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Convert (3–√,−1) into polar coordinates (r,θ) so that r≥0 and 0≤θ<2π
The sketch shows the graph of a function f, which is a straight line defined by y = mx + k such that the point V (-3,4) lies on the line, and the graph of a function g, which is a parabola with vertex R. The straight line and parabola intersect at P and Q. The points S and T lie on the parabola and straight line , respectively, between P and Q. The line ST is parallel to the y-axis.
1. Calculate m and k , and hence write down the equation for f.
2. Find the equation of the parabola.
3. Find the maximum length of ST . At what value of x will ST be at its longest?
4. What is the equation of the circle with center P and radius equal to the distance from P to the origin?
5. What is the equation of the hyperbola through the point V?
6. Use the graph to solve the inequality (f.g)(x)<0.
Identify the surface of the ρ = sinΦsinθ by converting them into equations in the Cartesian form. Show the complete solutions.
Identify the surface of the z2 = 4 + 4r2 by converting them into equations in the Cartesian form. Show the complete solutions.
A 9N force F1 and a 10N force F2 act in the same direction 2i+j-2k and 4i-3j respectively.
a) Find the resultant of the two forces
b)find the total work done if the forces make the object move 2m along the vector S=i+j+k
c)what is the maximum work done that can be achieve if the forces displace the object by 1m?
d)what is unit vector along which the object will move to achieve maximum work done?
f) find F1.F2
g) find F1*F2
A 9N force F1 and a 10N force F2 act in the same direction 2i+j-2k and 4i-3j respectively.
a) Find the resultant of the two forces
b)find the total work done if the forces make the object move 2m along the vector S=i+j+k
c)what is the maximum work done that can be achieve if the forces displace the object by 1m?
d)what is unit vector along which the object will move to achieve maximum work done?
f) find F1.F2
g) find F1*F2
Determine the coordinate of the center and the length of the radius.
X²+(y-2)²=10
Find the unit vector that is orthogonal to the vectors A=2i+j+k and B=-i+2j+k. Let the position of vectors of the vertices of triangle ∆ADC be OA=-2i+4j+k, OB=4i+j+k and OC=-7i+6k respectively. Use this information to answer
a)find the cosine of the angle between the side AB and AC
b)what is the the projection of the vector AC onto AB?
c)the area of the triangle ∆ABC can be calculated using?
d)find the area of the triangle ABC
A 9N force F1 and a 10N force F2 act in the same directions 2i+j-2k and 4i-3j respectively.
a) Find the resultant of the two forces
b)Find the total work done that the forces make the object move 2m along the vector s= i+j+k
c)find F1•F2
d)find F1 * F2
e)find the unit vector alone which the object will move to achieve maximum work done
f)what is the maximum work done that can be achieve if the tje forces displace the object by 1m
Given the two planes x - y + 2z = 0 and 3x + 2y - 6z + 4 = 0. Find a parametric equation for the intersection.
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#339914 on Dec 2023