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Kaylis [27]
4 years ago
15

Given that P = (-5, 5) and Q = (-13, 10), find the component form and magnitude of 2 vector PQ.

Mathematics
2 answers:
Brut [27]4 years ago
4 0
Define unit vectors along the x-axis and the y-axis as \hat{i} , \, \hat{j} respectively.

Then the vector from P to Q is
\vec{PQ} = (-13+5)\hat{i} + (10-5)\hat{j} = -8\hat{i} + 5\hat{j}
In component form, the vector PQ is (-8,5).

The magnitude of vector PQ is
√[(-8)² + 5²] = √(89) = 9.434

Answer:
The vector PQ is (-8, 5) and its magnitude is √89  (or 9.434).
algol [13]4 years ago
3 0

Answer:

<-16, 10>, square root of 178

Step-by-step explanation:

The other user was close, BUT he forgot to multiply his work by 2, and there were a few miscalculations.

The formula to find PQ respectively is <q1-p1,q2-p2> (Note: if they ask you to find QP then just flip the formula to <p1-q1,p2-q2>)

-13-(-5)=-8

10-5=5

Multiply them by 2 to get <-16,10>

To get the magnitude you use the same formula for the first part before, then you square both of them and add them together, then take the square root.

-13-(-5)=-8

-8^2=64

10-5=5

5^2=25

64+25=89

89*2=178

Take the square root: (square root of 178)

Then your done!

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blondinia [14]

First question: Answer is D

∵ Area of rectangle is L ⋅ W = 12 ⋅ 6 = 72 ft^{2}

∵ Area of the shaded region is 36 ft^{2}

∴ The area of the unshaded region =

the area of the whole rectangle - the shaded region =

72 - 36 = 36 ft^{2}

∴ The area of the unshaded region = 36 ft^{2}

Second question: Answer is A

∵ Area of triangle is \frac{1}{2}Bh =

\frac{1}{2} ⋅ x ⋅ 4 = 32ft^{2}

∵ Height (h) = 4 ft

∴ Base (B) = \frac{32}{4} ⋅ 2 = 8 ⋅ 2 = 16

∴ Base (B) = 16 ft

Third question: Answer is D

6.009 = 6 + 0.009

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104.0032 = One hundred four and thirty-two ten-thousandths

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∵ Perimeter of rectangle = 2(W+L) =

2(80+120) = 2 ⋅ 80 + 2 ⋅ 120 = 160 + 240 = 400 ft^{2}

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3 0
3 years ago
9x^2-y^2=1
Vinvika [58]
9x^2 - y^2 = 1

a.) 18x - 2y dy/dx = 0
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c.) substituting y = √(9x^2 - 1) into solution for part a gives
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3 years ago
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Westkost [7]

Answer:

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Step-by-step explanation:

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3 years ago
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Step-by-step explanation:

For answer refer to the attachment

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8 0
3 years ago
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notsponge [240]

Answer:

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Step-by-step explanation:

The order in which the guests arrive is important. For example, A,B,C,D is a different outcome to B,A,C,D. So we use the permutations formula to solve this question.

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