All categories

2 years ago

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

2 answers:

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]2 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!

You might be interested in

Jacob solves the system of equations by forming a matrix equation.

Lyrx [107]

Simultaneous equations can be solved using inverse matrix operation.

The complete steps of Jacob's solution are:

$\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]^{-1} \cdot \left[\begin{array}{cc}4&1\\-2&3\end{array}\right]\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14}\left[\begin{array}{cc}3&-1\\2&4\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

We have:

$4x + y = 2$

$-2x + 4y = -22$

Calculate the determinant of $\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

$|A| = 4 \times 3 -1 \times -2$

$|A| = 12 +2$

$|A| = 14$

So, the inverse matrix becomes

$A = \frac{1}{14}\left[\begin{array}{cc}4&1\\-2&3\end{array}\right]$

Replace the first column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of x

$x = \frac{1}{14}\left[\begin{array}{cc}2&1\\-22&3\end{array}\right]$

So, we have:

$x = \frac{1}{14}(2 \times 3 - 1 \times -22)$

$x = \frac{1}{14}(6 +22)$

$x = \frac{1}{14}(28)$

$x = 2$

Replace the second column with $\left[\begin{array}{c}2&-22\end{array}\right]$ to calculate the value of y

$y = \frac{1}{14}\left[\begin{array}{cc}4&2\\-2&-22\end{array}\right]$

So, we have:

$y = \frac{1}{14}(4 \times -22 - 2 \times -2)$

$y = \frac{1}{14}(-88 +4)$

$y = \frac{1}{14}(-84)$

$y = -6$

Hence, the complete process is:

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{cc}4&1\\-2&3\end{array}\right] \cdot \left[\begin{array}{c}2&-22\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \frac{1}{14} \left[\begin{array}{c}28&-84\end{array}\right]$

$\left[\begin{array}{c}x&y\end{array}\right] = \left[\begin{array}{c}2&-6\end{array}\right]$

Read more about matrices at:

brainly.com/question/11367104

6 0

1 year ago

Use the appropriate normal distribution to approximate the resulting binomial distributions. A convenience store owner claims th

Naddika [18.5K]

Answer:

0.9256

Step-by-step explanation:

Given that a convenience store owner claims that 55% of the people buying from her store, on a certain day of the week, buy coffee during their visit

Let X be the number of customers who buy from her store, on a certain day of the week, buy coffee during their visit

X is Binomial (35, 0.55)

since each customer is independent of the other and there are two outcomes.

By approximation to normal we find that both np and nq are >5.

So X can be approximated to normal with mean = np = 19.25

and std dev = $\sqrt{npq} \\=2.943$

Required probability = prob that fewer than 24 customers in the sample buy coffee during their visit on that certain day of the week

= $P(X$ (after effecting continuity correction)

= 0.9256

6 0

2 years ago

Tom supports North Storm Football Club. At the match between North Storm and West Stanford there were 71,167 spectators. If 41,1

dangina [55]

Answer:
30,058 spectator

Explanation:
The total number of spectators is equal to the sum of West Stanford's and North Storm's supporters.
We are given that:
Total number of spectators = 71,167 spectator
North Storm spectators = 41,109 spectator
So, to get the number of West Stanford spectators, all we have to do is subtract North Storm spectators from the total spectators as follows:
West Stanford spectators = 71,167 - 41,109 = 30,058 spectator

Hope this helps :)

8 0

2 years ago

Peter is at a lumber yard. He gets 2 free boxes of nails for every 10 boards he buys. Write an expression for the number of boxe

Sati [7]

A. The number of 10-boards Peter bought is equal to n divided by 10. Then, each of the 10-boxes will get two boxes of nails. The number of boxes of nails that Peter will have after buying n boards will be,

N = (2)(n/10)

Simplifying,

 N = n/5

b. If the number of boards are 90 then,

N2 = (90/10)(2)(100 nails/box)
N2 = 1800

Answer: 1800

7 0

2 years ago

Read 2 more answers

Consider the circle of radius 10 centered at the origin. provide answers accurate to two decimal places. (a) the equation of the

Shkiper50 [21]

(a) The equation of the tangent line can be written as
.. 3(x +6) -4(y -8) = 0
.. 3x -4y = -50
.. y = (3/4)x +25/2 . . . the equation of the tangent line

(b) The point of tangency will be the intersection of the circle with the perpendicular line through the circle center, y = (-1/5)x. A graphing calculator shows that point to be
.. (9.81, -1.96)

7 0

2 years ago

Read 2 more answers