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The motion of the ball dropped from height is a free fall motion due to
gravitational acceleration.
<h3>Correct response;</h3>- The equation that models the height is; <u>y = -16·x²</u>
To select the equation that models the height, <em>y</em>, of the ball <em>x</em> seconds after
its dropped;
<h3>Solution:</h3>From the above table, we have that the first difference is not a constant
The second difference is = 48 - 16 = 32
Taking the second difference as a constant, we have the following
quadratic sequence;
y = a·x² + b·x + c
Where;
x = The time in seconds
y = The height after <em>x</em> seconds
- At x = 0, we have;
200 = a·0² + b × 0 + c
Therefore;
c = 0
- At<em> x</em> = 1, we have;
184 = a × 1² + b × 1 + 200
184 = a + b + 200
a + b = -16
a = -16 - b
- At <em>x</em> = 2, we have;
136 = a × 2² + b × 2 + 200
136 = 4·a + 2·b + 200
-64 = 4·a + 2×b
Therefore;
-64 = 4 × (-16 - b) + 2×b
-64 = -64 - 4·b + 2×b
b = 0
a + b = -16
Therefore;
a + 0 = -16
a = -16
The equation that models the height is; y = <u>-16·x²</u>
Learn more about quadratic function here;
The most appropriate choice for Probability of an event will be given by-
P(7) =
What is Probability?
Probability gives us the information about how likely an event is going to occur
Probability is calculated by Number of favourable outcomes divided by the total number of outcomes.
Probability of any event is greater than or equal to zero and less than or equal to 1.
Probability of sure event is 1 and probability of unsure event is 0.
Here,
Sample space = {6, 7, 8}
Total number of outcomes = 3
Favourable outcomes = {7}
Number of favourable outcomes = 1
Probability of getting a 7 = P(7) =
To learn more about probability of an event, refer to the link:
#SPJ9
Tom started with total 72 chocolate wafers.
<u><em>Explanation</em></u>
The number of chocolate wafers taken by 8 members of the baseball team are in the sequence :
The above sequence is <u>arithmetic sequence</u> with first term(a₁)= 1 and common difference (d) = 2
<u>Formula for Sum</u> of first terms in arithmetic sequence is....
So, the Sum of 8 terms in that sequence....
That means, the total number of chocolate wafers taken by the baseball team members is 64. Tom ate 5 and then gave his brother 3 chocolate wafers at first.
So, the total number of chocolate wafers at starting