Using tabular form to write an equation for a linear function
[link] relates the number of rats in a population to time, in weeks. Use the table to write a linear equation.
w , number of weeks
0
2
4
6
P(w) , number of rats
1000
1080
1160
1240
We can see from the table that the initial value for the number of rats is 1000, so
Rather than solving for
we can tell from looking at the table that the population increases by 80 for every 2 weeks that pass. This means that the rate of change is 80 rats per 2 weeks, which can be simplified to 40 rats per week.
If we did not notice the rate of change from the table we could still solve for the slope using any two points from the table. For example, using
and
Is the initial value always provided in a table of values like
[link] ?
No. Sometimes the initial value is provided in a table of values, but sometimes it is not. If you see an input of 0, then the initial value would be the corresponding output. If the initial value is not provided because there is no value of input on the table equal to 0, find the slope, substitute one coordinate pair and the slope into
and solve for
A new plant food was introduced to a young tree to test its effect on the height of the tree.
[link] shows the height of the tree, in feet,
months since the measurements began. Write a linear function,
where
is the number of months since the start of the experiment.
The ordered pairs given by a linear function represent points on a line.
Linear functions can be represented in words, function notation, tabular form, and graphical form. See
[link] .
The rate of change of a linear function is also known as the slope.
An equation in the slope-intercept form of a line includes the slope and the initial value of the function.
The initial value, or
y -intercept, is the output value when the input of a linear function is zero. It is the
y -value of the point at which the line crosses the
y -axis.
An increasing linear function results in a graph that slants upward from left to right and has a positive slope.
A decreasing linear function results in a graph that slants downward from left to right and has a negative slope.
A constant linear function results in a graph that is a horizontal line.
Analyzing the slope within the context of a problem indicates whether a linear function is increasing, decreasing, or constant. See
[link] .
The slope of a linear function can be calculated by dividing the difference between
y -values by the difference in corresponding
x -values of any two points on the line. See
[link] and
[link] .
The slope and initial value can be determined given a graph or any two points on the line.
One type of function notation is the slope-intercept form of an equation.
The point-slope form is useful for finding a linear equation when given the slope of a line and one point. See
[link] .
The point-slope form is also convenient for finding a linear equation when given two points through which a line passes. See
[link] .
The equation for a linear function can be written if the slope
and initial value
are known. See
[link] ,
[link] , and
[link] .
A linear function can be used to solve real-world problems. See
[link] and
[link] .
A linear function can be written from tabular form. See
[link] .
Questions & Answers
Three charges q_{1}=+3\mu C, q_{2}=+6\mu C and q_{3}=+8\mu C are located at (2,0)m (0,0)m and (0,3) coordinates respectively. Find the magnitude and direction acted upon q_{2} by the two other charges.Draw the correct graphical illustration of the problem above showing the direction of all forces.
To solve this problem, we need to first find the net force acting on charge q_{2}. The magnitude of the force exerted by q_{1} on q_{2} is given by F=\frac{kq_{1}q_{2}}{r^{2}} where k is the Coulomb constant, q_{1} and q_{2} are the charges of the particles, and r is the distance between them.
Muhammed
What is the direction and net electric force on q_{1}= 5µC located at (0,4)r due to charges q_{2}=7mu located at (0,0)m and q_{3}=3\mu C located at (4,0)m?
Capacitor is a separation of opposite charges using an insulator of very small dimension between them. Capacitor is used for allowing an AC (alternating current) to pass while a DC (direct current) is blocked.
Gautam
A motor travelling at 72km/m on sighting a stop sign applying the breaks such that under constant deaccelerate in the meters of 50 metres what is the magnitude of the accelerate
velocity can be 72 km/h in question. 72 km/h=20 m/s, v^2=2.a.x , 20^2=2.a.50, a=4 m/s^2.
Mehmet
A boat travels due east at a speed of 40meter per seconds across a river flowing due south at 30meter per seconds. what is the resultant speed of the boat
which has a higher temperature, 1cup of boiling water or 1teapot of boiling water which can transfer more heat 1cup of boiling water or 1 teapot of boiling water explain your . answer
I believe temperature being an intensive property does not change for any amount of boiling water whereas heat being an extensive property changes with amount/size of the system.
Someone
Scratch that
Someone
temperature for any amount of water to boil at ntp is 100⁰C (it is a state function and and intensive property) and it depends both will give same amount of heat because the surface available for heat transfer is greater in case of the kettle as well as the heat stored in it but if you talk.....
Someone
about the amount of heat stored in the system then in that case since the mass of water in the kettle is greater so more energy is required to raise the temperature b/c more molecules of water are present in the kettle
pratica A on solution of hydro chloric acid,B is a solution containing 0.5000 mole ofsodium chlorid per dm³,put A in the burret and titrate 20.00 or 25.00cm³ portion of B using melting orange as the indicator. record the deside of your burret tabulate the burret reading and calculate the average volume of acid used?
No. According to Isac Newtons law. this two bodies maybe you and the wall beside you.
Attracting depends on the mass och each body and distance between them.
Dlovan
Are you really asking if two bodies have to be charged to be influenced by Coulombs Law?
Specific heat capacity is a measure of the amount of energy required to raise the temperature of a substance by one degree Celsius (or Kelvin). It is measured in Joules per kilogram per degree Celsius (J/kg°C).
AI-Robot
specific heat capacity is the amount of energy needed to raise the temperature of a substance by one degree Celsius or kelvin
ROKEEB
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