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Yanka [14]
3 years ago
5

What is the distance between the points (5, 1) and (-3, -5)? 2 2 10 4

Mathematics
1 answer:
mezya [45]3 years ago
4 0

Step-by-step explanation:

Hey, there!!

The given points are A(5,1) and B(-3,-5)

We have, distance formulae for AB is,

ab =  \sqrt{ {(x2 - x1)}^{2}  + ( {y2 - y1)}^{2} }

ab =  \sqrt{( { - 3 - 5)}^{2}  + ( { - 5 - 1)}^{2} }

ab =  \sqrt{(  { - 8)}^{2} + ( { - 6)}^{2}  }

ab =  \sqrt{64 + 36}

ab =  \sqrt{100}

Therefore, the distance between AB points is 10 units.

<em><u>Hope</u></em><em><u> </u></em><em><u>it helps</u></em><em><u>.</u></em><em><u>.</u></em><em><u>.</u></em>

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Find all values of k for which the equation 3x^2−4x+k=0 has no solutions.
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The given equation has no solution when K is any real number  and k>12

We have given that

3x^2−4x+k=0

△=b^2−4ac=k^2−4(3)(12)=k^2−144.

<h3>What is the condition for a solution?</h3>

If Δ=0, it has 1 real solution,

Δ<0 it has no real solution,

Δ>0 it has 2 real solutions.

We get,

Δ=k^2−144 here Δ is not zero.

It is either >0 or <0

Δ<0 it has no real solution,

Therefore the given equation has no solution when K is any real number.

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Answer:

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Step-by-step explanation:

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Using a linear approximation, estimate f(2.1), given that f(2) = 5 and f'(x) = √3x-1.
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Answer:

f\left( {2.1} \right) \approx 5.22360.

Step-by-step explanation:

The linear approximation is given by the equation

                            {f\left( x \right) \approx L\left( x \right) }={ f\left( a \right) + f^\prime\left( a \right)\left( {x - a} \right).}

Linear approximation is a good way to approximate values of f(x) as long as you stay close to the point x= a, but the farther you get from x=a, the worse your approximation.

We know that,

a=2\\f(2) = 5\\f'(x) = \sqrt{3x-1}

Next, we need to plug in the known values and calculate the value of f(2.1):

{L\left( x \right) = f\left( 2 \right) + f^\prime\left( 2 \right)\left( {x - 2} \right) }=5+\sqrt{3(2)-1}(x-2) =5+\sqrt{5}(x-2)

Then

f\left( {2.1} \right) \approx 5+\sqrt{5}(2.1-2)\approx5.22360.

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