1. Find two consecutive even integers whose product is 168

Sides of a Square

2. The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 149 in2. Find the lengths of the sides of the two squares.

Uniform Strip

3. Cynthia Besch wants to buy a rug for a room that is 12 ft wide and 15 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 108 ft2 of carpeting. What dimensions should the rug have?

Rectangular piece of metal

4. A rectangular piece of metal is 10 in longer than it is wide. Squares with sides 2 in long are cut from the four corners, and the flaps are folded upward to form an open box. If the volume of the box is 832 in2, what were the original dimensions of the piece of metal?

Area/Perimeter

5. A rectangle has an area that is numerically twice its perimeter. If the length is twice the width, what are its dimensions?

Tree Pythagorean problem

6. At a point on the ground 60 ft from the base of a tree, the distance to the top of the tree is 4 ft more than 2 times the height of the tree. Find the height of the tree.

Vertical motion

7.An astronaut on the moon throws a baseball upward. The astronaut is 6 ft 6in tall, and the initial velocity of the ball is 30 ft per second. The height of s of the ball in feet is given by the equation

S = -2.7t2 + 30t + 6.5

Where t is the number of seconds after the ball was thrown

a. After how many seconds is the ball 12 ft above the moon’s surface?

b.) How many seconds will it take for the ball to return to the surface?

...bursaria and how
they differentiate from one another.
In comparing the two specimen’s size I found that the Paramecium caudatum was larger in size than the bursaria. Paramecia are unicellular organisms and are usually less than 0.25mm in length and covered with minute hair-like projections called cilia. They are characterized by their cilia which are used in locomotion and during feeding. Paramecia feed on bacteria.
Paramecia have 2 nuclei, 1 macronucleus and 1 micronucleus. Some have up to 80 micronuclei! The organism cannot survive without macronucleus and cannot reproduce without micronucleus.
I used the 4x on the Parmecium caudatum to measure 11 cells they varied in length from 145.44-199.98um, width wise was 36.36-72.72um. The bursaria was measured at 10x and ranged in length size of 64.8-108um and width wise 36-50.4um. After recording this data I then calculated the mean, mode, median, range and standard deviation. I used the website www.easycalculation.com/statistics to help with these calculations.
To perform this measurements of sizes you would insert a slide into your microscope adjust the focus until you have the specimen in view and using the eyepiece reticle would position each specimen to measure the length and the width of each one that is being counted. To calculate the mean you add up all of the data for each category and then divide the result of the number of specimens. For...

...Arc Length
The definition of radian measure
s = rθ
The unit circle
An angle of 1 radian
Proof of the theorem
IT IS CONVENTIONAL to let the letter s symbolize the length of an arc, which is called arc length. We say in geometry that an arc "subtends" an angle θ; literally, "stretches under."
Now the circumference of a circle is an arc length. And the ratio of the circumference to the diameter is the basis of radian measure. That ratio is the definition of π.
π | = | C
D | . |
Since D = 2r, then
π | = | C
2r |
or,
C
r | = | 2π | . |
That ratio -- 2π -- of the circumference of a circle to the radius, is called the radian measure of 1 revolution, which are four right angles at the center. The circumference subtends those four right angles.
Radian measure of θ = | s
r |
Thus the radian measure is based on ratios -- numbers -- that are actually found in the circle. The radian measure is a real number that names the ratio of a curved line to a straight, of an arc to the radius. For, the ratio of s to r does determine a unique central angle θ.
Theorem. | | In any circles the same ratio of arc length to radius |
| | determines a unique central angle that the arcs subtend. |
Proportionally,
if and only if
θ1 = θ2.
We will prove this theorem below.
Example 1. If s is 4 cm, and r is 5 cm, then the number | 4
5 | , i.e. | s
r | , is the |...

...The Lengths of Leadership
This Freshman Seminar displayed the power of leadership in all of its forms. There are many types of leadership skills and characteristics; however, they all are encompassed by a set of core values one must follow to be a leader. We explored what could be called the ten commandments of leadership during class discussion and how they applied to a series of movies including Apollo 13, Courage Under Fire, Norma Rae, and Cry Freedom. In each movie, every character showed a different type of leadership, rather it be negative or positive. In this seminar we also distinguished between transactional and transformational leadership. In this research paper I will examine each film by identifying the concepts of leadership found within them, if they demonstrate transactional or transformational leadership, and how they relate to my personal experiences.
Apollo 13 displayed how even under life threatening circumstances, it is essential to stay focused and work together. Ground control acted with strong leadership as well as the astronauts whose lives were at risk. Ground controls actions had the potential to destroy the mission, leaving the astronauts dead; however, they worked tirelessly to save their lives. They had to understand the consequences of each move they made, and how they could calculate them to get the astronauts home safely. They gained insight by researching and simulating all of the components they were working with. Ken...

...fighting across vast lengths of trenches stretching from the English Channel to the northern borders of Switzerland as each army tried to outflank the other. No one in 1914 would have predicted the stalemate that was to follow; it was a common belief back home in Britain that it would all be 'over by Christmas'. The Germans had similar views at the start of the war; they thought they could rapidly capture France before invading Russia, therefore preventing a war on two fronts. But the failure of the Schlieffen plan halted Germany in 1914 slowing down any advances. This critical failure was one of the main reasons the war was such a long drawn out affair. It was no longer each side trying to capture the other in a war movement but, trench warfare. Defence was now the key to winning the war and was far superior than the offensive. For example the Hindenburg line that the Germans were in possession of was around 70 miles in length and stretched from Arras to St Quentin. It boasted a huge defensive system with concrete forts and gun emplacements backed by deep trenches. It was similar at Verdun, which was a vital fortress town. In February 1916 Falkenhayn launched a huge attack against the French but the French under command of Pétain defended Verdun obstinately and the Germans eventually had to retreat. This is one of the many battles, which proves that defence is stronger than the offence. The trenches were hard to capture by advancing troops...

