Chapter 6: Q 126. (page 383)

Piston Engines In a certain piston engine, the distance x (in cm) from the center of the drive shaft to the head of the piston is given by the function.
$x (θ) = \cos θ + \sqrt{16 + 0 \cdot 5 \cos (2 θ)}$
where $θ$ is the angle between the crank and the path of the piston head. See the figure. Find $x$ when $θ = 30 °$ and $θ = 45 °$ .

Short Answer

Expert verified

The value of $x$ when $θ = 30 °$ is $(\sqrt{\frac{3}{2} +} \frac{\sqrt{65}}{2})$ and value of x when $θ = 45 °$ is $2 \sqrt{2}$ .

Step by step solution

Step 1. Given information .

Consider the given value of $θ = 30 °$ and $θ = 45 °$ .

.Finding xθ when θ=30° .

$x (θ) = \cos θ + \sqrt{16 + 0 \cdot 5 \cos (2 θ)}$

Substitute the value in given formula .

role="math" localid="1646654361342" $x (30 °) = \cos 30 ° + \sqrt{16 + 0 \cdot 5 \cos (2 \times 30 °)} x (30 °) = \frac{\sqrt{3}}{2} + \sqrt{16 + \frac{1}{4}} = \frac{\sqrt{3}}{2} + \frac{\sqrt{65}}{2}$

Step 3. Finding the value of xθ when θ=45° .

Substitute the value in given formula $θ = 45 °$

$x (θ) = \cos θ + \sqrt{16 + 0 \cdot 5 \cos (2 θ)} x (45 °) = \cos 45 ° + \sqrt{16 + 0 \cdot 5 \cos 90 °} = \frac{1}{\sqrt{2}} + 4 = 2 \sqrt{2}$

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Short Answer

Step by step solution

Step 1. Given information .

.Finding xθ when θ=30° .

Step 3. Finding the value of xθ when θ=45° .

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Piston Engines In a certain piston engine, the distance x (in cm) from the center of the drive shaft to the head of the piston is given by the function.xθ=cosθ+16+0·5cos2θwhere θis the angle between the crank and the path of the piston head. See the figure. Find xwhen θ=30°and θ=45°.

Short Answer

Step by step solution

Step 1. Given information .

.Finding xθ when θ=30° .

Step 3. Finding the value of xθ when θ=45° .

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Statistics

Applied Mathematics

Logic and Functions

Calculus

Mechanics Maths

Study anywhere. Anytime. Across all devices.