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s344n2d4d5 [400]
3 years ago
12

PLZ ANSWER QUICK-MATH TRIG

Mathematics
1 answer:
IRISSAK [1]3 years ago
7 0

Answer:

FG = 9.7ft

Step-by-step explanation:

Find the diagram in the attachment.

The diagram is a right angled triangle since one of its angle is 90°

Using SOH CAH TOA to calculate the length FG which is the hypotenuse.

According to SOH

Sin∠G = Opposite/Hypotenuse

To get the ∠G,

∠F+∠H+∠G = 180°

18°+90°+∠G = 180°

∠G = 180°-108°

∠G = 72°

Sin72° = 9.2/FG

FG = 9.2/sin72°

FG = 9.67feet

FG = 9.7ft (to the nearest tenth of a foot)

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Step-by-step explanation:

We have been an integral \int \frac{9+\sqrt{x}+x}{x}dx. We are asked to find the general solution for the given indefinite integral.

We can rewrite our given integral as:

\int \frac{9}{x}+\frac{\sqrt{x}}{x}+\frac{x}{x}dx

\int \frac{9}{x}+\frac{1}{\sqrt{x}}+1dx

Now, we will apply the sum rule of integrals as:

\int \frac{9}{x}dx+\int \frac{1}{\sqrt{x}}dx+\int 1dx

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Using common integral \int \frac{1}{x}dx=\text{ln}|x|, we will get:

9\text{ln}|x|+\int x^{-\frac{1}{2}}dx+\int 1dx

Now, we will use power rule of integrals as:

9\text{ln}|x|+\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+\int 1dx

9\text{ln}|x|+\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+\int 1dx

9\text{ln}|x|+2x^{\frac{1}{2}}+\int 1dx

9\text{ln}|x|+2\sqrt{x}+\int 1dx

We know that integral of a constant is equal to constant times x, so integral of 1 would be x.

9\text{ln}|x|+2\sqrt{x}+x+C

Therefore, our required integral would be 9\text{ln}|x|+2\sqrt{x}+x+C.

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