Ask question

Ask question

All categories

4 years ago

13

Find the component form of the vector v ⃗ with ‖v ⃗ ‖=4√3 when drawn in standard position v ⃗ lies in Quadrant II and makes a 30

° angle with the positive y-axis. Give exact values.

1 answer:

nydimaria [60]4 years ago

8 0

The answer:

first of all, we should know that the expression of a vector V (a, b) can be written as follow:

V = r (Vx i + Vyj), where r is the length of the vector, it is r = sqrt(V²x + V²y)
Vx is the component lying on the x-axis and Vy on the y-axis

<span>v ⃗ lies in Quadrant II, means Vx is less than 0 (negative)
</span>
so Vx= -r sin30° and Vy= rcos30°

r= <span>‖v ⃗ ‖=4√3
</span>
so we have v = - 4√3sin30° i + 4√3 cos30° j

the components are

v(- 4√3sin30°, 4√3 cos30°) = (-2√3, 4√3 cos30°)

You might be interested in

Write an equation that represents the line.<br> Use exact numbers.<br> (-2,-1)<br> (4,6)

vazorg [7]

Check the picture below.

to get the equation of any straight line, we simply need two points off of it, so let's use those in the picture

$(\stackrel{x_1}{-2}~,~\stackrel{y_1}{1})\qquad (\stackrel{x_2}{4}~,~\stackrel{y_2}{6})~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{6}-\stackrel{y1}{1}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-2)}}} \implies \cfrac{6 -1}{4 +2} \implies \cfrac{ 5 }{ 6 }$

$\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{1}=\stackrel{m}{\cfrac{5}{6}}(x-\stackrel{x_1}{(-2)})\implies y-1=\cfrac{5}{6}(x+2) \\\\\\ y-1=\cfrac{5}{6}x+\cfrac{5}{3}\implies y=\cfrac{5}{6}x+\cfrac{5}{3}+1\implies y=\cfrac{5}{6}x+\cfrac{8}{3}$

6 0

2 years ago

If one basket contains five bottles each weighing 7 1/4 ANSYS and the other basket has six apples each weighing 6 1/2 ounces woo

Tems11 [23]

<em>Question:</em>

<em>If one basket contains five bottles each weighing 7 1/4 and the other basket has six apples each weighing 6 1/2 ounces. Which basket is heavier and by how much ?</em>

Answer:

The basket of bottles weighs more than the basket of apples by $3\frac{3}{4}$ ounces

Step-by-step explanation:

Given

$Bottles = 5$

$Weight(Bottle) = 7\frac{1}{4}$

$Apples = 6$

$Weight(Apple) = 6\frac{1}{2}$

Required

Determine which basket is heavy

and by how much?

First, we need the total weight of each basket.

For the bottles' basket

$Total\ Weight = Weight * Bottles$

$Total\ Weight = 7\frac{1}{4} * 5$

$Total\ Weight = \frac{29}{4} * 5$

$Total\ Weight = \frac{29 * 5}{4}$

$Total\ Weight = \frac{145}{4}$

$Total\ Weight = 36\frac{1}{4}$

For the bottles' basket

$Total\ Weight = Weight * Apples$

$Total\ Weight = 6\frac{1}{2} * 5$

$Total\ Weight = \frac{13}{2} * 5$

$Total\ Weight = \frac{13* 5}{2}$

$Total\ Weight = \frac{65}{2}$

$Total\ Weight = 32\frac{1}{2}$

By comparing both total weights, $36\frac{1}{4} > 32\frac{1}{2}$

Hence:

The basket of bottles weighs more than the basket of apples

Calculating the difference:

$Difference = 36\frac{1}{4} - 32\frac{1}{2}$

$Difference = \frac{145}{4} - \frac{65}{2}$

$Difference = \frac{145 - 130}{4}$

$Difference = \frac{15}{4}$

$Difference = 3\frac{3}{4}$

Hence:

It weighs more by $3\frac{3}{4}$ ounces

8 0

3 years ago

△ABC is mapped to △A′B′C′ using the rule (x, y)→(−x, −y) followed by (x, y)→(x, −y) .

Oxana [17]

Answer: B. △ABC is congruent to △A′B′C′ because the rules represent a rotation followed by a reflection, which is a sequence of rigid motions.

Step-by-step explanation:

5 0

4 years ago

Read 2 more answers

Which of the following shows the best communicative property of addition ?

kumpel [21]

Answer:

In the given options, 4+5 = 5+4 shows the best commutative property.

Step-by-step explanation:

One of the properties that can be applied on numbers is commutative property. Commutative property states that the order of the numbers on which any operation is being performed, can be swapped and the answer won't change.

Commutative property can be applied on addition, subtraction and multiplication.

<u>Commutative property of Addition:</u>

Commutative property of addition states that changing the order of adding two numbers does not change the result i.e. a+b = b+a

In the given options, 4+5 = 5+4 shows the best commutative property.

3 0

3 years ago

Find the missing angle thank you

Maksim231197 [3]

Straight lines will always add up to 180 degrees, so the angle that is missing here is supplementary to the other angle(adds up with the other angle to get 180) so we take 79 away from 180 and get 101 degrees

7 0

4 years ago

Read 2 more answers