Description
Algebra equations & inequalities, lines parabola and systems arithmetic and geometric progressions please follow assignment questions total question are 10. Plagiarism not more than 10%
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1. Denote the needed volume of 10% solution as 𝑥 (liters). Then the resulting solution will
have volume of 𝑥 + 60 liters and will contain 0.1𝑥 + 0.35 ∙ 60 liters of salt. For its
concentration to be 30%, it must be
0.1𝑥 + 0.35 ∙ 60 = 0.3(𝑥 + 60),
or
0.05 ∙ 60
0.2𝑥 = 0.05 ∙ 60, 𝑥 =
= 0.5 ∙ 30 = 𝟏𝟓 (liters).
0.2
2. The slope is the change of sales over the change of time, i.e.
65000 − 29000 36000
R. O
).
𝑚=
=
= 12000 (
5−2
3
year
a) Therefore, the equation of the line is
𝑦 = 12000(𝑥 − 2) + 29000 = 𝟏𝟐𝟎𝟎𝟎𝒙 + 𝟓𝟎𝟎𝟎.
b) For this to be 100000 or more, it must be 12000𝑥 + 5000 ≥ 100000, or
95
11
12000𝑥 ≥ 95000, 𝑥 ≥
=7 .
12
12
So the first such year is 𝟖th.
3. They’ll sell 3 ∙ 2 boxes in a day of January 2, 3 ∙ 2 ∙ 2 in January 3 and 3 ∙ 215−1 in January
15. It is 3 ∙ 214 = 3 ∙ 1024 ∙ 24 = 1024 ∙ 48 = 𝟒𝟗𝟏𝟓𝟐. Hardly possible
4. Her salary will be an arithmetic progression with the common difference of 100 (OMR),
i.e. it will be ...