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cricket20 [7]
3 years ago
10

In the graph below, find the coordinate of the image point. O is the origin and P is the point (4, 3). Ry and Rx are reflections

around the x- and y- axes.
Complete the following:

Mathematics
2 answers:
lidiya [134]3 years ago
8 0

Answer:

We have been given the points origin and P (4,3)

We have reflection rule which is:

(x,y)\text{when reflected around y-axis}\Rightarrow(-x,y)

(x,y)\text{when reflected around x-axis}\Rightarrow(x,-y)

The given point x=4 and y=3 when reflected around y-axis the point becomes:

(-4,3)

The given point x=4 and y=3 when reflected around x-axis the point becomes:

(4,-3)

yaroslaw [1]3 years ago
4 0

Answer with explanation:

When a point is reflected across either through x or y axis ,then perpendicular distance of that point from x or y axis called Preimage is equal to perpendicular distance of that point from x or y axis called image.

When a point is reflected through x axis or y axis,it totally depends on which quadrant the point is lying.

If point(a,b) is lying in first Quadrant ,and then we have to find it's reflection across x axis and y axis then coordinate of image point will be ,which will lie in fourth Quadrant and second quadrant respectively ,will have coordinates  (a,-b) and (-a,b) respectively.

These are rules of reflection across x and y axis of point(a,b),where a and b are positive real number

(a,b)_{x}=(a,-b)\\\\(a,b)_{y}=(-a,b)\\\\(-a,b)_{x}=(-a,-b)\\\\(-a,b)_{y}=(a,b)\\\\(-a,-b)_{x}=(-a,b)\\\\(-a,-b)_{y}=(a,-b)\\\\(a,-b)_{x}=(a,b)\\\\(a,-b)_{y}=(-a,-b)

Using the Same rule when point (4,3) is reflected around x and y axes

(4,3)_{x}=(4,-3)\\\\(4,3)_{y}=(-4,3)

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3 years ago
A bucket that weighs 5 lb and a rope of negligible weight are used to draw water from a well that is 60 ft deep. The bucket is f
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Answer:

The value is W= 2640 \  ft \cdot lb

Step-by-step explanation:

From the question we are told that

The weight of the bucket is F =  5 lb

The depth of the well is x_1 =  60 \ ft

The weight of the water is W_w  =  42 lb

The rate at which the bucket with water is pulled is v  = 1.5 \  ft/s

The rate of the leak is r = 0.15 lb/s

Generally the workdone is mathematically represented as

W =  \int\limits^{x_1}_{x_o} {G(x)} \, dx]

Here G(x) is a function defining the weight of the system (water and bucket ) and it is mathematically represented as

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Here I is the rate of water loss in lb/ft mathematically represented as

I  = \frac{r}{v}

=> I  = \frac{0.15 }{1.5 }

=> I  = 0.1

So

G(x) =  5  +  (42- 0.1x)

=> G(x) =  47- 0.1x)

So

W =  \int\limits^{60}_{0} {47- 0.1x} \, dx]

=> W =  [47x - \frac{0.1x^2}{2} ]|\left 60} \atop {0}} \right.

=> W= [47(60) - 0.05(60)^2]

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