Solving the missing side. Find the missing side. Round to the nearest tenth. Please show your work. Part 3. #9-10

Mathematics

1 answer:

KATRIN_1 [288]4 years ago

4 0

Answer:

9. 16.6 units

10. 18.1 units

Step-by-step explanation:

9. We are given the opposite and adjacent sides of the angle 38 degrees, so we want to use tangent, which is opposite / adjacent:

$tan(38)=13/x$

$x=13/tan(38)$ ≈ 16.6 units

10. We are given the adjacent and hypotenuse sides of the angle 25 degrees, so we want to use cosine, which is adjacent / hypotenuse:

$cos(25)=x/20$

$x=20*cos(25)$ ≈ 18.1 units

Hope this helps!

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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

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