Answer:
Explanation:
<u>Linear Dependence
</u>
Some variables are known or assumed to have linear dependence which means the graph of the ordered pairs (x,V) is a straight line.
If we know two points of the line, we can come up with the exact equation and therefore make predictions for other values of x
The linear depreciation gives us these points (2,820000) and (5,430000)
The general equation of the line is
Where V is the machine value and x is the number of years after purchase. We need to find the values of m and b.
Replacing the first point
Replacing the second point
Subtracting them
Replacing in any of the equations, say, the first one
Solving for b
The formula for the machine value V is
Answer:
a. The temperature of the copper changed more than the temperature of the water.
Explanation:
Because we're only considering the isolated system cube-water, the heat of the system should be constant, that implies the heat the cube loses is equal the heat the water gains (because by zero law of thermodynamics heat (Q) flows from hot body to cold body until reach thermal equilibrium and T1>T2). So:
(1)
But Q is related with mass (m), specific heat (c) and changes in temperature (
)in the next way:
(2)
Using (2) on (1):
Because we have an equality and 0.385 < 4.186 then 
to conserve the equality
Answer:
α = (ω²)/8π
Explanation:
The angular acceleration(α) of the carousel can be determined by using rotational
kinematics:
ω² =ωo² + 2αθ
Let's make α the subject of this equation ;
ω² - ωo² = 2αθ
α = (ω² −ωo²)/2θ
Now, from the question, since initially at rest, thus, ωo = 0
Also,since 2 revolutions, thus, θ = 2 x 2π = 4π since one revolution is 2π
Plugging in the relevant values to get ;
α = (ω²)/2(4π)
α = (ω²)/8π
<u>Answer</u>
27.7
<u>Explanation</u>
The ball was hit at an angle of 30°, with the horizontal at a speed of 10 m/s. We have to find the horizontal component of speed.
cosx = adjacent/hypotenuse
cos 30 = adjacent / 10
adjacent = 10 cos30
= 8.66 m/s ⇒ This is the horizontal speed.
Now find the horizontal distance.
Distance = speed × time
= 8.66 × 3.2
= 27.71
Answer to the nearest tenth = 27.7
The gravitational force between two masses m₁ and m₂ is
where
G = 6.67408 x 10⁻¹¹ m³/(kg-s²), the gravitational constant
d = distance between the masses.
Given:
F = 1.5 x 10⁻¹⁰ N
m₁ = 0.50 kg
m₂ = 0.1 kg
Therefore
1.5 x 10⁻¹⁰ N = (6.67408 x 10⁻¹¹ m³/(kg-s²))*[(0.5*0.1)/(d m)²]
d² = [(6.67408x10⁻¹¹)*(0.5*0.1)]/1.5x10⁻¹⁰
= 0.0222
d = 0.1492 m = 149.2 mm
Answer: 149.2 mm
