Answer:
h ’= 12,768 cm
Explanation:
For this exercise let's use the constructor equation
1 / f = 1 / p + 1 / q
where f is the focal length, p the distance to the object and q the distance to the image
the magnification equation is
m = h '/ h = -q / p
let's find the distance to the object
1 / p = 1 / f- 1 / q
1 / p = 1/20 - 1 / (- 37.5)
1 / p = 0.076666
p = 13.04 cm
now let's use the magnification equation
h ’= - q / p h
let's calculate
h ’= - (-37.5) / 13.04 4.44
h ’= 12,768 cm
The moon has phases because as it orbits earth, which causes the portion we see during each different phase to be shown.
Answer:
0.184 m/s
Explanation:
Momentum is conserved. If the velocity of the 0.24 kg mass is positive, then ...
m1v1+m2v2 = m3v3
(0.24 kg)(0.60 m/s) +(0.26 kg)(-0.20 m/s) = (0.24 +0.26 kg)(v)
v = (0.144 -0.052 kg·m/s)/(0.50 kg) = 0.184 m/s
The speed of the combined masses is 0.184 m/s.
_____
<em>Additional comment</em>
The positive sign indicates the combined masses are moving in the direction of the original 0.24 kg mass.
Explanation:
Given:
x₀ = 0 m
v₀ = 4.2 m/s
t = 11.6 s
a = 2.3 m/s²
Find: x
x = x₀ + v₀ t + ½ at²
x = 0 m + (4.2 m/s) (11.6 s) + ½ (2.3 m/s²) (11.6 s)²
x ≈ 203 m
Round as needed.
Let us say that x is the cut that we will make on the
sides to make a box, therefore the new dimensions are:
l = 15 – 2x
w = 8 – 2x
It is 2x since we cut on two sides.
We know that volume is:
V = l w x
V = (15 – 2x) (8 – 2x) x
V = 120x – 30x^2 – 16x^2 + 4x^3
V = 120x – 46x^2 + 4x^3
Taking the 1st derivative:
dV/dx = 120 – 92x + 12x^2
Set dV/dx = 0 to get maxima:
120 – 92x + 12x^2 = 0
Divide by 12:
x^2 – (92/12)x + 10 = 0
(x – (92/24))^2 = -10 + (92/24)^2
x - 92/24 = ±2.17
x = 1.66, 6
We cannot have x = 6 because that will make our w
negative, so:
x = 1.66 inches
So the largest volume is:
V = 120x – 46x^2 + 4x^3
V = 120(1.66) – 46(1.66)^2 + 4(1.66)^3
V = 90.74 cubic inches