<span>We are given that ||e|| = 1, ||f|| = 1. </span>
<span>Since ||e + f|| = sqrt(3/2), we have </span>
<span>3/2 = (e + f) dot (e + f) </span>
<span>= (e dot e) + 2(e dot f) + (f dot f) </span>
<span>= ||e||^2 + 2(e dot f) + ||f||^2 </span>
<span>= 1^2 + 2(e dot f) + 1^2 </span>
<span>= 2 + 2(e dot f). </span>
<span>So e dot f = -1/4. </span>
<span>Therefore, </span>
<span>||2e - 3f||^2 = (2e - 3f) dot (2e - 3f) </span>
<span>= 4(e dot e) - 12(e dot f) + 9(f dot f) </span>
<span>= 4||e||^2 - 12(e dot f) + 9||f||^2 </span>
<span>= 4(1)^2 - 12(-1/4) + 9(1)^2 </span>
<span>= 4 + 3 + 9 </span>
<span>= 16. </span>
Answer:
B.) Invalid Argument
Step-by-step explanation:
Just because Fido is not a cow does not mean that he will automatically be brown. It is already stated that some cows(something Fido is not) are colored brown.
Answer:
8.245*10^6
Step-by-step explanation:
scientific notation is known as c*10^n
c : any number from 1-10
n : the power of base 10
the number in our case between 1 and 10 is 8.245
but then we want to move the decimal 6 spaces to the right, so we multiply that by 10^6
The yield per acre will be given by:
[total amount of bushels sold]/[area of the field]
Total amount sold=64100+8120=72220
area=488 acres
thus
72220/488
=147.992~148 bushels per acre
Answer:
To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.
Begin with the right hand side:
R.H.S = cot θ = 
L.H.S = sin θ cos θ
so, sin θ cos θ ≠
So, the equation is not a trigonometric identity.
=========================================================
<u>Anther solution:</u>
To prove that ( sin θ cos θ = cot θ ) is not a trigonometric identity.
Assume θ with a value and substitute with it.
Let θ = 45°
So, L.H.S = sin θ cos θ = sin 45° cos 45° = (1/√2) * (1/√2) = 1/2
R.H.S = cot θ = cot 45 = 1
So, L.H.S ≠ R.H.S
So, sin θ cos θ = cot θ is not a trigonometric identity.
