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b. A wire five meters in length is cut into two pieces, out of which a...
8. A piece of wire of length L cm is cut into two pieces. One piece,...
8. A piece of wire of length L cm is cut into two pieces. One piece, of length x cm, is made into a circle; the rest is made into a square. Denote by A(z) the sum of the area of the circle and the area of the square. (a) (5 points) Find Im which makes A(z) MINIMUM, and find A(I'm). (b) (5 points) Find am which makes A(z) MAXIMUM, and find A(IM).
8. A piece of wire of length L cm is cut into two pieces. One piece,...
8. A piece of wire of length L cm is cut into two pieces. One piece, of length x cm, is made into a circle; the rest is made into a square. Denote by A(x) the sum of the area of the circle and the area of the square. (a) (5 points) Find I'm which makes A(z) MINIMUM, and find A(1m). (b) (5 points) Find xm which makes A(x) MAXIMUM, and find A(zm).
A wire that is 24 centimeters long is shown below. The wire is cut into two...
A wire that is
24
centimeters long is shown below.
The wire is cut into two pieces, and each piece is bent and formed
into the shape of a square.
Suppose that the side length (in centimeters) of one square
is
x
, as shown below.
24cm
x
(a) Find a function that gives
the total area
Ax
enclosed by the two squares (in square centimeters) in terms of
x
.
=Ax
(b) Find the side length
x
that minimizes...
A wire 3 meters long....Please read, different from other question I have posted today
A wire 3 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a frame for a stained glass ornament, while the other piece is bent intoa circle for a TV antenna. To reduce storage space, where should the wire be cut to minimize the total area of both figures? Give the length of wire used foreach:Where should the wire be cut to maximize the total area? Again, give the length of wire used...
A square loop made of copper wire is falling (moving downward due to gravity) out of...
A square loop made of copper wire is falling (moving downward
due to gravity) out of a region where there is a constant magnetic
field of magnitude Bext = 0.235 T. The magnetic field is
perpendicular to the plane of the loop, either into or out of the
page (it doesn't matter which direction).
The loop is falling with a constant
velocity because of the current induced in the loop
and the magnetic field.
What is the velocity of the...
7-19 DEO Finding Numbers In Exercises 5-10, find E u two positive numbers that satisfy the...
7-19
DEO Finding Numbers In Exercises 5-10, find E u two positive numbers that satisfy the given DEP requirements 5. The sum is S and the product is a maximum. 6. The product is 185 and the sum is a minimum. 7. The product is 147 and the sum of the first number plus three times the second number is a minimum. 8. The sum of the first number squared and the second number is 54 and the product is...
Consider a wire 1.00 meters in length with 0.100 mm diameter and resistivity, ? = 1.18 ...
Consider a wire 1.00 meters in length with 0.100 mm diameter and resistivity, ? = 1.18 x 10’(Ωm. Give all calculated answers to 3 significant figures and report voltages in millivolts. a) (10 pts) Calculate the resistance of the wire. ?)*+, = ________________________ b) (10 pts) The same wire is placed in an AC voltage divider circuit with a function generator. It follows, in series, a resistor, R=5.00 kΩ. An oscilloscope’s channel one shows a 9.10 peak-to-peak voltage sine wave...
A candy box is made from a piece of cardboard that measures 25 by 14 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box....
A candy box is made from a piece of cardboard that measures 25 by 14 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. Find the length of the side of the square that must be cut out if the volume of the box is to be maximized. What is the maximum volume? 14 in. A square with a side of length of 2.88 inches...
15 marks] B. A toroidal core with a mean diameter of 200 mm and a cross-sectional area of 800 mm has an air gap of length 1.1 mm cut in it Fringing and leakage of flux around the air gap may be negle...
15 marks] B. A toroidal core with a mean diameter of 200 mm and a cross-sectional area of 800 mm has an air gap of length 1.1 mm cut in it Fringing and leakage of flux around the air gap may be neglected (i) Determine the current required in a coil of 1100 turns to produce a flux density of 1 T The relative permeability , of the core material (iron) may be assumed to be 3000 for this level...
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b....
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b. f(-x) c. -f(x) d. f(x - 2) 2. Find the domain of each function below. Write your answer in interval notation. a. f(x) = x + 2 x2 + x - 6 b. 8(x) = (2x - 1 1 f(x + h) - f(x) 3. For the function f(x) = 2x2 – 3, find the difference quotient h 4. Use the graph of the...
8. A piece of wire of length L cm is cut into two pieces. One piece, of length x cm, is made into a circle; the rest is made into a square. Denote by A(z) the sum of the area of the circle and the area of the square. (a) (5 points) Find Im which makes A(z) MINIMUM, and find A(I'm). (b) (5 points) Find am which makes A(z) MAXIMUM, and find A(IM).
8. A piece of wire of length L cm is cut into two pieces. One piece, of length x cm, is made into a circle; the rest is made into a square. Denote by A(x) the sum of the area of the circle and the area of the square. (a) (5 points) Find I'm which makes A(z) MINIMUM, and find A(1m). (b) (5 points) Find xm which makes A(x) MAXIMUM, and find A(zm).
A wire that is
24
centimeters long is shown below.
The wire is cut into two pieces, and each piece is bent and formed
into the shape of a square.
Suppose that the side length (in centimeters) of one square
is
x
, as shown below.
24cm
x
(a) Find a function that gives
the total area
Ax
enclosed by the two squares (in square centimeters) in terms of
x
.
=Ax
(b) Find the side length
x
that minimizes...
A square loop made of copper wire is falling (moving downward
due to gravity) out of a region where there is a constant magnetic
field of magnitude Bext = 0.235 T. The magnetic field is
perpendicular to the plane of the loop, either into or out of the
page (it doesn't matter which direction).
The loop is falling with a constant
velocity because of the current induced in the loop
and the magnetic field.
What is the velocity of the...
7-19
DEO Finding Numbers In Exercises 5-10, find E u two positive numbers that satisfy the given DEP requirements 5. The sum is S and the product is a maximum. 6. The product is 185 and the sum is a minimum. 7. The product is 147 and the sum of the first number plus three times the second number is a minimum. 8. The sum of the first number squared and the second number is 54 and the product is...
A candy box is made from a piece of cardboard that measures 25 by 14 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. Find the length of the side of the square that must be cut out if the volume of the box is to be maximized. What is the maximum volume? 14 in. A square with a side of length of 2.88 inches...
15 marks] B. A toroidal core with a mean diameter of 200 mm and a cross-sectional area of 800 mm has an air gap of length 1.1 mm cut in it Fringing and leakage of flux around the air gap may be neglected (i) Determine the current required in a coil of 1100 turns to produce a flux density of 1 T The relative permeability , of the core material (iron) may be assumed to be 3000 for this level...
Name: 1. For the function f(x) = x2 – 1 find and simplify: a. f(-2) b. f(-x) c. -f(x) d. f(x - 2) 2. Find the domain of each function below. Write your answer in interval notation. a. f(x) = x + 2 x2 + x - 6 b. 8(x) = (2x - 1 1 f(x + h) - f(x) 3. For the function f(x) = 2x2 – 3, find the difference quotient h 4. Use the graph of the...
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