A cyclist going downhill is accelerating at 1.2 m/s2. If the final velocity of the cyclist is 16 m/s after 10 seconds, what is t
2 answers:
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<h2>Steps:</h2>
So for this, we will be doing a system of equations. Using the info from our question, our two equations are:
(let x = greater number and y = lesser number)
Now, for this I will be using the substitution method. Since we know that x = 4y - 1, substitute that into the second equation:
From here we can solve for y. Firstly, combine like terms:
Next, subtract 4y on both sides of the equation:
Next, multiply both sides by -1:
Now that we know the value of y, substitute it into either equation to solve for x:
In short, <u>5 is the lesser number and 19 is the greater number.</u>
Answer:
The answer that gives the best estimate is (1,1)
Step-by-step explanation:
i) As can be seen on of the lines intercepts the y axis at (0,-1). So the y
intercept or = -1. Therefore the equation for this line can be written as
y = x +
⇒ y =
x - 1 . It can also be seen from this graph that the
line passes through the point (2 , 2). Substituting these values for x and y
respectively we get 2 = 2 - 1 ∴
=
. The equation of the first line
can be written as y = x - 1 ⇒ 2y - 3x = -2
ii) As can be seen on the other line the intercept on the y axis is at (0,2). So
the y intercept or = 2. Therefore the equation for this line can be
written as y = x +
⇒ y =
x + 2 . It can also be seen from this
graph that the line passes through the point (1 , -1). Substituting these
values for x and y respectively we get 1 = 1 + 2 ∴
= -1 . The
equation of the second line can be written as y = - x + 2 or x + y = 2
iii) Solving the two equations of the two lines respectively as found in i) and
ii) we get y = 0.8. We multiply equation in ii) by 3 to get 3x + 3y = 6 and
when we add this to equation in i) we get 5y = 4 which means that y = 0.8.
If we substitute this value in ii) we get 0.8 + x = 2 , therefore x = 1.2.
iv) Therefore we get the solution of the two lines, which is the intersection
of the two lines as (1.2, 0.8). So the answer that gives the best estimate
is (1,1)