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grin007 [14]
3 years ago
12

A carpenter uses a hand saw to cut a piece of wood in half. The length of the saw blade is 40 cm, while the wood he is cutting i

s 8 cm across. Each time he extends the saw out with his arm, there is 5 cm of blade between the handle and the wood. When he pulls the saw toward his self with his arm, the saw handle is 25 centimetres from the wood. Each time he extends his arm out and pulls it back in, 1 second has passed. He starts with his arm extended out. Write an equation that models how far the tip of the saw is from the wood in terms of time.
Mathematics
1 answer:
Oxana [17]3 years ago
4 0

Answer:

The equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17

Step-by-step explanation:

The given parameters are;

Length of the saw blade = 40 cm

Thickness of the wood across = 8 cm

Length of blade between wood saw handle with hand extended = 5 cm

Length of the tip from the wood at the above time = 40 - 8 - 5 = 27 cm

Length of blade between wood saw handle with saw pulled inwards = 25 cm

Length of the tip from the wood at the above time = 40 - 8 - 25 = 7 cm

Time for one complete cycle = 1 second

We note that the basic equation for oscillatory motion is of the form;

x(t) = A·cos(ωt) + d

Where:

A = Amplitude of the motion = (27 - 7)/2 = 10 cm

ω = Angular frequency = 2·π/T

ωt = Motion's phase

t = Time of the motion

d = The middle location = 27 - 10 = 17 cm

T = The time to complete a cycle = 1 s

Therefore;

ω = 2·π

Given that he stars with his arm extended out, we have;

27 = 10×cos(2×π×0) + 17

Therefore, the equation that models how far from the tip of the saw is from the wood in terms of time is x(t) = 10×cos(2×π×t) + 17.

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Step-by-step explanation:

Sin A: 35/37

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Using acronym SohCahToa we know

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I hope this helps!

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The venticles of a right angle are a[0,4], b[3,-2] c[-3, -4] Find It's area.​
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Answer:

The area of this triangle is about 21.2132 square units.

Step-by-step explanation:

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Length of AB ===

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The points are 6 units apart vertically.

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The points are 3 units apart horizontally.

These lengths form a right triangle with the distance between the points as the hypotenuse, so you can use the pythagorean theorem to solve:

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AB is about 6.7082 units long.

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Same process as above.

Find the vertical distance:

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BC is about 6.3246 units long.

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