A shape has Symmetry if it can be folded about a line so that
its two parts match exactly. Indeed this is the definition of Symmetries of a Graph and the line is called as axis oF summetry of the graph.

asked 2021-02-26

The top string of a guitar has a fundamental frequency of 33O Hz when it is allowed to vibrate as a whole, along all its 64.0-cm length from the neck to the bridge. A fret is provided for limiting vibration to just the lower two thirds of the string, If the string is pressed down at this fret and plucked, what is the new fundamental frequency? The guitarist can play a "natural harmonic" by gently touching the string at the location of this fret and plucking the string at about one sixth of the way along its length from the bridge. What frequency will be heard then?

asked 2021-05-16

Give full and correct answer in how many ways can a set of two positive integers less than 100 be chosen?

asked 2021-05-22

Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .

a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.

b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.

c. Explain to Sheila what the graph of the area looks like.

d. Use the graph to approximate xx when the area of the shape is 20 square units.

a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.

b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.

c. Explain to Sheila what the graph of the area looks like.

d. Use the graph to approximate xx when the area of the shape is 20 square units.

asked 2021-03-31

A paraglider is flying horizontally at a constant speed.Assume that only two forces act on it in the vertical direction,its weight and a vertical lift force exerted on its wings by theair. The lift force has a magnitude of 1800 N.

(a) What is the magnitude and direction of the force that theparaglider exerts on the earth ?

(b)If the lift force should suddenly decrease to 1200 N, whatwould be the vertical acceleration of the glider ? For bothquestions, take the upward direction to be the + y direction.

(a) What is the magnitude and direction of the force that theparaglider exerts on the earth ?

(b)If the lift force should suddenly decrease to 1200 N, whatwould be the vertical acceleration of the glider ? For bothquestions, take the upward direction to be the + y direction.

asked 2021-02-10

Two light sources of identical strength are placed 8 m apart. An object is to be placed at a point P on a line ? parallel to the line joining the light sources and at a distance d meters from it (see the figure). We want to locate P on ? so that the intensity of illumination is minimized. We need to use the fact that the intensity of illumination for a single source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source.

asked 2021-06-10

Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it’s not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers-which is not fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.

asked 2020-10-28

a. In how many ways can the letters in the word CARLETON be arranged so that it contains either CA or AC as sub-words?

asked 2021-02-19

A uniform 8.40kg, spherical shell 50.0cm in diameter has foursmall 2.00kg masses attached to its outer surface and equallyspaced around it. This combination is spinning about an axisrunning through the center of the sphere and two of the smallmasses. What friction torque is needed to reduce its angular speedfrom 75.0rpm to 50.0rpm in 30.0s?

asked 2021-04-16

A rectangular block of copper has sides of length 10 cm, 20cm, and 40 cm. If the block is connected to a 6V sourceacross two of its opposite faces, what are (a) the maximum currentand (b) the minimum current that the block can carry?

asked 2021-04-13

As depicted in the applet, Albertine finds herself in a very odd contraption. She sits in a reclining chair, in front of a large, compressed spring. The spring is compressed 5.00 m from its equilibrium position, and a glass sits 19.8m from her outstretched foot.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.

a)Assuming that Albertine's mass is 60.0kg , what is \(\displaystyle\mu_{{k}}\), the coefficient of kinetic friction between the chair and the waxed floor? Use \(\displaystyle{g}={9.80}\frac{{m}}{{s}^{{2}}}\) for the magnitude of the acceleration due to gravity. Assume that the value of k found in Part A has three significant figures. Note that if you did not assume that k has three significant figures, it would be impossible to get three significant figures for \(\displaystyle\mu_{{k}}\), since the length scale along the bottom of the applet does not allow you to measure distances to that accuracy with different values of k.