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Geometry
Find the circumference and area of a circle with a diameter of 10 inches. Leave your answers in terms of pi.
C = 5π; A = 20π
C = 10π; A = 20π
C = 10π; A = 25π
C = 5π; A = 25π
Geometry
1.A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?
Geometry
(c) Show that for all values of θ the determinant
1 sin θ 1
− sin θ 1 sin θ
−1 − sin θ 1
lies between 2 and 4 inclusive. State one value of θ for which the determinant has the
value 2, and one for which it has the value 4.
1 sin θ 1
− sin θ 1 sin θ
−1 − sin θ 1
lies between 2 and 4 inclusive. State one value of θ for which the determinant has the
value 2, and one for which it has the value 4.
Geometry
) If z1 = 1 + 2i, find the set of values of z2 for which
(i) |z1 + z2| = |z1| + |z2| (ii) |z1 + z2| = |z1| − |z2|
(i) |z1 + z2| = |z1| + |z2| (ii) |z1 + z2| = |z1| − |z2|
Geometry
(b) Find the asymptotes of the hyperbola
x
2 − y
2 + 2x + y + 9 = 0.
x
2 − y
2 + 2x + y + 9 = 0.
Geometry
1. A statuary hall is elliptical in shape. It measures 42 feet wide and 96 feet long. If a person is standing at one focus, her whisper can be heard by a person standing at the other focus. How far apart are the two people?
2. A conic section is given by the equation 57x^2+14√3 xy+43y^2-576=0, identity and sketch the conics.
3. Find the area of the region inside both the rose curve r=sin〖(2θ)〗 and the circle r=cosθ. Choose the most appropriate graph and intervals to the best of your interest to solve this question
4. Sketch and identify the curve defined by the parametric equations
y=t+1, x=t^2-2t , -4≤t≤6
5. Identify and sketch the curve 9x^2-4y^2-72x+8y+176=0 using the appropriate graph. Find the equations of the asymptotes.
2. A conic section is given by the equation 57x^2+14√3 xy+43y^2-576=0, identity and sketch the conics.
3. Find the area of the region inside both the rose curve r=sin〖(2θ)〗 and the circle r=cosθ. Choose the most appropriate graph and intervals to the best of your interest to solve this question
4. Sketch and identify the curve defined by the parametric equations
y=t+1, x=t^2-2t , -4≤t≤6
5. Identify and sketch the curve 9x^2-4y^2-72x+8y+176=0 using the appropriate graph. Find the equations of the asymptotes.
Geometry
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?
Geometry
1. A door of a lecture hall is in a parabolic shape. The door is 56 inches across at the bottom of the door and parallel to the floor and 32 inches high. Sketch and find the equation describing the shape of the door. If you are 22 inches tall, how far must you stand from the edge of the door to keep from hitting your head?
Geometry
f a chord of the parabola y^2 = 4ax is a normal at one of its ends, show that its mid-point lies on the curve 2(x − 2a) = y^2/a + 8a^3/y^2
Geometry
Verify that the point P(acosθ,bsinθ) lies on the ellipse
x^2/ a^2+ y^2/ b^2= 1,
where a and b are the semi-major and semi-minor axes respectively of the ellipse . Find the gradient of the tangent to the curve at P and show that the equation of the normal at P is axsinθ−by cosθ = (a^2 −b^2)sinθ cosθ. If P is not on the axes and if the normal at P passes through the point B(0,b), Show that a^2 > 2b^2. If further, the tangent at P meets the y-axis at Q, show that
|BQ| =
a^2/ b^2
.
x^2/ a^2+ y^2/ b^2= 1,
where a and b are the semi-major and semi-minor axes respectively of the ellipse . Find the gradient of the tangent to the curve at P and show that the equation of the normal at P is axsinθ−by cosθ = (a^2 −b^2)sinθ cosθ. If P is not on the axes and if the normal at P passes through the point B(0,b), Show that a^2 > 2b^2. If further, the tangent at P meets the y-axis at Q, show that
|BQ| =
a^2/ b^2
.
