164 is 55% of what number? Please somebody help me
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Answer:
The horizontal displacement is 11 units, the vertical displacement is 9 units, and the projection angle is 39.3 degrees.
Step-by-step explanation:
We can start using the definition of displacement in one dimension between any 2 points which is the difference between them, so we have
And apply it to get the horizontal and vertical displacements.
Once we have found them, we can use trigonometric functions to find the projection angle with respect the horizontal.
Linear displacements.
Using the definition of displacement, we can write the horizontal displacement as
So we can use the given points on the displacement formula
In the same manner we can look at the y components of those points to find the vertical displacement
Thus the horizontal displacement is 11 units and the vertical displacement is 9 units.
Projection angle.
The projection angle with respect the horizontal is the angle that is made between the line that connects the points P1 and P2 and the horizontal, so we can use the linear displacements previously found to write
Solving for the angle we get
Replacing values
Which give us
So the projection angle is 39.3 degrees.
*I've tried looking up to see if I can find what the part B and c of this question is, but unfortunately, I can't find them. However, I have tried answering this question by answering part a, and also going ahead to answer how to state and explain the secrets of winning the game. I'm pretty sure most of the questions would be answered in the process.
Answer/Step-by-sep explanation:
Using an equation, in slope-intercept form, we can derive an equation that models the relationship of the height of each basket and the number of balls it contains.
The slope-intercept form is given as: , where,
m = slope/rate of change
b = y-intercept/strating value/height of the basket when it's empty.
✍️Baseball Equation:
Using two pairs, (0, 54) and (5, 39) from the given table of values,
Slope/rate of change (m) = .
y-intercept, b, = the starting value, or the value of y when x = 0. Therefore, b = 54
This means that the baseball basket was at a height of 54 units when it was empty.
m = -3, means the baseball basket kept reducing at an average rate of -3 units in height as each ball was added.
To derive the baseball equation, substitute m = -3, and b = 54 into .
✅Thus, base ball equation would be:
✍️Golf Ball Equation:
Using two pairs, (0, 45) and (5, 35) from the given table of values,
Slope/rate of change (m) = .
y-intercept, b, = the starting value, or the value of y when x = 0. Therefore, b = 45
This means that the golf ball basket was at a height of 45 units when it was empty.
m = -2, means the golf ball basket kept reducing at an average rate of -2 units in height as each ball was added.
To derive the baseball equation, substitute m = -2, and b = 45 into .
✅Thus, golf ball equation would be:
Now, to win the game, we have to find out how many number of exact balls (x) we need to add in each basket equally, for both baskets to be at the same height.
To do this, set the equation of the baseball equal to that of the golf ball.
Thus:
Collect like terms
Divide both sides by -1
✅To win the game, add 9 balls each to both basket to make the height of both baskets equal.
Let's check to see if both baskets will yield the same height if we add 9 balls each basket.
✍️Height (y) of Golf ball basket if we add 9 balls (x):
Substitute x = 9 into
✍️Height (y) of Baseball basket if we add 9 balls (x):
Substitute x = 9 into
✅As we can see, both baskets will be at the same height of 27 units when we add 9 balls to each basket.
The game will be won if we do this.