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Complete Question
Write a rational equation that relates the desired percentage p, to the amount A of a 30% solution that needs to be added to 1 liter of 10% acid solution to make a blend that is p% acid, where 0<p<100 . What is a reasonable restriction on the set of possible values of ? Explain your answer.
Answer:
100(0.1 + 0.3A)= (1 + A) P
Step-by-step explanation:
A of a 30% solution that needs to be added to 1 liter of 10% acid solution to make a blend that is p% acid,
Hence,
10% of 1 + 30% of A = p%(1 + A)
0.10 + 0.3A = (p/100)(1 + A)
Divide both sides by 1 + A
0.1 + 0.3A/ 1 + A = p/100
Cross Multiply
100(0.1 + 0.3A) = 1 + A(p)
From the above calculation, we can see that, the blend that would be formed is not lower than 10% or greater than 30%
10% < p< 30%
We need Pythagoras theorem here
a^2+b^2 = c^2
a, b = legs of a right-triangle
c = length of hypotenuse
Let S=shorter leg, in cm, then longer leg=S+2 cm
use Pythagoras theorem
S^2+(S+2)^2 = (10 cm)^2
expand (S+2)^2
S^2 + S^2+4S+4 = 100 cm^2 [collect terms and isolate]
2S^2+4S = 100-4 = 96 cm^2
simplify and form standard form of quadratic
S^2+2S-48=0
Solve by factoring
(S+8)(S-6) = 0 means (S+8)=0, S=-8
or (S-6)=0, S=6
Reject nengative root, so
Shorter leg = 6 cm
Longer leg = 6+2 cm = 8 cm
Hypotenuse (given) = 10 cm
Answer:
hehc dhcbshhceucuiifvbrifrjvrjv
Step-by-step explanation:
Answer: P(landing on orange)=1 - [2/3 + 1/12 + 1/12]
so <em><u>=1/6</u></em>
Answer:
i think it is 110
Step-by-step explanation:
sorrt if i am wrong
