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aivan3 [116]
2 years ago
12

What is the distance between (-1,4) and (2,0)

Mathematics
1 answer:
Ivahew [28]2 years ago
7 0

Answer: 5

The Distance between the coordinates of two points is measured by distance formula.

Step-by-step explanation:

The Distance between the coordinates of two points P(x1,y1) and Q(x2,y2) is measured by

Distance PQ= \sqrt{}(x2-x1)²+(y2-y1)²

So, the distance between (-1,4 ) and (2,0) can be calculated by

Distance= \sqrt{}(2-(-1))²+(0-4)²

              = \sqrt{}(3)²+(-4)²

              =\sqrt{}9+16 = \sqrt{}25                                                  as    \sqrt{}25 = 5

Distance = 5

So the distance between the two coordinates is 5.

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A central angle theta in a circle of radius 7 m is subtended by an arc of length 8 m. Find the measure of theta in degrees. (Rou
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Answer: In degrees , The measure of \theta=65.5^{\circ}

In radians , the measure of  \theta =\dfrac{8}{7}\text{ radians}.

Step-by-step explanation:

We know that the formula for length of arc is given by :-

l=\theta r

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r= radius of the circle.

As per given , we have

Radius of circle : r=7 m

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Substitute these values in the above formula , we get

8=\theta (7)\\\\\Rightarrow\ \theta =\dfrac{8}{7}\text{ radians}

Hence, the measure of \theta =\dfrac{8}{7}\text{ radians}.

To convert it into degrees we multiply it with \dfrac{180^{\circ}}{\pi}

The measure of \theta =\dfrac{8}{7}\times\dfrac{180^{\circ}}{\pi}

=(\dfrac{8\times180}{7\times3.14})^{\circ}=65.5141037307^{\circ}

\approx65.5^{\circ}

Hence, the measure of \theta=65.5^{\circ}

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