Rip van Winkle fell asleep for a very long time. When he fell asleep, his beard was 888 millimeters long, and each passing week
it grew 222 additional millimeters.
Graph the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks).
Please help me to understand how to graph this problem.
Graph the length of Rip van Winkle's beard (in millimeters) as a function of time (in weeks).
Please help me to understand how to graph this problem.
2 answers:
Let x = time in weeks.
Let y = length of Rip van Winkle's beard, measured in mm
At the beginning, his beard was 888 mm long, thus
when x = 0, y = 888.
Each week, y increases by 222 mm.
Hence
y = 222x + 888
This represents a linear equation with
slope = 222,
y-intercept = 888
At x = 1, y = 222 + 888 = 1110 mm
To plot the straight line, select two points:
(0, 888) from the y-intercept
(1, 1110)
The straight line graph is illustrated below. The two points are depicted on the line.
Let y = length of Rip van Winkle's beard, measured in mm
At the beginning, his beard was 888 mm long, thus
when x = 0, y = 888.
Each week, y increases by 222 mm.
Hence
y = 222x + 888
This represents a linear equation with
slope = 222,
y-intercept = 888
At x = 1, y = 222 + 888 = 1110 mm
To plot the straight line, select two points:
(0, 888) from the y-intercept
(1, 1110)
The straight line graph is illustrated below. The two points are depicted on the line.
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Answer:
The ratio corresponds to the tangent of ∠I.
Step-by-step explanation:
Let’s revisit the trigonometric ratios:
- sin Ф =
- cos Ф =
- tan Ф =
For triangle HIJ
∵ m∠J = 90°
- The hypotenuse is the side opposite the right angle.
So, HI is the hypotenuse.
∵ HJ = 3 units
∵ IH = 5 units
- We’ll apply the Pythagorean Theorem to solve for HJ.
∵ (HJ)² + (IJ)² = (IH)²
∴ 3² + (IJ)² = 5²
∴ 9 + (IJ)² = 25
- Subtract 9 from both sides.
∴ (IJ)² = 16
- Taking the square root on both sides gives:
∴ IJ = 4 units
To determine the tangent of ∠I, identify the sides that are opposite and adjacent to it.
∵ HJ is opposite to ∠I
∵ IJ is adjacent to ∠I
- Utilizing the rule of tan above:
∴ tan(∠I) =
∴ tan(∠I) =
The ratio indicates the tangent of ∠I.