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3 years ago

Please tell me the answer with explanation.

Mathematics

1 answer:

nikitadnepr [17]3 years ago

7 0

Answer:

HELLO DEAR,

GIVEN:-

10sin⁴A + 15cos⁴A = 6

=> 10(sin²A)² + 15cos⁴A = 6

=> 10{(1 - cos²A)²} + 15cos⁴A = 6

=> 10{1 + cos⁴A - 2cos²A} + 15cos⁴A = 6

=> 10 + 10cos⁴A - 20cos²A + 15cos⁴A = 6

=> 25cos⁴A - 20cos²A + 4 = 0

=> 25cos⁴A - 10cos²A - 10cos²A + 4 = 0

=> 5cos²A(5cos²A - 2) - 2(5cos²A - 2) = 0

=> (5cos²A - 2)(5cos²A - 2) = 0

=> cos²A = 2/5

=> cosA = √2/√5 [ secA = √5/√2]

therefore,

sinA = √[1 - 2/5] = √3/√5 [ cosecA = √5/√3]

now,

27cosec^6A + 8sec^6A

=> 27 × {(√5/√3)²}³ + 8 × {(√5/√2)²}³

=> 27 × 125/27 + 8 × 125/8

=> 125 + 125

=> 250.

HENCE, 27cosec^6A + 8sec^6A = 250.

I HOPE IT'S HELP YOU DEAR,

THANKS

Step-by-step explanation:

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Answer:

y = -2

Step-by-step explanation:

SOLUTION :-

Solve the equation.

Add 8 to both sides in order to isolate the equation.

$=> y - 8 + 8 = -10 + 8$

$=> y = -2$

∴ y = -2

VERIFICATION :-

To verify the solution of y , just put the solution (y = -2) in place of y in equation and check whether L.H.S = R.H.S.

L.H.S :-

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R.H.S. :-

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Answer:

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3 years ago

Ana drew a map of the Panama Canal. In the scale Ana used for the map, 4 centimeters represents 20 kilometers. The actual length

yawa3891 [41]

Answer:

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Step-by-step explanation:

If actual length of Panama Canal = 20 kilometers

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= $\frac{4}{20}$

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3 years ago

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Answer:

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Step-by-step explanation:

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In this question:

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3 years ago

A line m is perpendicular to an angle bisector of ∠A. The sides of ∠A intersect this line m at points M and N. Prove that △AMN i

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Answer:

Step-by-step explanation:

Given: A line m is perpendicular to the angle bisector of ∠A. We call this

intersecting point as D. Hence, in figure ∠ADM=∠ADN =90°.

AD is angle bisector of ∠A. Hence, ∠MAD=∠NAD.

To Prove: ΔAMN is an isosceles triangle. i.e any two sides in ΔAMN are

equal.

Solution: Now, In ΔADM and ΔADN

∠MAD=∠NAD ...(1) (∵Given)

AD=AD ...(2) (∵common side)

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Hence, from equation (1),(2),(3) ΔADM ≅ ΔADN

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Now, In Δ AMN

AM=AN (∵ Proved)

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7 0

3 years ago

Please tell me the answer with explanation.​

Please tell me the answer with explanation.