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Ad libitum [116K]
3 years ago
14

Find the unit vector in the direction of (4,-4). Write your answer in component form. Do not approximate any numbers in your ans

wer.
Mathematics
1 answer:
aniked [119]3 years ago
7 0

Answer:

(\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} }  )

Step-by-step explanation:

The unit vector for a nonzero vector, say u, in the direction of u is given by:

û = \frac{u}{|u|}             ---------------(i)

Where;

|u| = magnitude of vector u

From the question;

u = (4, -4)

First let's calculate the magnitude of u as follows;

|u| = \sqrt{(4)^2 + (-4)^2}

|u| = \sqrt{16 + 16}

|u| = \sqrt{32} = 4\sqrt{2}

Now, substitute u and |u| into equation (i) as follows;

û = \frac{(4, -4)}{4\sqrt{2} }

û = (\frac{4}{4\sqrt{2} }, \frac{-4}{4\sqrt{2} }  )

û = (\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} }  )

Therefore, the unit vector is (\frac{1}{\sqrt{2} }, \frac{-1}{\sqrt{2} }  )

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In the circle below, DB = 22 cm, and m<DBC = 60°. Find BC. Ignore my handwriting.​
Karo-lina-s [1.5K]

Answer:

BC=11\ cm

Step-by-step explanation:

step 1

Find the measure of the arc DC

we know that

The inscribed angle measures half of the arc comprising

m\angle DBC=\frac{1}{2}[arc\ DC]

substitute the values

60\°=\frac{1}{2}[arc\ DC]

120\°=arc\ DC

arc\ DC=120\°

step 2

Find the measure of arc BC

we know that

arc\ DC+arc\ BC=180\° ----> because the diameter BD divide the circle into two equal parts

120\°+arc\ BC=180\°

arc\ BC=180\°-120\°=60\°

step 3

Find the measure of angle BDC

we know that

The inscribed angle measures half of the arc comprising

m\angle BDC=\frac{1}{2}[arc\ BC]

substitute the values

m\angle BDC=\frac{1}{2}[60\°]

m\angle BDC=30\°

therefore

The triangle DBC is a right triangle ---> 60°-30°-90°

step 4

Find the measure of BC

we know that

In the right triangle DBC

sin(\angle BDC)=BC/BD

BC=(BD)sin(\angle BDC)

substitute the values

BC=(22)sin(30\°)=11\ cm

6 0
3 years ago
The bakery makes 6 pies. Each slice is V8 of the whole pie. How many slices are there
ANEK [815]

Answer:

6

Step-by-step explanation:

4 0
3 years ago
Evaluate A + 3B if possible. HELP ASAP!
madreJ [45]

Answer:

Not possible.

Step-by-step explanation:

Addition of Matrix A and Matrix B is possible only if the order of matrix A is same as the order of matrix B.

Order of a matrix with m rows and n columns is m\times n.

Here, matrix A is \left[\begin{array}{ccc}2&-4\\-4&10\\0&-8\end{array}\right]

Matrix B is \left[\begin{array}{ccc}0&-4&6\\2&-10&4\end{array}\right].

Multiplying a matrix by a constant doesn't change its order.

So, order of matrix A is 3\times 2 as it has 3 rows and 2 columns.

The order of matrix 3B is 2\times 3 as it has 2 rows and 3 columns.

Therefore, addition is not possible as the order is different.

4 0
3 years ago
Find the geometric mean of 32 and 2
Dmitry [639]
The geometric mean of 32 and 2 is 8
7 0
2 years ago
(Geometry), homework please Help me , will rate brainliestttt
amid [387]

9 the smallest angle is always opposite the smallest side


Answer: choice d, angle B


They couldn't match the choice letters with the angles? Geez.


10.  That's an isoscles triangle


d + d + 116 = 180


2d = 64


d=32


choice a


11. 62+45+k=180


k=180-107 = 73


choice b



6 0
2 years ago
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