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pochemuha
3 years ago
14

Find vector C and D in relation to B. Need help with the actual reasoning.

Mathematics
1 answer:
lord [1]3 years ago
8 0

Answer:

c = -6

d = 2

Step-by-step explanation:

After reflection about the x-axis:

A --> A'

(2,3) --> (2,-3)

(4,3) --> (4,-3)

(2,6) --> (2,-6)

After translation:

(2 + c, -6 + d) --> (-4, -4)

2+c = -4

c = -6

-6+d = -4

d = 2

After translation by < c , d >, any point maps from (x , y) to:

< x , y > + < c , d >

< x+c , y+d >

c is the no. of units of horizontal movement:

+ve for right wards

-ve for left wards

d is the no. of units of vertical movement:

+ve for upwards

-ve for downwards

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a bag contains 10 white gold balls and 6 striped golf balls. a golfer wants to add 112 golf balls to the bag. he wants the ratio
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Step-by-step explanation:

First we find the ratio of white to striped balls

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Striped golf balls = 6

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We are told a golfer wants to add extra 112 balls to the already 16 balls

And the ratio after adding 112 balls must stay the same

First we label the extra golf balls to be added x and y

x = white golf balls

y = striped golf balls

So since we know the 112 balls added is a combination of the extra white golf balls and striped golf balls, we create an equation for that, labelling it (1)

x + y = 112 (1)

And we are told that after putting these extra balls the ratio must remain the same, which is 5/3

which will be (10 white balls + x) divided by (6 striped ball + y) will be equals to 5/3

So we create another equation for this, labelling it (2)

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So we have two simultaneous equations

We pick (1)

x + y = 112

We either make x or y the subject of formula, I choose to make x the subject of formula, we label the equation (3)

take y to the other side, causing it to change to -y

x = 112 - y (3)

We then work with (2)

(10+x)/(6+y) = 5/3

We cross multiply

3(10+x) = 5(6+y)

We open the brackets

Making the equation simplified and labelling it (4)

30 +3x = 30 + 5y

Collect like terms

3x -5y = 30-30

3x -5y = 0 (4)

Remember from (3) we know that

x = 112 -y

So we put (3) in (4)

3(112 - y) - 5y = 0

Open bracket

336 -3y -5y =0

336 -8y = 0

Transfer -8y to the other side, changing to +8y

336 = 8y

Divide both sides by 8

336/8 = y

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y = 42

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So we put y = 42 in (3)

x = 112 - y

x = 112 -42 = 70

x = 70

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