Answer with Step-by-step explanation:
Let a mass weighing 16 pounds stretches a spring feet.
Mass=
Mass=
Mass,m= Slug
By hook's law
A damping force is numerically equal to 1/2 the instantaneous velocity
Equation of motion :
Using this equation
Auxillary equation
Complementary function
To find the particular solution using undetermined coefficient method
This solution satisfied the equation therefore, substitute the values in the differential equation
Comparing on both sides
Adding both equation then, we get
Substitute the value of B in any equation
Particular solution,
Now, the general solution
From initial condition
x(0)=2 ft
x'(0)=0
Substitute the values t=0 and x(0)=2
Substitute x'(0)=0
Substitute the values then we get
We have the equation 1/2x + 200 =1200 so we know that we have 200 already as one of the numbers so 1/2 is half of x + 200 equals 1200 since we have 200 we know that 1/2 of x is going to be 1000 because 1000+200=1200 meaning x is 2000. So your answer would be x=2000 or 1/2 2000 + 200=1200
42% = 210
1% = 210 ÷ 42 = 5
100% = 5 x 100 = 500
500 people were surveyed.
Neither P, nor A are on the sketch
I guess P is the upper right corner of the rectangle
and A=(0,1)
P belongs to the line going through (1,0) and B(0,y)
<span>but we don't know the y-coordinate of B </span>
<span>the triangle is right and isosceles, so pythagoras a²+a²=2² ... 2a²=4 ... a²=2 ... a=sqrt2 </span>
now look at the right triangle BOA
<span>his hypotenuse is AB=sqrt2 and the <span>the kathete</span> OA is 1 </span>
so y²+1²=(sqrt2)² ... y²+1=2 ... y²=1.. y=1
so the coordinates of B are (0,1)
the line going through (1,0) and (0,1) is L(x)=-x+1
P belongs to this line, so the coordinates of P are P(x,-x+1) (0<x<1)
b) so if that's P, the height of the rectangle is -x+1 and the width=2x
<span>so its area A(x)=2x*(-x+1)= -2x²+2x
I hope my answer has come to your help. Thank you for posting your question here in Brainly.
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