Answer:
Step-by-step explanation:
The population of a city is 250,000 and the annual growth rate is 2.2%
General equation for exponential growth is
Where y is final population and P is the initial population
'r' is the rate of growth and x is the number of years
p = 25000 and r= 2.2%= 0.022. Replace all the values in the general equaiton
Answer:
Step-by-step explanation:
From what I understand about parabolic motion in the English system, the equation for flight is
where is the initial upwards velocity and
is the initial height from which the object was launched. Filling in that equation with those values gives you
. That's a.
In order to determine how long it will take the ball (or rocket...the problem is mixing up the 2) to reach its max height you need to put the equation into vertex form, since the vertex of a parabola is the absolute max (or min depending upon the parabola) of the function. The absolute max is the heighest that the ball will go. Completing the square is the way to solve this. Begin by setting the equation equal to 0, the moving the 3 over by subtraction:
Now factor out the -16 since the leading coefficient HAS to be a positive 1:
Now take half the linear term (half of 4t which is 2), square it (4) and add it into the parenthesis:
BUT since you added in a 4*-16 on the left you have to add it in on the right:
which simplifies to
Now bring the 67 over by addition and you have your vertex:
.
The vertex is (2, 67). The 2 stands for time, so 2 seconds, and the 67 stands for feet, so at 2 seconds the max height is 67 feet.
How long it will be in the air is found by factoring to find the zeros. These can be found by plugging the quadratic into the quadratic formula and getting that the zeros are -0.046 and 4.046
So the quadratic starts a tiny tiny bit to the left of the origin, but for all intents and purposes we can say it starts at the origin (x = 0) and ends at
x = 4.05 seconds. Which makes sense if you know anything about parabolic motion and physics. The vertex indicates not only the time and the max height at that time, it also is indicative of the halfway mark. Meaning that if it takes 2 seconds to reach its max height, it will hit the ground at 4 seconds. And 4.05 is close enought to 4 (but since you were told to round to the nearest hundredth, that .05 matters). Sorry it's so long, but it's not a question that can be answered with just a few sentences.
Answer:
3
Step-by-step explanation:
Given a line with points; (2, 5) (3, 8).
1. Find the slope of the given line
The formula for finding the slope is:
Substitute in the values;
simplify;
= 3
2. Find the slope of the parallel line;
Remember, when two lines are parallel, they run alongside each other, of infinitely long, but they never touch. Hence two parallel lines have the same slope. Therefore, the slope of a line that is parallel to the given one will also have the same slope as the given one, which is 3.
Step-by-step explanation:
The two equation will intersect each other at the point which will be the solution of the given two equations , and the given equations are ,
On subtracting the given equations we have,
Put this value in any equation , we have ,
Hence the lines will Intersect at ,