Simplify the expression: 42 + 8 ÷ 2.

Write the vector u as a sum of two orthogonal vectors, one of which is the vector projection of u onto v, projvu u=(-8,8) , v= (

Jobisdone [24]

Answer:

none of the given options is true

Step-by-step explanation:

Given: u=(-8,8) , v= (-1,2)

To find: vectors $w_1,w_2$ such that $u=w_1+w_2$

Solution:

A vector is a quantity that has both magnitude and direction.

$proj_vu=\frac{u\cdot v}{\left | v \right |^2}(v)\\=\frac{(-8,8)\cdot (-1,2)}{(\sqrt{ (-1)^2+2^2})^2}(-1,2)\\=\frac{8+16}{5}(-1,2)\\=\frac{1}{5}(-24,48)\\=(-4.8,9.6)$

Let $w_1=(-4.8,9.6)$

So,

$w_2=u-w_1\\=(-8,8)-(-4.8,9.6)\\=(-8+4.8,8-9.6)\\=(-3.2,-1.6)$

So, u = $(-4.8,9.6)+(-3.2,-1.6)$

So, none of the given options is true

8 0

3 years ago

On Monday, Mrs. Smith drove 3.56 miles to go to the grocery store, 5.9 miles to go to the bank, and 12.087 miles to go out to di

Yuki888 [10]

Answer:

22

Step-by-step explanation:

3.56 = 4

5.9 = 6

12.087 = 12

4+6+12 = 22

6 0

3 years ago

Use to isolate the variable.

diamong [38]

What do you need help will I don't see an question or anything

6 0

2 years ago

If x+ay =b and ax-by=c Then find out x , y . (with process)

n200080 [17]

Answer:

The solution of the given system of equations is,

$x=\frac{b^2+ac}{a^2+b};\; y=\frac{ab-c}{a^2+b}$

Step-by-step explanation:

The given equations are :

x + ay = b .......(1)

ax - by = c .......(2)

We will use 'Substitution Method' to solve the given system of equations.

In this method, we will find out the value of either of the two variables that is 'x' and 'y' from one of the two equations in terms of the another variable and then substitute that value in the other equation to find the value of the another variable.

Now, we will be finding out the value of 'x' in terms of 'y' from equation (1) and then substitute it in the equation (2).

Consider the equation (1), that is,

x + ay = b ⇒ x = b - ay ........(3)

Substitute the value of 'x' from (3) in (2), we get

a(b - ay) - by = c

⇒ab - a²y - by = c

⇒-a²y - by = c - ab

⇒-y(a²+b) = c - ab

⇒y(a²+b) = ab - c

$\implies y=\frac{ab-c}{a^{2}+b}$