The distance covered by the hiker if he traveled a horizontal distance of 120 ft at and angle of 6° will be given by:
cos θ=adjacent/hypotenuse
let the hypotenuse be h, adjacent =120 ft, θ=6°, thus plugging in the values we shall have:
cos 6=120/h
h=120/cos 6
h=120.661 ft
Answer: 120.661 ft
( a ) The system of equations:
2 r + b = 8.403 r + b = 9.35( b ) Graph is in the attachment.
( c ) Each item costs:
b = $6.50, r = $0.95We can prove it: 2 * 0.95 + 6.50 = 8.40
3* 0.95 + 6.50 = 9.35
Answer:
the rate of change in volume is dV/dt = 4π mm³/s = 12.56 mm³/s
Step-by-step explanation:
since the volume V of a cylinder is related with the height H and the radius R through:
V = πR²*H
then the change in time is given by the derivative with respect to time t
dV/dt = (∂V/∂R)*(dR/dt) + (∂V/∂H)*(dH/dt)
the change in volume with radius at constant height is
(∂V/∂R) = 2*πR*H
the change in volume with height at constant radius is
(∂V/∂H) = πR²
then
dV/dt = 2π*R*H *(dR/dt) + πR²*(dH/dt)
replacing values
dV/dt = 2π* 2 mm * 20 mm * (-0.1 mm/s) + π (2 mm) ²* 3 mm/s = 4π mm³/s
dV/dt = 4π mm³/s = 12.56 mm³/s
Answer:
Kindly check explanation
Step-by-step explanation:
Given that :
Total amount to spend = $55
Amount of food and drinks purchased = $14.25
Amount put on gaming card = $(55 - 14.25) = $40.75
Cost per game = $1.25
Number of games (g) he can play
Number of games g:
Amount put on gaming card / cost per game
= $40.75 / $1.25
= 32.6 games
g ≤ 32
We would have two circles of 5cm diameter each, and a rectangle of the length pi*diameter and 2cm, so lets add them:
total = 2circles + rectangle
total = 2(2*pi*(5/2)^2) + pi*diameter*heigth
= 4*pi*(2.5)^2 + pi*5*2
= 109.9
that is the surface area of a bar soap 109.9 cm^2
