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4 years ago

Which point does not lie on the circle centered at (3,2) with radius 5

Mathematics

1 answer:

patriot [66]4 years ago

6 0

The point which does not lie on the circle centered at (3,2) with radius 5 is given below.

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

where (h, k) are the coordinates of the centre and r is the radius

Here (h, k) = (3, 2) and r = 5,

hence

(x - 3)² + (y - 2)² = 25 ← equation of circle

If an ordered pair lies on the circle then it satisfies the equation, if not then it does not lie on the circle.Substitute the coordinates of the points into the left side of the equation of the circle and check validity.

(0 , 6) : (0 - 3)² + (6 - 2)² = 9 + 16 = 25 ← lies on circle

(3, - 3) : (3 - 3)² + (- 3 - 2)² = 0 + 25 = 25 ← lies on circle

(- 2, 2) : (- 2 - 3)² + (2 - 2)² = 25 + 0 = 25 ← lies on circle

(3, 0) : (3 - 3)² + (0 - 2)² = 0 + 4 = 4 ≠ 25 ← not on circle

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Analysis of an accident scene indicates a car was traveling at a velocity of 69.5 mph (31.1 m/s) along the positive x-axis at th

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We can find the acceleration via

${v_f}^2-{v_i}^2=2a\Delta x$

We have

$\left(5.20\dfrac{\rm m}{\rm s}\right)^2-\left(31.1\dfrac{\rm m}{\rm s}\right)^2=2a(115\,\mathrm m)$

$\implies\boxed{a=-4.09\dfrac{\rm m}{\mathrm s^2}}$

Then by definition of average acceleration,

$a_{\rm ave}=\dfrac{v_f-v_i}t$

so that

$-4.09\dfrac{\rm m}{\mathrm s^2}=\dfrac{5.20\frac{\rm m}{\rm s}-31.1\frac{\rm m}{\rm s}}t$

$\implies\boxed{t=6.33\,\mathrm s}$

We alternatively could have found the time without knowing the acceleration. Since acceleration is constant, the average velocity is

$v_{\rm ave}=\dfrac{x_f-x_i}t=\dfrac{v_f+v_i}2$

Then

$\dfrac{115\,\rm m}t=\dfrac{5.20\frac{\rm m}{\rm s}+31.1\frac{\rm m}{\rm s}}2$

$\implies\boxed{t=6.33\,\mathrm s}$

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3 years ago

Sociologists say that 85% of married women claim that their husband's mother is the biggest bone of contention in their marriage

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Answer:

(A) 0.377,

(B) 0.000,

(D) 0.047

Step-by-step explanation:

We assume that having a bone of intention means not liking one's Mother-in-Law

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(B) P(none of the six dislike their Mother-in-Law) =

(100% - 85%)^6 =

0.15^6 =

0.000

P(exactly 4 dislike their Mother-in-Law) + P(exactly 5 dislike their Mother-in-Law) + P(exactly 6 dislike their Mother-in-Law) =

C(6,4) * (.85)^4 * (1-.85)^2 + C(6,5) * (.85)^5 * (.15)^1 + C(6,6) * (.85)^6 = (15) * (.85)^4 * (.15)^2 + (6) * (.85)^5 * .15 + (1) * (.85)^6 =

0.953

(D) P(no more than 3 dislike their Mother-in-Law) =

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C(6,0) * (.85)^0 * (.15)^6 + C(6,1) * (.85)^1 * (.15)^5 + C(6,2) * (.85)^2 * (.15)^4 + C(6,3) * (.85)^3 * (.15)^3 =

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3 years ago

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antoniya [11.8K]

<u>Answer:</u>

(0.5, -0.5)

<u>Step-by-step explanation:</u>

We are given a line segment on the graph with two known points (ending points) and we are to find its mid point.

We know the formula for the mid point:

$Midpoint = ( \frac {x_1 + x_2} {2} ,\frac {y_1 + y_2} {2} )$

Substituting the coordinates of the given points in the above formula:

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