The quotient of a number and 4 is at most 5

Find two unit vectors orthogonal to both given vectors. i j k, 4i k

Maurinko [17]

The cross product of two vectors gives a third vector $\mathbf v$ that is orthogonal to the first two.

$\mathbf v=(\vec i+\vec j+\vec k)\times(4\,\vec i+\vec k)=\begin{vmatrix}\vec i&\vec j&\vec k\\1&1&1\\4&0&1\end{vmatrix}=\vec i+3\,\vec j-4\,\vec k$

Normalize this vector by dividing it by its norm:

$\dfrac{\mathbf v}{\|\mathbf v\|}=\dfrac{\vec i+3\,\vec j-4\,\vec k}{\sqrt{1^2+3^2+(-4)^2}}=\dfrac1{\sqrt{26}}(\vec i+3\,\vec j-4\vec k)$

To get another vector orthogonal to the first two, you can just change the sign and use $-\mathbf v$ .

6 0

3 years ago

In physics, we can find the amount of force needed to push or pull an object by multiplying the object’s mass by the object’s ac

MariettaO [177]

750 X 2.5 =1875

Hope this helps!

8 0

3 years ago

Read 2 more answers

Consider an experiment with sample space S 5 50, 1, 2, 3, 4, 5, 6, 7, 8, 96 and the events A 5 {0, 2, 4, 6, 8} B 5 {1, 3, 5, 7,

Brut [27]

Answer with Step-by-step explanation:

S={0,1,2,3,4,5,6,7,8,9}

A={0,2,4,6,8}

B={1,3,5,7,9}

C={0,1,2,3,4}

D={5,6,7,8,9}

a.A'=S-A

A'={0,1,2,3,4,5,6,7,8,9}-{0,2,4,6,8}

A'={1,3,5,7,9}

b.C'=S-C

C'={0,1,2,3,4,5,6,7,8,9}-{0,1,2,3,4}

C'={5,6,7,8,9}

c.D'=S-D

D'={0,1,2,3,4,5,6,7,8,9}-{5,6,7,8,9}

D'={0,1,2,3,4}

d. $A\cup B=$ {0,2,4,6,8} $\cup$ {1,3,5,7,9}

$A\cup B=$ {0,1,2,3,4,5,6,7,8,9}=S

e. $A\cup C$ ={0,2,4,6,8} $\cup$ {0,1,2,3,4}

$A\cup C$ ={0,1,2,3,4,6,8}

f. $A\cup D$ ={0,2,4,6,8} $\cup$ {5,6,7,8,9}

$A\cup D$ ={0,2,4,5,6,7,8,9}

8 0

3 years ago

PLS HELP ME, I REALLY NEED THIS RIGHT NOW, 100 POINTS, IF YOU ANSWER WITH NO EXPLANATION, OR ANSWER FOR THE POINTS YOU WILL BE R

Reika [66]

9514 1404 393

Answer:

0 ≤ m ≤ 7
0.4541 cm/month; average rate of growth over last 4 months of study

Step-by-step explanation:

Part A:

The study was concluded after 7 months. The fish cannot be expected to maintain exponential growth for any significant period beyond the observation period. A reasonable domain is ...

0 ≤ m ≤ 7

__

Part B:

The y-intercept is the value when m=0. It is the length of the fish at the start of the study.

__

Part C:

The average rate of change on the interval [3, 7] is given by ...

(f(7) -f(3))/(7 -3) = (4(1.08^7) -4(1.08^3))/4 = 1.08^3·(1.08^4 -1)

≈ 0.4541 cm/month

This is the average growth rate of the fish in cm per month over the period from 3 months to 7 months.

3 0

2 years ago

Find the area of the rhombus. A= square units

Olin [163]

The answer should be 24 square units.

5 is the hypotenuse and the one we need is the base and the height. They gave us the height, which was 6 in total but 3 for the triangle. But we needed to find the base.

In order to do that, we need to use the Pythagorean Theorem.

a^2+b^2=c^2

3^2+b^2=5^2

9+b^2=25

Subtract 9 from both sides

b^2=16

Then square root both sides.

b=4.

Now that we have the base, you can then find the area of the triangle.

BH/2
4*3/2
12/2
6

So one triangle equals to 6. Then multiply that by 4 to find the area of the rhombus. Which would be 24 square units.

7 0

3 years ago