CPhill

There are 1760 yards in a mile...so

1760 yards / (176 yards/lap) =10 laps

OK, Angelica

Here's the first one

N = 24C      where N is the number of bottles of water and C is the number of cases

And here's the second

C = $10(N-1) + $60     where N is the number of minutes and C is the cost

I'll let you finish the tables !!!

We can use

H_max = (V₀)² *[sin(Θ)]² / [2 *(9.8m/s²)]

Where H_max is the max height, V₀ is the original velocity and Θ is the launch angle

So we have

8m = (V₀)² * [sin(10°)]²/ [19.6m/s²]

And rearranging, we have

8m * [19.6m/s²]/[sin(10°)]² = (V₀)²      take the (positive) square root of both sides to solve for V₀

 V₀  =  about 72.1 m/s

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Notice that the angle that the platform makes with its support post is just 90 degrees. But 79 of those degrees have already been accounted for, so the remaining number of degrees in the apex angle of the triangle formed by the post, the distance the observer is from the post and the distance the observer is from the plattform = 90 - 79 = 11°

So we have a right triangle with a known angle - 11° - an adjacent side to that angle = 10m, and we're looking for the hypoteneuse (the distance the observer is from the bottom of the platform).

And the trig function that relates these is the cosine....so we have

cos(11°) = 10/h    where h = the hypoteneuse = the distance from the observer to the bottom of the platform

Rearanging gives us

h = 10/cos(11°) = about 10.187m ......rounded to the nearest meter, it would be 10m - but I don't really like that answer much, since the hypoteneuse is actually longer than any other side of the triangle!!!

So, we know the hypoteneuse of a right triangle (72ft. 10 in) and we know an angle, 57°, and we're trying to find the adjacent side to that angle (the distance from the surveyor to the building). The trig function that relates these is the cosine.

So we have (conveting 72ft 10in into decimal form)

cos(57°) = adjacent / (72.833 ft)    multiply both sides by 72.833 ft.

(72.833 ft.) * cos(57°) = adjacent side = about 39.67 ft. = 40 ft.

And that's the (rounded) distance from the surveyor to the building......

135/10 = 13 + 5/10  = 13 + 1/2

It appears that, from the illustration, that the bird is above the nest...if I'm interpreting the picture correctly. The angle of elevation to the nest is 62°, but the angle of elevation to the bird itself is 67°.

So we have

Height above ground = 15*tan(67°) = about 35.34 ft.

(2/5) + 4/(10x + 5) = 7/(2x + 1)  

Note that 

4/(10x + 5)   = 4/[5(2x + 1)] = (4/5)/(2x + 1)

So we have

(2/5) + (4/5)/(2x + 1) = 7(2x + 1)     mutiply through by 5 to get rid of the fractions

2 + 4/(2x + 1) = 35/(2x + 1)              subtract 4/(2x + 1) from both sides

2 = 35/(2x + 1) - 4/(2x + 1)               simplify

2 = 31/(2x + 1)                                  cross-multiply

2(2x + 1) = 31                                    simplify

4x + 2  = 31                                       subtract 2 from both sides

4x = 29                                              divide by 4 on both sides

x = 29/4

50*6/10-6+36=

Using the order of operations, we have

300/10 - 6 + 36 =

30 - 6  + 36 =

24 + 36 =

60