What is the relationship among direct variation,lines,rates of change, and slope?

1 answer:

5 0

A direct variation is a proportional equation. Such as:

For every 3 cookies, linda gets 1 glass of milk. The equation for this is y=3x where y is the glasses and x is the cookies. this is a direct variation. It also has a linear line. Linear means straight. Rate of change and slope are the exact same thing. They are the value of 'm' in y=mx+b

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The isosceles triangle theorem states that if two sides of a triangle are congruent, then the angles those sides are congruent.

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7 0

3 years ago

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A 40-foot y’all monument sits on top of a hill. Eye is standing at a point on the hill and observes the top of the monument at a

aleksley [76]

Answer:

54.8 feet

Step-by-step explanation:

We assume that the distance of interest is the direct line distance from the observation point to the bottom of the monument, segment PH in the diagram below.

This can be found using the Law of Sines.

∠PMH is the complement of the angle of elevation to the top of the monument, so is 40°.

∠MPH is the difference in the angles of elevation, so is 28°.

The Law of Sines tells us the ratio of side lengths is the same as the ratio of the sines of the opposite angles, so ...

PH/MH = sin(∠PMH)/sin(∠MPH) = sin(40°)/sin(28°)

Multiplying by MH, we can find the length of PH:

PH = (40 ft)(sin(40°)/sin(28°)) ≈ 54.7669 ft

PH ≈ 54.8 ft . . . . the distance Pete must climb to reach the monument.