...University of Kerbala
college of dentistry
First Stage
Group "D"
Name: Ahmed Mohammed Ali
Name of exp: The focal length of convex mirror
Date of exp: 16/1/2015
Sub group: Ali Emad - mobeen jafer - mortadha abd al-aaly
Apparatus
Convex mirror and holder, small plane mirror and wooden clamp Convex lens and holder. two mounted pins, metre rule or optical bench.
Method:
Place a mounted pin at a distance from the convex lens greater than the focallength so that a real image of the pin is produced. Locate this image by means of the second pin. Place the convex mirror between this second pin and the lens and adjust its position until the light reflected from the mirror passes back through the lens and forms an image coincident with the object pin. This occurs when the rays of light leaving the lens strike the mir normally and are reflected back along their original paths. Note. It is often a good plan to invert this procedure and do the reflection part of the experiment first. There is then no danger of wasting time on an object position which produces an image whose distance from the lens is less than the radius of curvature of the mirror.
Theory:
O is the object pin and I the realimage formed when the mirror is not present.When te mirror is interposed so that the rays strike it normally and are reflected back through the lens to form an image coincident with O, the centre of curvature of the mirror coincides with I.
Hence PI=...

...Lab 4: Skeletal Muscle Function
Exercise 5: The Length-Tension Relationship
Materials and Methods
In this experiment I used a frog anesthetized with ms222. The frog’s skin is cut and removed from both the legs, the Achilles tendon is cut and the tendon and calf muscle are removed from the lower legs. The femur muscle is also cut. Attached to the legs are femur clamps which are connected to the transducer arm, stimulation electrodes are then positioned against the muscle. I plugged the output of the transducer to the data acquisition by putting the black plug to recording input 1. Two metal stimulating electrodes are then pushed against the excised muscle. I then connected the blue plug to the negative stimulator output on the data acquisition unit and then connected the second electrode by plugging the red plug to the positive stimulator output on the unit. I then set my voltage to 2 by pressing the arrows on the control panel then set the length of the muscle by adjusting the arm on the stand frog is attached too. After achieving the right height I then shocked the frog which displayed a line on the data screen. I measured the amount of tension produced by the muscle by measuring the amplitude of the upward deflection on the line tracing. I recorded the peak of the deflection and the amplitude response which you will later see on graph 1.
Questions
1. In the sarcomere of the skeletal muscle, actin is found in? Actin is found in the...

...of the cliff. The length of his fishing line, l, which is measured from the tip of his fishing rod to the place his line enters the water, and the angle between his line and the water, θ, are changing as the river carries his line downstream. The horizontal distance, r, from the edge of the cliff to the place his line enters the water increases at a rate of 1ft/2sec as the river carries it downstream.
1. Draw a diagram of the situation, using l, r and θ.
2. Complete the table below where A represents the area of the triangle formed by the height of the line, the distance from the base of the cliff, and the length of the line.
t, in sec
r, in ft
A, in ft2
4
2
15
16
8
60
20
10
75
3. What is an equation for r(t)?
r = .5t
4. What is an equation for A(t)?
A = 7.5(.5t)
5. Sketch the graphs of r(t) and A(t) on the same axes. Indicate which is which.
6. In any equation y = mx + b, the constant m is used to represent the slope. In a linear equation, the slope is equivalent to Δy/Δx (the average rate of change of y with respect to x) and is equivalent to dy/dx (the instantaneous rate of change of y with respect to x). What is the rate of change in the distance from the edge of the cliff to the place the fisherman’s line enters the water with respect to time? Use the equation for r(t) you found in #3 and include correct units.
m = ½ ft/sec Δr/Δt = 2-8...

...00
$1,800.00+$600.00=$2,400.00
John put 2400 in each investment.
4. The length of a football field is 180 feet more than its width. If the perimeter of the field is 1,060 feet, find the length of the field
x= length y= width
x=y+180
2x+2y=1060
x-y=180
2x+2y=1060
2(y+180)+2y=1060
2y+360+2y=1060
4y+360-360=1060-360
y=175
x=y+180
x=175+180
x=355
The length of the field is 355ft, and the width of the field is 175.
5. At a school choir concert, 256 students are standing in rows. If the number of students in each row is equal to the total number of rows, find the number of students in each row.
6.
16*16=256
The answer would be 16
7. If 6 times a number is decreased by 8, the result is 40. What is the number?
8. 6x-8=40
6x=40
x=8
The answer would be 8
9. Merry had $20,000 to invest. She invested part of this money in bonds paying 10% annual simple interest and the rest of the money in a savings account giving 5% annual interest. At the end of the year, she received $1,800 as extra income. How much money did merry place in the savings account?
0.1x+0.05(20.000-x)=1800
0.1x+1000-0.05x=1800
0.05x=1800-1000=800
x=800/0.05=16000
16000 at 10%
4000 at 5%
10. The length of a rectangular field is 50 feet less than its width. If the perimeter of the field is 840 feet, find the length of the field
2x+2y=840
2(y-50)+2y=840
2y-100+2y=840
4y=940
y=235
x=235-50
x=185...

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