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2 years ago

What is the maximum number of solutions each of the following systems could have?

Mathematics

2 answers:

Marrrta [24]2 years ago

4 0

Answer:

Two distinct concentric circles: 0 max solutions

Two distinct parabolas: 4 max solutions

A line and a circle: 2 max solution

A parabola and a circle: 4 max solutions

Step-by-step explanation:

Two distinct concentric circles:

The maximum number of solutions (intersections points) 2 distinct circles can have is 0. You can see an example of it in the first picture attached. The two circles are shown side to side for clarity, but when they will be concentric, they will have same center and they will be superimposed. So there can be ZERO max solutions for that.

Two distinct parabolas:

The maximum solutions (intersection points) 2 distinct parabolas can have is 4. This is shown in the second picture attached. This occurs when two parabolas and in perpendicular orientation to each other.

A line and a circle:

The maximum solutions (intersection points) a line and a circle can have is 2. See an example in the third picture attached.

A parabola and a circle:

The maximum solutions (intersection points) a parabola and a circle can have is 4. If the parabola is compressed enough than the diameter of the circle, there can be max 4 intersection points. See the fourth picture attached as an example.

goblinko [34]2 years ago

4 0

Answer:

0,2,2,4

Step-by-step explanation:

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Suppose that public opinion in a large city is 55% in favor of increasing taxes to support renewable energy and 45% against such

Harman [31]

Answer:

The approximate probability that more than 360 of these people will be against increasing taxes is P(Z> 0.6-0.45)

√0.45*0.55/600

The right answer is B.

Step-by-step explanation:

According to the given data we have the following:

sample size, h=600

probability against increase tax p=0.45

The probability that in a sample of 600 people, more that 360 people will be against increasing taxes.

We find that P(P>360/600)=P(P>0.6)

The sample proposition of p is approximately normally distributed mith mean p=0.45

standard deviation σ=√P(1-P)/n=√0.45(1-0.45)/600

If x≅N(u,σ∧∧-2), then z=(x-u)/σ≅N(0,1)

Now, P(P>0.6)=P(P-P > 0.6-0.45)

σ √0.45*0.55/600

=P(Z> 0.6-0.45)

√0.45*0.55/600

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Find dy/dx implicitly and find the largest interval of the form −a < y < a or 0 < y < a such that y is a differentia

mylen [45]

Answer:

dy/dx = -1/√(1 - x²)

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Step-by-step explanation:

Given the function cos y = x

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-siny dy/dx = 1

dy/dx = -1/siny (equation 1)

But cos²y + sin²y = 1

=> sin²y = 1 - cos²y

=> siny = √(1 - cos²y) (equation 2)

Again, we know that

cosy = x

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Using (equation 3) in (equation 2), we have

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Finally, using (equation 4) in (equation 1), we have

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The largest interval is when

√(1 - x²) = 0

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=> x = ±1

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-1 < x < 1

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natima [27]

Answer:

The expression representing the total price of the truck including the sales tax is 1.07p

Step-by-step explanation:

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