sqrt(160) =
sqrt (16 * 10) =
sqrt(16) * sqrt(10) =
4 * sqrt(10) ≈ 12.65
3hr, 12minutes = 3.2 hrs
And Distance / Time = Rate....so
23miles / 3.2hours = 7.1875 mph = rate of Natalie's friend
Thus....it's impossible that Natalie ran 12mph slower than this !!!!!
Adam is taller.....
Adam's height - Mark's height =
[10 - 100tan (2.3)] - [10 - 100tan(2.6) ] =
≈ [5.96ft - 5.46 ft] =
≈ .50 ft ..... and Adam is ≈ 6 inches taller
.
We are looking for the intersection of
y = 45000 and
y = 15000 [ (1.074)^t + e^(.062t) ]
Here's a graph : https://www.desmos.com/calculator/zmejtzneea
The time is about 6 years....
(secΘtanΘ)/sinΘ =
(1 / cos Θ) * (sinΘ)/(cosΘ) * 1 /(sinΘ) =
(1/cos^2Θ) * ( sinΘ/sinΘ) =
sec^2Θ * 1 =
sec^2Θ
6.67e-9 =
6.67 x 10^-9 =
.00000000667
3x^2-15x+k
This is a parabola.... the x coordinate of the minimum value = -b/2a
= 15/ (2(3) ) = 15/6 =
5/2
So...we have
1 = 3(5/2)^2 - 15(5/2) + k simplify
1 = 3(25/4) - 75/2 + k
1 = 75/4 - 75/2 + k
1 = -75/4 + k
4/4 + 75/4 = k = 79/4
Here's a graph that confirms this : https://www.desmos.com/calculator/rzief47yod
15 * (5/3) = 75 / 3 = $25
Mexican food.....nothing is a close second.....!!!!!
(d) is correct
