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3 years ago

Dilate the given points distance from the origin (x,y) (0.8x, 0.8y) . The point (-10,-20) becomes & point (15,25) become

Mathematics

1 answer:

dalvyx [7]3 years ago

8 0

Answer: The point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

Step-by-step explanation:

When a point (x,y) is dilated by a scale factor k from the origin, then the new points become

$(kx,ky).$

The given rule of dilation : (x,y) →(0.8x, 0.8y)

The first point is (-10,-20), so its image will be

$(-10,-20)\to (0.8\times-10,0.8\times-20)=(-8,-16)$

So, the point (-10,-20) becomes (-8,-16).

The second point is (15,25), so its image will be

$(15,25)\to (0.8\times15,0.8\times25)=(12,20)$

So, the point (15,25) becomes (12,20).

Hence, the point (-10,-20) becomes (-8,-16) & point (15,25) becomes (12,20).

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Write an equation for an ellipse centered at the origin, which has foci at (\pm\sqrt{8},0)(± 8 ,0)(, plus minus, square root o

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Answer:

The equation of ellipse centered at the origin

$\frac{x^2}{18} +\frac{y^2}{10} =1$

Step-by-step explanation:

given the foci of ellipse (±√8,0) and c0-vertices are (0,±√10)

The foci are (-C,0) and (C ,0)

Given data (±√8,0)

the focus has x-coordinates so the focus is lie on x- axis.

The major axis also lie on x-axis

The minor axis lies on y-axis so c0-vertices are (0,±√10)

given focus C = ae = √8

Given co-vertices ( minor axis) (0,±b) = (0,±√10)

b= √10

The relation between the focus and semi major axes and semi minor axes are $c^2=a^2-b^2$

$a^{2} = c^{2} +b^{2}$

$a^{2} = (\sqrt{8} )^{2} +(\sqrt{10} )^{2}$

$a^{2} =18$

$a=\sqrt{18}$

The equation of ellipse formula

$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1$

we know that $a=\sqrt{18} and b=\sqrt{10}$

Final answer:-

The equation of ellipse centered at the origin

$\frac{x^2}{18} +\frac{y^2}{10} =1$

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3 years ago

Read 2 more answers

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Answer:

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Step-by-step explanation:

Given that

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And, for another job The generator rents for 4 hours and the total cost is $40

We need to find out the hourly rates

For the first one

= $48 ÷ 6 hours

= $8

For the second one

= $40 ÷ 4 hours

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Hence, the hourly rates are $8 and $10 respectively

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3 years ago

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Answer:

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Step-by-step explanation:

Since we are being asked by the integration limits in first octant (positive x, positive y and positive z) we need to know where does the plane intersect this axes. For this we have:

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for x=0 and z=0

3y=21

y=7

for z=0 and y=0

x=21

This means that the integration limits are:

X from 0 to 21

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