I will attach google sheet that I used to find regression equation.
We can see that linear fit does work, but the polynomial fit is much better.
We can see that R squared for polynomial fit is higher than R squared for the linear fit. This tells us that polynomials fit approximates our dataset better.
This is the polynomial fit equation:
I used h to denote hours. Our prediction of temperature for the sixth hour would be:
Here is a link to the spreadsheet (
<span>https://docs.google.com/spreadsheets/d/17awPz5U8Kr-ZnAAtastV-bnvoKG5zZyL3rRFC9JqVjM/edit?usp=sharing)</span>
Answer:
Option A - Neither. Lines intersect but are not perpendicular. One Solution.
Option B - Lines are equivalent. Infinitely many solutions
Option C - Lines are perpendicular. Only one solution
Option D - Lines are parallel. No solution
Step-by-step explanation:
The slope equation is known as;
y = mx + c
Where m is slope and c is intercept.
Now, two lines are parallel if their slopes are equal.
Looking at the options;
Option D with y = 12x + 6 and y = 12x - 7 have the same slope of 12.
Thus,the lines are parrallel, no solution.
Two lines are perpendicular if the product of their slopes is -1. Option C is the one that falls into this category because -2/5 × 5/2 = - 1. Thus, lines here are perpendicular and have one solution.
Two lines are said to intersect but not perpendicular if they have different slopes but their products are not -1.
Option A falls into this category because - 9 ≠ 3/2 and their product is not -1.
Two lines are said to be equivalent with infinitely many solutions when their slopes and y-intercept are equal.
Option B falls into this category.
Answer:
D
Step-by-step explanation:
Answer:
a)
The combined resistance of a circuit consisting of two resistors in parallel is given by:
where
R is the combined resistance
are the two resistors
We can re-write the expression as follows:
Or
In order to see if the function is increasing in r1, we calculate the derivative with respect to r1: if the derivative if > 0, then the function is increasing.
The derivative of R with respect to r1 is:
We notice that the derivative is a fraction of two squared terms: therefore, both factors are positive, so the derivative is always positive, and this means that R is an increasing function of r1.
b)
To solve this part, we use again the expression for R written in part a:
We start by noticing that there is a limit on the allowed values for r1: in fact, r1 must be strictly positive,
So the interval of allowed values for r1 is
From part a), we also said that the function is increasing versus r1 over the whole domain. This means that if we consider a certain interval
a ≤ r1 ≤ b
The maximum of the function (R) will occur at the maximum value of r1 in this interval: so, at
Answer:
30
Step-by-step explanation:
x=6
4 by 6 =24
24 + 6 =30
