All categories

4 years ago

Find a ⋅ b. a = 4i - 4j, b = 4i + 5j

Mathematics

2 answers:

Alchen [17]4 years ago

8 0

ANSWER

$a \cdot \: b = - 4$

EXPLANATION

The dot product of two vectors

$a = xi + yj$

and

$b = mi + nj$

is given by

$a \cdot \: b = mx + ny$

The given vectors are:

$a = 4i - 4j$

$b = 4i + 5j$

Applying the above definition of dot products, we obtain:

$a \cdot \: b = 4 \times 4 + - 4 \times 5$

$a \cdot \: b = 16 - 20$

$a \cdot \: b = - 4$

svetoff [14.1K]4 years ago

7 0

Answer:

value of a.b = -4

Step-by-step explanation:

We need to find a.b

a= 4i-4j

b = 4i+5j

We know that i.i =1, j.j=1, i.j =0 and j.i=0

a.b = (4i-4j).(4i+5j)

a.b = 4i(4i+5j)-4j(4i+5j)

a.b = 16i.i +20i.j-16j.i-20j.j

a.b = 16(1) +20(0)-16(0)-20(1)

a.b = 16 +0-0-20

a.b = 16-20

a.b =-4

So, value of a.b = -4

You might be interested in

Question 4 (Essay Worth 10 points)

enot [183]

As the GCF is 3x let us write a polynomial and then multiply it by 3x.

Here is a polynomial: $x^{2} +5x-1$

If we multiply it by 3x we get $(3x)( x^{2} +5x-1)$ . Since we have a product (two expressions being multiplied together) this is factored. So this is the factored form of the polynomial we created with GCF of 3x.

Let’s multiply the terms in the parenthesis by 3x to get the same polynomial but written a different way:
$3 x^{3}+15 x^{2} -3x$ . This is the factorable polynomial and the one we had before is the factored polynomial (also an equivalent form)

To get another equivalent form I could multiply out only the first term. This gives us $3 x^{3}+3x(5x-1)$ another equivalent form.

3 0

3 years ago

If your expression contains square roots, during which step of PEMDAS do you solve them? A parentheses B exponents C multiplicat

Zielflug [23.3K]

Answer:

Step-by-step explanation:

Roots can also be represented as indicies (exponents) and thus should be treated like them. For example, square root could also be written as exponent 1/2.

3 0

4 years ago

Inverse of y=log(x+1)

atroni [7]