I need help again, thanks.
1 answer:
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Answer:
"To the nearest year, it would be about 9 years"
Step-by-step explanation:
11c)
This is compound growth problem. It goes by the formula:
Where
F is the future amount
P is the present (initial) amount
r is the rate of growth, in decimal
t is the time in years
Given,
P = 20,000
r = 8% = 8/100 = 0.08
F = double of initial amount = 2 * 20,000 = 40,000
We need to find t:
To solve exponentials, we can take Natural Log (Ln) of both sides:
Using the rule shown below we can simplify and solve:
We can write:
To the nearest year, that would be about 9 years
Answer:
(x, y) = (1, 3)
Step-by-step explanation:
The "work" of solving by graphing is typing the equations into a graphing calculator and highlighting the point of intersection.
___
If you're graphing these by hand, there are a couple of strategies you can use. One is to make use of the intercepts of the line. For each of these, you need to rearrange the equation to a suitable form.
<u>3y -6 = 3x</u>
To put this into "intercept form", put the variable terms on one side of the equal sign and the constant on the other. Then divide by the constant and express the resulting variable coefficients as denominators.
3x -3y = -6
x/(-6/3) +y/(-6/-3) = 1
x/(-2) + y/2 = 1 . . . . . . The x-intercept is -2; the y-intercept is 2.
Plot the intercept points and draw a line through them.
<u>y +2x = 5</u>
The intercepts for this one are found by dividing by 5:
x/(5/2) + y/5 = 1 . . . . . . The x-intercept is 2.5; the y-intercept is 5.
The other strategy you can use for this one is to rearrange the equation to slope-intercept form and make use of those numbers.
y = -2x + 5
The y-intercept is 5 (as we already found above), and the slope is -2. That means the line drops 2 units for each unit it goes to the right. Apart from the y-intercept, other points on this line will be (1, 3), (2, 1), (3, -1).
<u>Solution</u>
When you plot these lines, you find they intersect at (1, 3). That is the solution to the system of equations, the values of x and y that satisfy both equations.
Recall your d = rt, distance = rate * time
one car is going at 55kph, at say hmmm "t" time
the second car zooms by at 75kph, an hour later, thus " t + 1 "
notice, overtaking the 1st car, simply means, the second car comes from behind approaches the first car from behind and "gets there", at that very second, both cars have travelled a distance, say "d"
if the first car travelled "d" kilometers
for the second car to "get there" has to had travelled "d" distance as well
solve for "t"
one car is going at 55kph, at say hmmm "t" time
the second car zooms by at 75kph, an hour later, thus " t + 1 "
notice, overtaking the 1st car, simply means, the second car comes from behind approaches the first car from behind and "gets there", at that very second, both cars have travelled a distance, say "d"
if the first car travelled "d" kilometers
for the second car to "get there" has to had travelled "d" distance as well
solve for "t"