<span>Given cotA + cotB + cotC = sqrt3
to prove triangle ABC is equilateral
we prove this by assuming ABC to be equialteral and establishing the truth
of the statement cotA + cotB + cotC =sqrt3
since ABC is equialteral angleA=angleB=angleC=60 degrees
cotA=cotB=CotC = cot60= 1/sqrt3
therefore cotA + cotB + cotC = 1/sqrt3 + 1/sqrt3 + 1/sqrt3
=3/sqrt3
=sqrt3 which is equal to the RHS ( right hand side) of the expression
hence our assumption that ABC is equilateral is true</span>
Answer:
<u>Option A. 11.15 in³ </u>
Step-by-step explanation:
The question is as following:
A snow cone is a tasty treat with flavored ice and a spherical bubble gum ball at the bottom. The radius of the cone is 1.75 inches, and its height is 3.5 inches. If the diameter of the bubble gum ball is 0.5 inches, what is the closest approximation of the volume of the cone that can be filled with flavored ice?
A.) 11.15 in³
B.) 11.22 in³
C.) 0.07 in³
D.) 33.67 in³
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<u>Solution:</u>
Volume of the cone = π r² h/3
Vcone = 3.14 * (1.75in)² * 3.5in/3
Vcone = 3.14 * 3.0625 in² * 1.167
Vcone = 11.22 in³
Volume of the gum ball = 4/3 * π * r³
Vball = 4/3 * 3.14 * (0.5in/2)³
Vball = 4/3 * 3.14 * (0.25in)³
Vball = 4/3 * 3.14 * 0.015625 in³
Vball = 0.065 in³
11.22 in³ - 0.065 in³ = 11.155 in³
<u>The answer is option A. 11.15 in³ </u>
Answer:
52.4
Step-by-step explanation:
% change = 100 x final initial/initial
Answer:
19
Step-by-step explanation:
1. 7 - (-12)
2. 7 <em>- (-12)</em><em> </em>
The 12 will become a positive because when there is a "-" sign in front of the parenthesis you'll have to change it to a positive.
3. 7 + 12 = 19
You will now have to add them together. The answer will be 19.
Answer:
What does the top say its a little cut?
Step-by-step explanation: