Step-by-step explanation:
(a) If g is the number of gallons left in the tank, and t is the time in hours since 8AM:
g = 8 gal − (1 gal / 24 mi) (60 mi / 1 hr) (t hr)
g = 8 − 2.5t
(b) If d is the distance traveled:
d = 60 mi/hr × t hr
d = 60t
(c) When George runs out of gas, g = 0.
0 = 8 − 2.5t
t = 3.2
The distance he travels is:
d = 60(3.2)
d = 192
George travels 192 miles.
3.2 hours after 8AM, the time is 11:12AM.
Answer:
188976
Step-by-step explanation:
2032 x 93 = 188976
I assume you're just solving for x. Factorize the left side as
3 sin²(x) - 3 sin⁴(x) = 3 sin²(x) (1 - sin²(x)) = 0
Recall that
sin²(x) + cos²(x) = 1
so that the equation further reduces to
3 sin²(x) cos²(x) = 0
Also recall the double angle identity,
sin(2x) = 2 sin(x) cos(x)
which lets us rewrite the equation as
3/2² (2 sin(x) cos(x))² = 3/4 sin²(2x) = 0
Solve for x :
3/4 sin²(2x) = 0
sin²(2x) = 0
sin(2x) = 0
2x = arcsin(0) + 2nπ or 2x = π - arcsin(0) + 2nπ
(where n is any integer)
2x = 2nπ or 2x = (2n + 1) π
x = nπ or x = (2n + 1)/2 π
Notice that this means the solution set is
{…, -2π, -3π/2, -π, -π/2, 0, π/2, π, 3π/2, 3π, …}
so we can condense the solution further to
x = nπ/2
with any integer n.
Answer:
Step-by-step explanation:
3 less then the quotient of 6 and a number, increased by 9
((6/n) - 3) + 9.....when n = 3
((6/3) - 3) + 9
2 - 3 + 9
-1 + 9
8 <====
Answer:
about 2.81 km/h
Step-by-step explanation:
It can be useful to draw a diagram.
The lines pointing to due north from points B and P are parallel, so the angle BCP and the bearing of point C from P are the same, 30°. The angle BPC will be the difference of bearings of B and C at P, so is 47-30=17°. This is enough information to solve the triangle using the Law of Sines:
PB/sin(C) = CB/sin(P)
CB = PB·sin(P)/sin(C) = (1200 m)·sin(17°)/sin(30°) ≈ 701.7 m
The speed of the boat is then ...
x = distance/time = (0.7017 km)/(1/4 h) = 2.8068 km/h
