Answer:
5,070
Step-by-step explanation:
For this case we have that by definition, the discriminant of a quadratic expression is given by:
If the discriminant is less than zero then the expression has two different complex roots.
In this case we have the following expression:
So we have to:
The discriminant is given by:
Then, if we want two complex roots it must be fulfilled that:
Thus, the expression has two complex roots for all values greater than 4.
ANswer:
Two circles<span> of </span>radius<span> 4 are </span>tangent<span> to the </span>graph<span> of y^</span>2<span> = </span>4x<span> at the </span>point<span> (</span>1<span>, </span>2<span>). ... I know how to </span>find<span> the </span>tangent<span> line from a circle and a given </span>point<span>, but ... </span>2a2=42. a2=8. a=±2√2. Then1−xc=±2√2<span> and </span>2−yc=±2√2. ... 4 from (1,2<span>), so you could </span>find these<span> centers, and from there the</span>equations<span> of the circle
</span>
Answer:
- 273 mL of 5%
- 117 mL of 15%
Step-by-step explanation:
Let q represent the quantity of 15% dressing used. Then the amount of 5% dressing is (390 -q). The amount of vinegar in the mix is ...
0.15q + 0.05(390 -q) = 0.08(390)
0.10q = 31.2 -19.5 = 11.7 . . . . . . subtract 0.05(390) and simplify
q = 117 . . . . . . . . . . . . . . . . . . multiply by 10
390-q = 273
The chef should use 273 mL of the first brand (5% vinegar) and 117 mL of the second brand (15% vinegar).
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<em>Additional comment</em>
You may have noticed that the value of q is (0.08 -0.05)/(0.10 -0.05)×390. The fraction of the mix that is the highest contributor is the ratio of the difference between the mix value and least contributor, divided by the difference between the contributors: (8-5)/(15-5) = 3/10, the fraction that is 15% vinegar. This is the generic solution to mixture problems.
