Core Math Investigation
1) When x is more than 0 and increases (e.g. from 5 to 6), y increases
at a much faster rate and becomes very big. When x increases when it
is less then 0 (e.g. from –10 to –9), y increases very slowly.
2) (i) The value of a affects the value of x proportionally. For
example we can compare the equations y = 1 + 2x and y = 5 + 2x. In the
second equation, the value of a has been change to 5. As we can see
from the results in Tables 1 and 2, all the values of y for y = 5 + 2x
are greater by 4, when x is the same.
(ii) As we have seen in (i), the effect of a does not affect the value
of y, as it is a constant added to the solution of 2x . Hence, the
value of a affects x proportionally, no matter what the value of x is.
3) (i) For b = -1, b causes the value of y decrease rapidly as x
increases. This is because when x becomes larger, bx will be a very
small number as bx will be small as b is negative while x is positive.
For b = 0, y remains constant throughout, no matter what the value of
x is. This is because 0x will always give 0. For b = 1, the
relationship is the same as in (1), as 1x will always lead to a rapid
rate of increase for y when x> 0.
(ii) For b = -1, b causes y to increase greatly when x gets smaller,
as b is a negative number and so bx will give a large number when both
b and x are negative. For b = 0, y remains constant throughout, no
matter what the value of x is. This is because 0x will always give 0.
For b = 1, the relationship is the same as in (1), as 1x will always
lead to a very slow rate of increase for y when x <0.
Step Three: The next step will involve getting the variable by itself, in this case ‘x’ is the variable. So, to get ‘x’ by its self we must subtract 100 from both sides.
Assume an 11-bit floating point format in which the most significant bit is the sign bit, the next 4 bits represent the 4-bit biased exponent field, and the last 6 bits represent the normalized significand with implied bit.
3. How small must the combination of F and X be to make this an
in the linear regression model. The R for the linear model is -.632 and the R in
% -8.3% -9% (c) 0% 0% 0% 0% Using indexation: (a) 100 117 133 150 167 (b) 100 93 86 79 71 (c) 100 100 100 100 100 VERTICAL ANALYSIS = == == ==
When two values, x1 and x2, with errors e1 and e2 are multiplied, the resulting error, e, is
This is the perfect opportunity to take that expression or equation that was built in the first half and start the process of finding x. Combining terms and subtracting numbers from both sides will aid in the process of the ultimate goal of finding the unknown number. Many times teachers us a balance with chess pieces and students have a hard time visualizing why 2 paws have to be taken from both sides. The Napping House (1984) clearly depicts how subtraction needs to occur on both sides of the equation. Ultimately, just like balancing equations, the story ends beautifully with everyone and everything
Alternatively solve the quadratic equation but substituting the value of y = x and y = 2x
“Consider the parabola y = (x−3)2 + 2 = x2−6x+11 and the lines y=x and y=2x.
Contribution per unit of product B = ` 30 - ` 20 = ` 10
with the change in Y. In this case, on the graph above, AB and you