Area of circle = π · r²
9 π = π · r²
9 = r²
3 = r
Volume of sphere = (4/3)π · r³
= (4/3)π · (3)³
= 4π · 3²
= 4π · 9
= 36π
Answer: the volume of the sphere is 36π
<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>
x is the radius, so you just have to do circumference backwards so that you can find the diameter and cut it in half, thats how you find x
Answer:
Step-by-step explanation:
a.
Kenji ran faster than the class average by 0.25 of a standard deviation while Nedda was slower than the average in her class.
b.
Rachel: average - 1st deviation
Kenji: average - 0.25 standard deviation
Nedda: slower than average so it's definitely not her.
Since Rachel is faster than the average and differs by the most standard deviations compared with Kenji,
So, Rachel is the faster one.