Answer:
Step-by-step explanation:
Standard form:
Vertex form:
(h, k) is the vertex
x is the coordinate of the vertex
To find x use the formula:
a=1
b=-2
c=-6
Substitute:
Substitute x in equation:
h=1
k=-7
Substitute h, and k into the vertex formula:
<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:
3125 cm
Step-by-step explanation:
The distance between two villages is 0.625 km. Find the length in centimetres between the two villages on a map with a scale of 1:5000.
We are given the scale of
1: 5000
This means
1 km = 5000 cm
Hence:
1 km = 5000cm
0.625 km = x cm
Cross Multiply
x cm = 0.625 × 5000 cm
x cm = 3125 cm
Therefore, the length in centimetres between the two villages is 3125cm
Answer:
The left side 45.041¯645.0416‾ is not less than the right side 42 which means that the given statement is false.
