The function <em>position</em> of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.
<h3>What are the parametric equations for the motion of a particle?</h3>
By mechanical physics we know that the function <em>velocity</em> is the integral of function <em>acceleration</em> and the function <em>position</em> is the integral of function <em>velocity</em>. Hence, we need to integrate twice to obtain the function <em>position</em> of the particle:
Velocity
v(t) = ∫ t² dt - 7 ∫ t dt + 6 ∫ dt
v(t) = (1 / 3) · t³ - (7 / 2) · t² + 6 · t + C₁
Position
s(t) = (1 / 3) ∫ t³ dt - (7 / 2) ∫ t² dt + 6 ∫ t dt + C₁ ∫ dt
s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + C₁ · t + C₂
Now we find the values of the <em>integration</em> constants by solving the following system of <em>linear</em> equations:
0 = C₂
63 / 4 = C₁ + C₂
The solution of the system is C₁ = 63 / 4 and C₂ = 0. The function <em>position</em> of the particle is s(t) = (1 / 12) · t⁴ + (7 / 6) · t³ + 3 · t² + (63 / 4) · t.
To learn more on parametric equations: brainly.com/question/9056657
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Answer:
256
Step-by-step explanation:
1+2+4+8+16+32+64+128+256
7x-5y=21 when x=4 from the coordinate point of (4,y)
Next,
7x-5y=21
Substitute x with 4
7(4)-5y=21
28-5y=21
Add 5 to each side
28-5y+5y=21+5y
28=21+5y
Subtract 21 to each side
28-21=21+5y-21
7=5y
Divided 5 to each side
7/5=5y/5
y=7/5
Or
y=1 2/5
Check:
7x-5y=21
Substitute x with 4 and y with 7/5
7(4)-5(7/5)=21
28-7=21
21=21. As a result, (4,7/5) is your correct answer. Hope it help!
Answer:
Step-by-step explanation:
Given
The attached triangle
Required
Determine the value of x
x represents the height of the triangle.
And the area of a triangle is calculated as:
Where
The expression becomes
Divide through by 2