The length of the shadow is 124.7 in
<u>Explanation:</u>
<u />
Given:
Angle, θ = 30°
Height of the fence, h = 72 in
Length of the shadow, l = ?
Given:
tan 30° = 
Therefore, the length of the shadow is 124.7 in
The diver will hit the water when the height is zero, so we will want to set our height function equal to zero
0 = -4t^2 + 11t + 3
we will then factor to find out value of t that make the function equal to zero
0 = (-4t - 1 ) ( t - 3 )
This means our function equals zero when t = -1/4 s and t = 3 seconds
Since time cannot be negative, our final solution is t = 3 seconds
Answer: The graph is shown below
The solution to the system is (x,y) = (2,3)
=============================================================
Explanation:
To graph 
, we need two points. Generating any (x,y) point involves picking a random x value to find its paired y value. For instance, if you plugged in x = 0, you should get to y = -2 which is the y intercept. Then trying something like x = 2 will lead to y = 3. This line goes through (0,-2) and (2,3). This line is shown in red below.
The blue line is horizontal and goes through 3 on the y axis. Every point on this horizontal line has the same y coordinate of 3. The x value doesn't matter, so it's not part of the equation y = 3.
The intersection of the red and blue line is the solution to the system. That intersection occurs at (x,y) = (2,3). This means x = 2 and y = 3 pair up together to make both original equations true.
Since this system has at least one solution, we consider it a consistent system.
Answer:
8 m/s^2
Step-by-step explanation:
You can use the equation a = v^2 / r
That is acceleration is equal to velocity squared divided by the radius which in this problem is the length of the string. The velocity is 4m/s and the r the radius is 2 m. Now you can square 4 m/s to get 16 m^2/s^2 THEN you divide by 2 m and the m^2 turns to just m and the 16 to an 8. So, that leaves you with acceleration or in this case centripetal acceleration equals 8 m/s^2.
a = 8 m/s^2 or 8 meters per second squared.
Answer:
Slope is 2; y-intercept is (0,-6)
Step-by-step explanation:
Slope intercept form looks like 3y = 2x - 6
In the equation y=mx+b, M is always the slope, and B is always the y-intercept. Therefore if you look back at the problem the slope number should be in front of the x which makes it 2. Since the y-intercept is always b, y = -6.
Slope or m = 2; y-intercept is (0,-6)
