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kipiarov [429]
3 years ago
7

If →u and →v are the vectors below, find the vector →w whose tail is at the point halfway from the tip of →v to the tip of →v−→u

and whose head is at the point halfway from the tip of →u to the tip of →v. Assume all vectors are in standard position.
u: (-1,-1,-1) v:(2,3,-5)
Mathematics
1 answer:
S_A_V [24]3 years ago
5 0
Û = (-1, -1, -1)
^v = (2, 3, -5)
^v - û = (2 + 1, 3 + 1, -5 + 1) = (3, 4, -4)
Half way from ^v to ^(v - u) = ((3 - 2)/2, (4 - 3)/2, (-4 + 5)/2) = (1/2, 1/2, 1/2)
Halfway from û to ^v = ((2 + 1)/2, (3 + 1)/2, (-5 + 1)/2) = (3/2, 2, -2)

The required vector ^w = ((3/2 - 1/2), (2 - 1/2), (-2 - 1/2)) = (1, 1/2, -5/2)
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Three vertices of parallelogram WXYZ are X(–2,–3), Y(0, 5), and Z(7, 7). Find the coordinates of vertex W
Serhud [2]

The coordinates of the vertex W are (5 , -1)

Step-by-step explanation:

In the parallelogram, the diagonal bisect each other

To find a missing vertex in a parallelogram do that:

  • Find the mid-point of a diagonal whose endpoints are given
  • Use this mid-point to find the missing vertex
  • The mid point rule is (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

∵ WXYZ is a parallelogram

∴ Its diagonals are WY and XZ

∵ The diagonal bisect each other

- That mean they have the same mid-point

∴ They intersect each other at their mid-point

∵ x = (-2 , -3) and z = (7 , 7)

∴ x_{1} = -2 and x_{2} = 7

∴ y_{1} = -3 and y_{2} = 7

- Substitute them in the rule of the mid point to find the

   mid-point of XZ

∴ M_{XZ}=(\frac{-2+7}{2},\frac{-3+7}{2})=(2.5 , 2)

∴ The mid-point of diagonals WY and XZ is (2.5 , 2)

Let us use it to find the coordinates of vertex W

∵ W = (x , y) and Y = (0 , 5)

∴ x_{1} = x and x_{2} = 0

∴ y_{1} = y and y_{2} = 5

- Equate 2.5 by the rule of the x-coordinate of the mid-point

∵ 2.5=\frac{x+0}{2}

- Multiply both sides by 2

∴ 5 = x + 0

∴ 5 = x

∴ The x-coordinate of point W is 5

- Equate 2 by the rule of the y-coordinate of the mid-point

∵ 2=\frac{y+5}{2}

- Multiply both sides by 2

∴ 4 = y + 5

- Subtract 5 from both sides

∴ -1 = y

∴ The y-coordinate of point W is -1

The coordinates of the vertex W are (5 , -1)

Learn more:

You can learn more about the mid-point in brainly.com/question/10480770

#LearnwithBrainly

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Step-by-step explanation:

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Step-by-step explanation:

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The school cafeteria sells two types of wraps vegetarian and chicken the vegetarian wrap costs $1.00 and the chicken wrap costs
IRINA_888 [86]

Answer:

35

Step-by-step explanation:

Let's make a system of equations for the vegetarian and chicken wraps; one for the total cost of them and one for the total amount sold.

Vegetarian wraps will be represented by variable v and chicken wraps will be represented by the variable c.

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Subtract these equations.

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Divide both sides by 2.40.

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Substitute this value for c into the second equation.

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Subtract 68 from both sides.

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The number of vegetarian wraps sold amounted to 35 in total.

3 0
3 years ago
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DedPeter [7]

Answer:

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Step-by-step explanation:

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V = 1/3 * 5 * 4 = 20/3

20/3  or  6.67  or  6 \frac{2}{3}

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