Shaun has a set of blocks. When he separates the blocks into groups of 21, he has 34 groups of blocks. How many groups of blocks
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Given:
x: [1 2 3 4 5 6 7]
y: [9 9.5 10.25 11.25 12.5 14 15.75]
Let the function which models the data be
y(x) = ax² + bx + c
Apply the function to the first three data points
a + b + c = 9 .(1)
4a + 2b + c = 9.5 (2)
9a + 3b + c = 10.25 (3)
Subtract (1) from (2).
3a + b = 0.5
or
b = 0.5 - 3a (4)
Subtract (1) from (3).
8a + 2b = 1.25 (5)
Substitute (4) into (5).
8a + 2(0.5 - 3a) = 1.25
2a = 0.25
a = 0.125
From (4),
b = 0.5-3*0.125 = 0.125
From (1),
c = 9 - 0.125 - 0.125 = 8.75
The function is
y = 8.75 + 0.125x + 0.125x²
Check that the function works for x=4,5,6,7.
From the calculator, obtain
y(4) = 11.25 Correct
y(5) = 12.5 Correct
y(6) = 14 Correct
y(7) = 15.75 Correct
The graph of the function is shown below.
Answer: y = 8.75 + 0.125x + 0.125x²
x: [1 2 3 4 5 6 7]
y: [9 9.5 10.25 11.25 12.5 14 15.75]
Let the function which models the data be
y(x) = ax² + bx + c
Apply the function to the first three data points
a + b + c = 9 .(1)
4a + 2b + c = 9.5 (2)
9a + 3b + c = 10.25 (3)
Subtract (1) from (2).
3a + b = 0.5
or
b = 0.5 - 3a (4)
Subtract (1) from (3).
8a + 2b = 1.25 (5)
Substitute (4) into (5).
8a + 2(0.5 - 3a) = 1.25
2a = 0.25
a = 0.125
From (4),
b = 0.5-3*0.125 = 0.125
From (1),
c = 9 - 0.125 - 0.125 = 8.75
The function is
y = 8.75 + 0.125x + 0.125x²
Check that the function works for x=4,5,6,7.
From the calculator, obtain
y(4) = 11.25 Correct
y(5) = 12.5 Correct
y(6) = 14 Correct
y(7) = 15.75 Correct
The graph of the function is shown below.
Answer: y = 8.75 + 0.125x + 0.125x²
Given expression is
Now convert mixed fraction as improper fraction as
Now we can convert
So the answer is
Now convert mixed fraction as improper fraction as
Now we can convert
So the answer is