given data. It is used to show the relation of two variables and it can be determined, more accurately, by the Least Square Method.

To use the method, follow the steps:

1) Calculate the mean of the two variables:

$X = \frac{\Sigma x_{i}}{n}$