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3 years ago

Prove cotA+cotB+cotC >= square root of 3

1 answer:

7 0

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

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∆LMN ∼ ∆PON. What is the value of x? Select one: a. 28 1/3 b. 36 c. 20 d. 25

yawa3891 [41]

Answer:

Option B. 36

Step-by-step explanation:

From the figure attached,

ΔLMN ~ ΔPON

Therefore, corresponding sides of these similar triangles will be in the same ratio.

$\frac{LM}{OP}=\frac{MN}{ON}=\frac{LN}{PN}$

$\frac{LM}{OP}=\frac{MN}{ON}$

$\frac{42}{14}=\frac{x}{12}$

x = $\frac{42\times 12}{14}$

x = 36

Therefore, measure of side MN = x = 36 units

Option B. will be answer.

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3 years ago

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3 years ago

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4 years ago

Write a expression for 18.68+11.72+19.76+18.68

Ilia_Sergeevich [38]

ANSWER:

The simplified form of the given expression 18.68+11.72+19.76+18.68 after applying BODMAS rule is 4684.

SOLUTION:

The expression given to us is 18.68+11.72+19.76+18.68. We are to simplify the equation.

To simplify the equation we have to follow the BODMAS rule.

Which sets different mathematical operations at different levels of priority.

BODMAS mean brackets, of, division, multiplication, addition and subtraction.

To solve different mathematical equations we have to follow this order of priority to get the correct answer.

Now applying BODMAS rule to the given expression we have to solve it to get an answer.

18.68+11.72+19.76+18.68

As the rule states we have to do multiplication before addition. Therefore,

1224+792+1444+1224

Now pursuing the equation for addition we get

2016+2668=4684

Hence the simplified form of the given expression after applying BODMAS rule is 4684.

3 0

3 years ago