All categories

2 years ago

Given that OA= 11x +6y, OB=4x +10y and CO= - 13x+11y, write down each of the following vectors in its simplest form.

Mathematics

1 answer:

levacccp [35]2 years ago

8 0

Answer:

BA = 7x -4y
AC = 2x -17y

Step-by-step explanation:

a) BA = OA -OB = (11x+6y) -(4x +10y)

BA = 7x -4y

b) AC = -CO -OA = -(-13x +11y) -(11x +6y)

AC = 2x -17y

_____

The vector OC is the opposite of the vector CO.

You might be interested in

James is four years younger than Austin. If three times James' age is increased by the square of Austin's age, the result is 28.

lara31 [8.8K]

Let's use J for James's age and A for Austin's age. The equations are:

J = A - 4
3J + A² = 28

Just plug (A - 4) in the place of J in the second equation. This gives you:

3(A - 4) + A² = 28
-->
A² + 3A - 12 = 28
-->
A² + 3A - 40 = 0
-->
(A - 5)(A + 8) = 0
-->
A = 5 or -8

-8 is nonsense, so Austin is 5 years old. Therefore, James is 1 year old.

7 0

1 year ago

On a road map, the locations A, B and C are collinear. Location C divides the road from location A to B, such that AC:CB = 1:2.

koban [17]

Answer:

C. (-1,-2)

Step-by-step explanation:

Since C internally divides AB in the ratio AC/CB = 1/2 = m/n where m = 1 and n = 2, we use the formula for internal division.

Let A = (x₁, y₁) = (5, 16), B = (x₂, y₂) and C = (x, y) = (3, 10)

So x = (mx₂ + nx₁)/(m + n)

y = (my₂ + ny₁)/(m + n)

Substituting the values of the coordinates, we have

x = (mx₂ + nx₁)/(m + n)

3 = (1 × x₂ + 2 × 5)/(2 + 1)

3 = (x₂ + 10)/3

multiplying through by 3, we have

9 = x₂ + 10

x₂ = 9 - 10

x₂ = -1

y = (my₂ + ny₁)/(m + n)

10 = (1 × y₂ + 2 × 16)/(2 + 1)

10 = (x₂ + 32)/3

multiplying through by 3, we have

30 = y₂ + 32

y₂ = 30 - 32

y₂ = -2

So, the coordinates of B are (-1, -2)

3 0

1 year ago

Sierra is selling bracelets to raise money for the Language Club at school. Each bracelet with yellow beads sells for $5. Each b

matrenka [14]

Answer:

Correct answer is:

$5y+6r=660\\y=2r+8$

Step-by-step explanation:

Given that Number of bracelets with yellow beads is represented by $y$

Each bracelet with yellow beads is sold for $5.

Total money raised by bracelets with yellow beads = Number of bracelets sold $\times$ Money raised by sale of one such bracelet = $5y$

Also Given that Number of bracelets with Orange beads is represented by $r$

Each bracelet with orange beads is sold for $6.

Total money raised by bracelets with orange beads = Number of bracelets sold $\times$ Money raised by sale of one such bracelet = $6r$

Given that total money raised by sale of both type of bracelets is $660.

so, the first equation becomes:

$5y+6r=660 ....... (1)$

It is also given that "<em>The number of bracelets with yellow beads that Sierra sold is 8 more than twice the number of bracelets with orange beads</em>"

$\Rightarrow r =2r+8 ...... (2)$

So, by equation (1) and (2), the system of equations is:

$5y+6r=660\\y=2r+8$

5 0

1 year ago

PLEASE HELP A pizza parlor sells 320 pizzas per night when they charge $9.00 per pizza. The owner believes increasing the price

Sonja [21]

1. $9.00+$0.15=$9.15
2. 320-4=316

6 0

2 years ago

Alchen [17]

Answer: C)27:1

Step-by-step explanation:

Given, Kent has two similar cylindrical pipes, Pipe A and Pipe B. The radius of Pipe A is 6 cm, and the radius of Pipe B is 2 cm.

Volume of cylinder = $\pi r^2h$ , where r= radius and h = height.

Also, If two figures are similar then ratio of volume is equal to the cube of any dimension .

The ratio of the volume of Pipe A to the volume of Pipe B is given by :-

$\dfrac{\text{Volume of pipe A}}{\text{Volume of pipe B}}=\dfrac{6^3}{2^3}\\\\=\dfrac{216}{8}=\dfrac{27}{1}$

Thus, the ratio of the volume of Pipe A to the volume of Pipe B = 27:1

So, the correct option is C)27:1.

7 0

1 year ago