The angle of elevation from the bottom of a scenic gondola ride to the top of a mountain is 31 degrees. if the vertical distance from the bottom to the top of the mountain is 902 feet and the gondola moves at a speed of 155 feet per minute, how long does the ride last? round to the nearest minute

The ride lasts 10 minutes.

Step-by-step explanation:

The triangle that is formed is attached.

In order to find out how long the ride lasts, we need to figure out the horizontal distance

From trigonometry we have:

Therefore

Now the amount of time the gondola ride lasts is equal to the distance divided by the speed of the gondola:

To the nearest minute this is 10 minutes.

answer: the price of one pound cabbage = $ 0.8

the point (10,8) represents that the cost of 10 pounds cabbage is $ 8

step-by-step explanation:

since, here is a proportional relation between the number of pounds of cabbage (x) and the price in dollars (y).

therefore, we can write,

⇒ y = k x

where k is the constant of proportionality.

now, point (5,4) is in the line.

thus, it will satisfies the above equation of line.

⇒ 4 = 5 k

⇒ k = 0.8

thus, the equation of the line is,

y = 0.8 x

a) for x = 1,

y = 0.8

therefore, the cost of one pound of cabbage is 0.8 dollars.

b) in the below graph (10,8) represents that the cost of 10 pounds of cabbage is 8 dollars.

c.

step-by-step explanation:

substitution for (0,1)

y=x^2+4x+1

1=0^2+4(x)0+1

1=0+4(x)0+1

1=4(x)0+1

1=0+1

1=1

substitution for (-3,-2)

y=x+1

-2=-3+1

-2=-2