Answer:
x = 3/2 - ((y + 4)²)/2
Step-by-step explanation:
The coordinates of the focus of the parabola = (1, -4)
The directrix of the parabola is the line, x = 2 (parallel to the y-axis)
The general form of a parabola having a directrix parallel to the y-axis is presented as follows;
(y - k)² = 4·p·(x - h)
The coordinates of the focus = (h + p, k)
The line representing the directrix is x = h - p
Therefore, by comparison, we have;
(1, -4) = (h + p, k)
k = -4
h + p = 1
∴ p = 1 - h
From the directrix, we have;
2 = h - p
∴ 2 = h - (1 - h) = 2·h - 1
2·h = 2 + 1
h = 3/2
p = 1 - h
∴ p = 1 - 3/2 = -1/2
p = -1/2
By substitution of the values of <em>k</em>, <em>p</em>, and <em>h</em>, in the general equation of the parabola, (y - k)² = 4·p·(x - h), we get;
(y - k)² = 4·p·(x - h) = (y - (-4))² = 4·(-1/2)·(x - (3/2)) = (y + 4)² = -2·(x - 3/2)
The equation of the parabola in vertex form is therefore;
x = (-1/2)·(y + 4)² + 3/2 = 3/2 - (y + 4)²/2
Answer: gal / min
Step-by-step explanation:
Answer:
Acceleration would be one.
If you accelerate at 5m/s/s you gain more speed.
However if you accelerate at -5m/s/s you lose speed.
In this context 0 would be you dint gain speed or lose speed you move at the same speed
Step-by-step explanation:
hope that helped
Answer:
Step-by-step explanation:
In the first part the given polynomial is
, we have to divide this polynomial by (x-1) using synthetic division.
Here are the steps of synthetic division
Step 1: Set up the synthetic division table in which the coefficients are written in descending power of x.
Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.
Step 3: Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. Here, a is 1(taken from divisor)
Step 4: Add the column made in step 3. Repeat these steps until the last column reached.
In the second part,
It is given that divisor polynomial is the factor of given polynomial then we have to tell the remainder which is 0 because if divisor polynomial is the factor the it will completely divide the given polynomial which gives remainder 0.
In the third part,
Given when one uses the synthetic division to divide by (x-3) then what number is used to multiply each term that is dropped down or added.
As explained the steps of synthetic division in first part
x-3=0 ⇒ x=3 which is a
In step 3, Multiply a by the value just written on the bottom row and write this value just down of the number written next of leading coefficient. So, 3 is multiplied.
As explained in Step 2: Drop down the leading coefficient i.e the coefficient of highest power of x to the bottom row.
The columns which is formed by above steps are added.