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Darina [25.2K]
2 years ago
6

If sin A = 3/8, find the value of cosec A - sec A.​

Mathematics
1 answer:
alexira [117]2 years ago
6 0

Answer:

\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}

Step by step explanation:

\text{Given that,}\\\\~~~~~~\sin A = \dfrac 38 \\\\\implies \sin^2 A = \dfrac 9{64}\\\\\implies  1 - \cos^2 A = \dfrac{9}{64}\\\\\implies \cos ^2 A = 1 - \dfrac 9{64}\\\\\implies \cos^2 A = \dfrac{55}{64}\\\\\implies \cos A =\pm\sqrt{\dfrac{55}{64}}\\ \\\implies \cos A = \pm\dfrac{\sqrt{55}}8\\\\

\implies \dfrac 1{\cos A} = \pm\dfrac{8}{\sqrt{55}}

\text{Now,}\\\\\csc A - \sec A\\\\=\dfrac{1}{\sin A}- \dfrac{1}{\cos A}\\\\=\dfrac 83 -\left(\pm \dfrac 8{\sqrt {55}} \right)\\ \\\text{Hence,}\\\\\csc A - \sec A = \dfrac 83 + \dfrac{8}{\sqrt{55}}\\\\\csc A - \sec A = \dfrac 83 - \dfrac{8}{\sqrt{55}}

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8x-3(2x-4)≤ 3(x-6)
OlgaM077 [116]

The solution to the inequality expression is x ≥ 30

<h3>How to solve the inequality expression?</h3>

The inequality expression is given as:

8x - 3(2x - 4) ≤ 3(x - 6)

Open the brackets in the above inequality expression

8x - 6x + 12 ≤ 3x - 18

Collect the like terms in the above inequality expression

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Evaluate the like terms in the above inequality expression

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Hence, the solution to the inequality expression is x ≥ 30

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2 years ago
The exponential decay graph shows the expected depreciation for a new boat, selling for $3500, over 10 years a. Write an exponen
Alex Ar [27]
For the answer to the question above,  
<span>V(n) = a * b^n, where V(n) shows the value of boat after n years. 
V(0) = 3500 
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n = 0 
V(0) = a * b^0 = 3500 
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V(2) = a * b^2 
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We can check it for n = 1 which is close to 2500 in the graph: 
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And in the graph we have V(3) ≈ 1500, 
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Now n = 9.5 
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V(9.5) ≈ 258</span>
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3 years ago
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Answer:

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Answer:

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