There will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
<h3>What is a circle?</h3>
It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)
We have a circle and a parabola:
As we know the standard form of a circle:
The standard form of the parabola:
If we plug the value of y from the parabola equation in the circle equation, we get a quartic equation(4th order equation)
The solution of the quartic equation will be 4.
Thus, there will be four ways a circle and a parabola can intersect because the solution of the quartic equation will be 4.
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Answer:
∴35.97 mg caffeine would be left in the system after 5 hours.
Step-by-step explanation:
Given that,
A cup of coffee has approximately 310 mg of caffeine.
Caffeine decrease at a rate 35% per hour.
Exponential Function:
y(t)= Amount caffeine after t hours
= Initial amount of caffeine
r= rate of decrease
t = Time in hour.
Here y(t)=?, = 310 mg, r=35%=0.35, t= 5 hours
=35.97 mg
∴35.97 mg caffeine would be left in the system after 5 hours.
15x + 2 = 45x + 4
Subtract 2 from both sides, as well as subtracting 45x from both sides.
15x - 45x = 4 - 2
-30x = 2
Divide both sides by -30.
x = 2/-30
x = - 1/15
~Hope I helped!~
Answer:
24 and 48
Today, the son is 24 years old, and the father is 48 years old.
Step-by-step explanation:
(x - 10) + (2x - 10) = 52
3x + 20 = 52
3x = 72
x = 24
The father is 2 times his son's age.
2x
= 2(24)
= 48
So, the son is 24 and the father is 48.
10 years ago, son was 14 and father was 38, if added, this adds up to 52, so we know our calculations are correct.
Looking at this in terms of sets, let's call O the set of all owls, and F the set of all things that can fly. What this original statement is saying every animal that's a member of the set of all owls is also a member of the set of all things that can fly, or in other words, O⊂F (O is a subset of F). Negating this tells us that, while there's <em>at least one</em> element of O that also belongs to F, O is not contained entirely in F (O⊆F, in notation), so a good negation or our original statement might be:
<em>Not all owls can fly.</em>
