2 years ago

Consider f(x)=7x^2+8/x−6. Complete the following statements.

Mathematics

1 answer:

kirill [66]2 years ago

7 0

Answer:

Step-by-step explanation:

Iwis

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If tanA+sinA=m and tanA-sinA=n.prove that m^2-n^2=4√mn

mash [69]

Let $a=\tan A$ and $b=\sin A$ . Then

$m^2-n^2=(a+b)^2-(a-b)^2=(a^2+2ab+b^2)-(a^2-2ab+b^2)=4ab$

$\implies m^2-n^2=4\tan A\sin A$

and

$mn=(a+b)(a-b)=a^2-b^2$

$\implies4\sqrt{mn}=4\sqrt{\tan^2A-\sin^2A}$

The expression under the square root can be rewritten as

$\tan^2A-\sin^2A=\dfrac{\sin^2A}{\cos^2A}-\sin^2A=\sin^2A\left(\dfrac1{\cos^2A}-1\right)=\sin^2A(\sec^2A-1)$

Recall that

$\sin^2A+\cos^2A=1\implies\tan^2A+1=\sec^2A$

so that

$\tan^2A-\sin^2A=\sin^2A\tan^2A$

and assuming $\sin A>0$ and $\tan A>0$ , we end up with

$4\sqrt{\tan^2A-\sin^2A}=4\tan A\sin A$

so that

$m^2-n^2=4\sqrt{mn}$

as required.

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2 years ago

Fraction (12 4/9 + 1 2/9) +3 5/9

sveticcg [70]

12 4/9 + 1 2/9=13 6/9+3 5/9=16 11/9 that answer is farther simpled 17 2/9
so the final answer is 17 2/9

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3 years ago

Based on the graph below, what is the y-intercept? -5 -3 3 5

Crank

The y-intercept is -3

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In the expression a=k over b, what is k ?

andreyandreev [35.5K]

Answer: k=ab

Step-by-step explanation:

a= $\frac{k}{b}$

ab=k

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2 years ago

What is the width of a rectangle with an area of 300 square feet and a length of L feet?

k0ka [10]

300/L . Just divide area by one side

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