Answer:
The diver will be 8 feet from the end of the board when he hits the water.
Step-by-step explanation:
The diver hits the water when y = 0.
To find the distance, we have to find the values of x when y = 0.
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
.
This polynomial has roots such that , given by the following formulas:
In this problem, we have that:
So
Then
It is a horizontal distance, so the answer is a positive value.
The diver will be 8 feet from the end of the board when he hits the water.
Answer:
Step-by-step explanation:
Hi there!
<u>What we need to know:</u>
- Linear equations are typically organized in slope-intercept form:
- where m is the slope of the line and b is the y-intercept (the value of y when the line crosses the y-axis)
- Parallel lines will always have the same slope but different y-intercepts.
<u>1) Determine the slope of the parallel line</u>
Organize 3x = 2y into slope-intercept form. Why? So we can easily identify the slope, m.
Switch the sides
Divide both sides by 2 to isolate y
Now that this equation is in slope-intercept form, we can easily identify that is in the place of m. Therefore, because parallel lines have the same slope, the parallel line we're solving for now will also have the slope . Plug this into :
<u>2) Determine the y-intercept</u>
Plug in the given point, (4,0)
Subtract both sides by 6
Therefore, -6 is the y-intercept of the line. Plug this into as b:
I hope this helps!
Answer:
Its 4:)
Step-by-step explanation:
Answer:
x squared over 4 plus y squared over 8 equals 1
Step-by-step explanation:
The general equation of ellipse is given as;
(x²/a²) + (y²/b²) = 1
The coordinates of a foci are: (±c, 0) where;
c² = b² - a²
However, we know that equation of directrix is; x = ±a/e
Now, Directrix is given ±4
Thus, a/e = 4
a = 4e
We also know that c = ae from ellipse foci coordinates.
Thus, ae = 2
since ae = 2, then (4e)e = 2
4e² = 2
e² = 2/4
e = 1/2
Thus;
a = 4 × 1/2
a = 2
Since c² = b² - a²;
2² = b² - 2²
4 = b² - 4
b² = 8
From (x²/a²) + (y²/b²) = 1, we can put our values to get;
x²/4 + y²/8 = 1
Answer:
The lengths of the sides are 12cm, 28cm and 36cm.
Step-by-step explanation:
Let the smallest side be 4x, the middle side be 7x and the largest side be 9x.
Smallest side + middle side + largest side = 60cm
4x + 7x + 9x = 60
20x = 60
x = 60 ÷ 20
x = 3
Smallest side (4x) = 3 × 4
= 12
Middle side (7x) = 7 × 4
= 28
Largest side (9x) = 9 × 4
= 36