The path of a projectile launched from a 26-ft-tall tower is modeled by the equation y = −16t2 + 64t + 26. What is the maximum height, in feet, reached by the projectile?

The maximum height of the projectile is 90 ft

Step-by-step explanation:

Here, we want to get the maximum height reached by the projectile

The answer here will be the y-coordinate value of the vertex form of the given equation

so firstly, we have to write the equation in the vertex form

We have this as;

y = -16t^2 + 64t + 26

That will be;

y = a(x-h)^2 + k

y = -16(x-2)^2 + 90

where the vertex of the equation is;

(-h,k)

K

in this case is 90 and thus, that is the maximum height of the projectile

The correct options are;

City A tends to be warmer than City B

City A has more variable temperatures than city B

Step-by-step explanation:

For City A

The number line is from 20 to 70

The whiskers range = 30 to 63

The box range = Interquartile range = 50 to 60

Therefore;

Q₁ = 50

Q₃ = 60

The median = Q₂ = 55

For City B

The number line is from 20 to 70

The whiskers range = 40 to 70

The box range = Interquartile range = 43 to 55

Therefore;

Q₁ = 43

Q₃ = 55

The median = Q₂ = 53

Therefore;

The range of a box plot for City A is 63 - 30 = 33

The range of a box plot for City B is 70 - 40 = 30

The interquartile range for City A = 60 - 10 = 10

The interquartile range for City B = 55 - 43 = 12

The minimum temperature for City A = 30

The maximum temperature for City A = 63

The minimum temperature for City B = 40

The maximum temperature for City B = 70

Comparing the averages of the temperatures of each quartile, we have;

For City A

Total average temperature, T₁

T₁ = 0.25*40*30 + 0.25*52.5*30+0.25*57.5*30+0.25*61.5*30 = 1586.25

For City B

Total average temperature, T₂

T₂ = 0.25*41.5*30 + 0.25*48*30+0.25*54*30+0.25*62.5*30 = 1545

Hence, T₁ > T₂

Therefore, City A tends to be warmer than City B

Also

City A has more variable temperatures than city B as the range is larger and   25% of City B are between 40 and 43 and another 25% is between the temperatures of 53 and 55 and also 75% of City B are between 40 and 55 while 75% of City A are between 60 and 30.