B.) Hibiscus Street
The key thing to remember is the slope of the lines. The equation for a line in slope intercept form is
y = ax + b
where
a = slope
b = y intercept
So the equation for Oak Street is y = 2/3x - 7. So it's slope is 2/3. And any street that has the same slope will be given a tree name. And any street that's perpendicular will be given a flower name. You can determine is a line is perpendicular if it has a slope that's the negative reciprocal. So a street that's perpendicular to Oak street will have a slope of -3/2.
Now you've just been given the equation to a new street that's y = -3/2x - 2. Since the slope is -3/2 and Oak street has a slope of 2/3, the new street is perpendicular to Oak street. And given the naming scheme, that means that the new street will have the name of a flower. So let's look at the available street names and pick a flower.
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A.) Weeping Willow Street
* Nope a Weeping Willow is a tree. So this name won't work.
B.) Hibiscus Street
* Yes. A Hibiscus is a flower, so this name is suitable.
C.) Oak Street
* Nope. Not only is this a tree instead of a flower, but there's already an Oak street. So bad choice.
D.) Panther Street
* Nope, this is an animal, not a flower. Bad choice.
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You're trying to find constants
such that
. Equivalently, you're looking for the least-square solution to the following matrix equation.
To solve
, multiply both sides by the transpose of
, which introduces an invertible square matrix on the LHS.
Computing this, you'd find that
which means the first choice is correct.
The factors of 40 are 1, 2, 4, 5, 8, 10, 20, and 40. So therefore, the numbers would be 2 and 4.
11 days, 21 hours, and 52 minutes have elapsed
(this answer is assuming he would have a normal heart rate of 70 bpm)
First, you would divide 1,200,703 by 70:
1,200,703/70=17,152.9
This is the amount of minutes that have elapsed.
Then, you convert the minutes to hours by dividing by 60:
17,152.9/60=285.8816667 (285 hours and 52 minutes)
This gives you how many hours and minutes have elapsed.
Finally, you calculate the number of days that have elapsed by dividing 285 by 24 (there are 24 hours in a day):
285/24=11.875 (11 days and 21 hours).
Put all of the amounts together to get the final answer:
11 days, 21 hours, and 52 minutes have elapsed
