The solution to the question is:
c is 6 = ![\sqrt{a^{2} + b^{2} -2abcosC }](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%20-2abcosC%20%7D)
b is 5 = ![\sqrt{a^{2} + c^{2} -2accosB }](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-2accosB%20%20%7D)
cosB is 2 = ![\frac{a^{2} + c^{2} - b^{2} }{2ac}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%20b%5E%7B2%7D%20%20%20%7D%7B2ac%7D)
a is 4 = ![\sqrt{b^{2} + c^{2} -2bccosA }](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-2bccosA%20%7D)
cosA is 3 = ![\frac{b^{2} + c^{2} -a^{2} }{2bc}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-a%5E%7B2%7D%20%20%20%7D%7B2bc%7D)
cosC is 1 = ![\frac{b^{2} + a^{2} - c^{2} }{2ab}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20%20%2B%20a%5E%7B2%7D%20-%20c%5E%7B2%7D%20%20%7D%7B2ab%7D)
<h3>What is cosine rule?</h3>
it is used to relate the three sides of a triangle with the angle facing one of its sides.
The square of the side facing the included angle is equal to the some of the squares of the other sides and the product of twice the other two sides and the cosine of the included angle.
Analysis:
If c is the side facing the included angle C, then
=
+
-2ab cos C-----------------1
then c = ![\sqrt{a^{2} + b^{2} -2abcosC }](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%20-2abcosC%20%7D)
if b is the side facing the included angle B, then
=
+
-2accosB-----------------2
b = ![\sqrt{a^{2} + c^{2} -2accosB }](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-2accosB%20%20%7D)
from equation 2, make cosB the subject of equation
2ac cosB =
+
- ![b^{2}](https://tex.z-dn.net/?f=b%5E%7B2%7D)
cosB = ![\frac{a^{2} + c^{2} - b^{2} }{2ac}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%20b%5E%7B2%7D%20%20%20%7D%7B2ac%7D)
if a is the side facing the included angle A, then
=
+
-2bccosA--------------------3
a = ![\sqrt{b^{2} + c^{2} -2bccosA }](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-2bccosA%20%7D)
from equation 3, making cosA subject of the equation
2bcosA =
+
- ![a^{2}](https://tex.z-dn.net/?f=a%5E%7B2%7D)
cosA = ![\frac{b^{2} + c^{2} -a^{2} }{2bc}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-a%5E%7B2%7D%20%20%20%7D%7B2bc%7D)
from equation 1, making cos C the subject
2abcosC =
+
- ![c^{2}](https://tex.z-dn.net/?f=c%5E%7B2%7D)
cos C = ![\frac{b^{2} + a^{2} - c^{2} }{2ab}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20%20%2B%20a%5E%7B2%7D%20-%20c%5E%7B2%7D%20%20%7D%7B2ab%7D)
In conclusion,
c is 6 = ![\sqrt{a^{2} + b^{2} -2abcosC }](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E%7B2%7D%20%2B%20b%5E%7B2%7D%20%20-2abcosC%20%7D)
b is 5 = ![\sqrt{a^{2} + c^{2} -2accosB }](https://tex.z-dn.net/?f=%5Csqrt%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-2accosB%20%20%7D)
cosB is 2 = ![\frac{a^{2} + c^{2} - b^{2} }{2ac}](https://tex.z-dn.net/?f=%5Cfrac%7Ba%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-%20b%5E%7B2%7D%20%20%20%7D%7B2ac%7D)
a is 4 = ![\sqrt{b^{2} + c^{2} -2bccosA }](https://tex.z-dn.net/?f=%5Csqrt%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-2bccosA%20%7D)
cosA is 3 = ![\frac{b^{2} + c^{2} -a^{2} }{2bc}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20%2B%20c%5E%7B2%7D%20-a%5E%7B2%7D%20%20%20%7D%7B2bc%7D)
cosC is 1 = ![\frac{b^{2} + a^{2} - c^{2} }{2ab}](https://tex.z-dn.net/?f=%5Cfrac%7Bb%5E%7B2%7D%20%20%2B%20a%5E%7B2%7D%20-%20c%5E%7B2%7D%20%20%7D%7B2ab%7D)
Learn more about cosine rule: brainly.com/question/4372174
$SPJ1
Answer is 1.538
Using (x1,y1)(x2,y2)
x1=0
Y1=2
X2=5.2
Y2=10
Volume=length times width times height
it is possible for us to have a shorter length but have greater volume if the other 2 dimentions (width and height) are sufficiently great to compensate
example
box a is length 2, width 10 and height 20, volume is 400 cubic units
box b is length 3, width 4, and height 5, volume is 60 cubic units
the width and heigth must be greater
Answer:
-2/3
Step-by-step explanation:
rise/run
She worked 4 days on the food drive because to do math with these two fractions, you have to give them the same denominator. So, 12 2/3 becomes 12 4/6. Then, how many times does 3 go into 12? 4 times so the answer is 4. Hope this helped :)