The 8 is in the tenths place it would look like 8/10 .8 its .08 for 8/100
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' + k
v = 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
Answer: y = -x + 5
Step-by-step explanation:
A slope-intercept equation is in the form y = <em>m</em>x + <em>b</em> where <em>m</em> is the slope and <em>b</em> is the <em>y</em>-intercept. Since we are given the slope, we will plug it in with the point they gave us, and solve for <em>b</em>.
y = <em>m</em>x + <em>b</em>
(1) = (-1)(4) + <em>b</em>
1 = -4 + b
5 = b
Lastly, we will write our equation by substituting <em>m</em> with -1 and <em>b</em> with 5.
y = <em>m</em>x + <em>b</em>
y = -1x + 5 or y = -x + 5
<em> Read more about </em><em>slope-intercept equations</em><em> here:</em>
<em>brainly.com/question/27497166</em>
Answer: The rate of change decreased.
Step-by-step explanation:
Using the diagonal dimension and the height we can solve for the diameter of the cylinder using the Pythagorean theorem.
x^2 + 9.5^2 = 19.3^2
x^2 + 90.25 = 372.49
x^2 = 372.49 - 90.25
x^2 = 282.24
x = √282.24
x = 16.8
Now we know the diamteer and height, we can calculate the volume using the formula V = pi * r^2 * h
r = 1/2 the diameter = 16.8/2 = 8.4
using 3.14 for pi
Volume = 3.14 * 8.4^2 * 9.5
V = 3.14 * 70.56 * 9.5
v = 3.14 * 670.32
v = 2104.8 cubic meters