Answer:
a. v(t)= -6.78
+ 16.33 b. 16.33 m/s
Step-by-step explanation:
The differential equation for the motion is given by mv' = mg - γv. We re-write as mv' + γv = mg ⇒ v' + γv/m = g. ⇒ v' + kv = g. where k = γ/m.Since this is a linear first order differential equation, We find the integrating factor μ(t)=
=
. We now multiply both sides of the equation by the integrating factor.
μv' + μkv = μg ⇒ v' + kv = g ⇒ [v]' = g. Integrating, we have
∫ [v]' = ∫g
v = 
+ c
v(t)= + c
.
From our initial conditions, v(0) = 9.55 m/s, t = 0 , g = 9.8 m/s², γ = 9 kg/s , m = 15 kg. k = y/m. Substituting these values, we have
9.55 = 9.8 × 15/9 + c
= 16.33 + c
c = 9.55 -16.33 = -6.78.
So, v(t)= 16.33 - 6.78. m/s = - 6.78 + 16.33 m/s
b. Velocity of object at time t = 0.5
At t = 0.5, v = - 6.78
+ 16.33 m/s = 16.328 m/s ≅ 16.33 m/s
The rate of change is $55 per hour. The means that the hourly rate of the designer is $55 per hour
<h3>Linear equation</h3>
A linear equation is in the form:
y = mx + b
where y, x are variables, m is the slope of the line and m is the y intercept.
Let y represent the total cost of hiring for x hours. Hence:
- Using the points (0, 125) and (15, 950)
The rate of change is $55 per hour. The means that the hourly rate of the designer is $55 per hour
Find out more on linear equation at: brainly.com/question/14323743
I am not 100% sure but I am pretty sure the answer is (3,-1,4)
Answer:
80
Step-by-step explanation:
10 limits it to 50, 60, 70, 80, and 90
2 eliminates none since 50=25, 60=30, 70=35, 80=40 and 90=45
8 divided by each number only leaves one option of 80. (80/8= 10) (80/10=8) (80/2=40)
Answer:
Step-by-step explanation:
Given that,
Radius of the cone, r = 5 units
Height of the cone, h = 6 units
We need to find the volume of the cone. The formula for the volume of the cone is given by :
Substitute all the values,
So, the volume of the cone is 
.
