Matt is climbing a mountain. When his elevation is higher than 1600 meters, breathing is difficult for Matt. Write an inequality
2 answers:
Answer:
h>1600.
Step-by-step explanation:
We are told that Matt is climbing a mountain. When his elevation is higher than 1600 meters, breathing is difficult for Matt. We are asked to write an inequality that describes h, the elevation at which breathing is difficult for Matt.
We know when elevation (h) will be higher than 1600 meters Matt will face difficulty in breathing. We can represent this situation as: .
Therefore, inequality representing the elevation at which breathing is difficult for Matt will be .
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The slope of two parallel lines are equal.
Let us find slope of given equation.
The general slope intercept form is given by :
where m is slope
our equation is :
Now we have to convert our equation into slope intercept form.
let us try to isolate y on the left side.
taking 5x to the right side we have ,
dividing both sides by -15,
coefficient of x is slope,
so slope is 1/3
slope of line parallel to it is also same that is 1/3 .
Correct option is D.
Step-by-step explanation:
Q3
(a) If 0 < |x − 1| < δ, then |f(x) − 2| < 2
What this means is, how far can x stray from the x=1 line such that f(x) stays within 2 units of the y=2 line (0 < f(x) < 4).
If we move 2 units left of x=1, we get f(x) = 4.
If we move about 3.5 units right of x=1, we get f(x) = 4.
Therefore, δ can't be more than 2.
(b) If 0 < |x| < δ, then |f(x) − 3| < 1
What this means is, how far can x stray from the x=0 line such that f(x) stays within 1 unit of the y=3 line (2 < f(x) < 4).
If we move 1 unit left of x=0, we get f(x) = 4.
If we move 1 unts right of x=0, we get f(x) = 2.
Therefore, δ can't be more than 1.
Since f(x) isn't continuous within this domain, we can't conclude that the limit exists.
Q4
(a) Yes. If δ = 0.25, then 0.75 < x < 1.25, and f(x) > 200.
(b) No. f(1) = 300, so even if δ = 0, f(x) will be less than 400.
(c) Yes. If δ ≈ 0.1, then 0.9 < x < 1, and f(x) > 450.
