Pressure= F/A
Given, F=30 N
Area=20 m^2
Putting values in formula,
Pressure = 30/20
=3/2
=1.5 Pascals
The student's path traces out a rectangle and she ends up at the same spot, so her <u>displacement</u> is 0 m.
On the other hand, she travels a <u>total distance</u> equal to the perimeter of that rectangle,
4.0 m + 8.0 m + 4.0 m + 8.0 m = 24 m
To find the tangent plane to the surface f(x,y,z)=0 at a point (X,Y,Z) we use the following method:
<span>Calculate grad f = (f_x, f_y, f_z). The normal vector to the surface at the point (X,Y,Z) is grad f(X,Y,Z). The equation of a plane with normal vector n which passes through the point p is (r-p).n=0, where r=(x,y,z) is the position vector. So the equation of the tangent plane to the surface through the point (X,Y,Z) is ((x,y,z)-(X,Y,Z)).grad f(X,Y,Z)=0. </span>
<span>Now in your case we have f(x,y,z)=y-x^2-z^2, so grad f=(-2x,1,-2z), and the equation of the tangent plane at the point (X,Y,Z) is </span>
<span>((x,y,z)-(X,Y,Z)).(-2X,1,-2Z)=0, </span>
<span>that is </span>
<span>-2X(x-X)+1(y-Y)-2Z(z-Z)=0, </span>
<span>i.e. </span>
<span>-2Xx+y-2Zz = -2X^2+Y-2Z^2. (1) </span>
<span>Now compare this equation with the plane </span>
<span>x + 2y + 3z = 1. (2) </span>
<span>The two planes a_1x+b_1y+c_1z=d_1, a_2x+b_2y+c_2z=d_2 are parallel when (a_1,b_1,c_1) is a multiple of (a_2,b_2,c_2). So the two planes (1),(2) are parallel when (-2X,1,-2Z) is a multiple of (1,2,3), and we have </span>
<span>(-2X,1,-2Z)=1/2(1,2,3) </span>
<span>for X=-1/4 and Z=-3/4. On the paraboloid the corresponding y coordinate is Y=X^2+Z^2=1^4+9^4=5/2. </span>
<span>So the tangent plane to the given paraboloid at the point (-1/4,5/2,-3/4) is parallel to the given plane.</span>
To find the mass of benzene, we must first solve for the volume of benzene inside the cylindrical drum. To calculate the volume of the partially filled cylindrical drum, refer to the working formula below:
Volume = L {(R^2)cos-1[(R-H)/R)] - (R-H)(2RH-H^2)^0.5}
Where:
L = length of the drum = 2 meters
R = radius of the drum = 4 meters
H = height of the liquid = 0.85 meter
substituting the given to the formula, we get
Volume = 5.087 m3
To solve for the mass of benzene, we must multiply the volume with the density.
Density = 0.879 g/cm3 or 879 kg/m3
Mass of benzene = Volume x Density
Mass of benzene = 5.087 x 879 = 4,471.5 kg
<em>ANSWER: Mass of benzene = 4,471.5 kg</em>
Velocity differs from speed in that velocity indicates a particle's <span>direction of motion.
Therefore, your correct answer is: D</span><span>irection
Good luck with your studies, I hope this helps~!</span>
