What is the independent variable of an equation?
1 answer:
You might be interested in
The number of bags of chips sold is 8 and the number of packs of cookies sold is 12
<em><u>Solution:</u></em>
Let "a" be the number of bags of chips sold
Let "b" be the number of packs of cookies sold
Given that,
Cost of one bag of chips = $ 1.50
Cost of one pack of cookies = $ 1.25
Yesterday Abigail made $27 from selling a total of 20 bags of chips and packs of cookies
<em><u>So we can frame a equation as:</u></em>
Number of bags of chips sold + number of packs of cookies sold = 20
a + b = 20 ---- eqn 1
Also given that Abigail made $27 from selling
number of bags of chips sold x Cost of one bag of chips + number of packs of cookies sold x Cost of one pack of cookies = $ 27
1.5a + 1.25b = 27 ---- eqn 2
<em><u>Let us solve eqn 1 and eqn 2 to find values of "a" and "b"</u></em>
From eqn 1,
a = 20 - b ---- eqn 3
Substitute eqn 3 in eqn 2
1.5(20 - b) + 1.25b = 27
30 - 1.5b + 1.25b = 27
-0.25b = -3
<h3>b = 12</h3>Therefore from eqn 3,
a = 20 - b = 20 - 12 = 8
<h3>a = 8</h3><em><u>Thus we have:</u></em>
number of bags of chips sold = 8
number of packs of cookies sold = 12
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.
