Question

Circle A has a radius of 9 units. Point R lies 5 units away from A. A chord drawn through R is partitioned by the diameter of A passing through R into two segments, one of which has a length of 7 units. Is the length of the other segment longer or shorter than 7 units? Justify your answer.

Answer #1

7) A rope of length R has one end tied to a fixed point and the
other end tied to a pail full of water. The pail of water of mass M
is brought into vertical circular motion. The rope can sustain a
tension of To and no more before breaking. a) What is the minimum
speed of the pail at the top of the circle if no water is to spill
out? What is the tension in the rope...

Assume a planet (Earth for example) is an uniform sphere of
radius R and it has a narrow radial tunnel through its center.
Assume that we can position an object anywhere along this tunnel or
outside the planet (again Earth as an example). Let
Fr equal magnitude of the gravitational force
on the object that is traveling through the center of the planet.
When the object is found at the planet’s surface, how far from the
surface is there a...

A bead of mass m is made to slide around on a ring of radius R
standing on its side. The bead is attached to one end of a spring
with string constant k,
and the other end of the spring is attached to one point on the
ring, halfway up one side. There is gravity, g, and you may ignore
friction. For simplicity, we will assume that the equilibrium
length of the spring (when it has no tension) is...

A) A very long hollow cylinder has a 15 cm radius and has
positive charge spread evenly over its surface, amounting to a
linear charge density of 7 nC/m. Apply Gauss's Law to determine the
electric field at r =20 cm away from the center, in units
of N/C. As usual, do not include the unit in your answer.
B) A very long hollow cylinder has a 15 cm radius and has
positive charge spread evenly over its surface, amounting...

In this activity, you'll construct a segment bisector by
completing a geometric construction.
In order to construct a segment bisector, a line segment that
divides another line segment into two congruent segments, you will
want to use a straightedge and a
compass.
The first tool you need to know how to use is a straightedge, in
order to create a line. A straightedge can work in many ways. If
you're using actual paper and a pencil, a straightedge can be...

10. A spherical conductor of radius R = 1.5cm carries the charge of
45μ,
(a) What is the charge density (ρ) of the sphere?
(b) Calculate the electric field at a point r = 0.5cm from the
center of the sphere.
(c) What is the electric field on the surface of the sphere?
11. Two capacitors C1 and C2 are in series with a voltage V across
the series combination.
Show that the voltages V1 and V2 across C1 and...

1. Which describes the vector calculation of the Biot-Savart
law?
a. The length element in the direction of the
current is crossed into a vector directed from that element toward
the point of measurement.
b. The length element in the direction of the current
is dotted into a vector directed from that element toward the point
of measurement.
c. The magnetic field vector is crossed into a vector
directed from a current-length element toward the point of...

5. Suppose that the incenter I of ABC is on the triangle’s Euler
line. Show that the triangle is isosceles.
6. Suppose that three circles of equal radius pass through a
common point P, and denote by A, B, and C the three other points
where some two of these circles cross. Show that the unique circle
passing through A, B, and C has the same radius as the original
three circles.
7. Suppose A, B, and C are distinct...

You are the foreman of the Bar-S cattle ranch in Colorado. A
neighboring ranch has calves for sale, and you are going to buy
some calves to add to the Bar-S herd. How much should a healthy
calf weigh? Let x be the age of the calf (in weeks), and
let y be the weight of the calf (in kilograms).
x
1
5
8
16
26
36
y
44
53
71
100
150
200
Complete parts (a) through (e), given...

This question tests your understanding of the various form of
"breakevens". A proposed project has the following facts:
o Investment required today, t=0, $10M (cash outflow)
o Length of project, 8 years o Forecast unit sales per year,
600,000
o Sales price per unit, $80
o Variable cost, $36 per unit
o Fixed costs, $20M per year - (includes $5M of
depreciation)
o Taxes, 20%
o Net working capital which consists of, inventory +A/R -A/P,
requires an investment of $500K...

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