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Ostrovityanka [42]
3 years ago
6

Find the critical numbers of f(x)=2secx+tanx in 0

Mathematics
1 answer:
Juli2301 [7.4K]3 years ago
3 0
Using the range of [ 0 , 2π ]


\bf f(x)=2sec(x)+tan(x)\implies \cfrac{df}{dx}=2sec(x)tan(x)+sec^2(x)
\\\\\\
0=2sec(x)tan(x)+sec^2(x)
\\\\\\
-sec^2(x)=2sec(x)tan(x)\implies \cfrac{-sec^2(x)}{2sec(x)}=tan(x)
\\\\\\
\cfrac{-sec(x)}{2}=tan(x)\implies \cfrac{-\frac{1}{cos(x)}}{\frac{2}{1}}=\cfrac{sin(x)}{cos(x)}
\\\\\\
-\cfrac{1}{2cos(x)}=\cfrac{sin(x)}{cos(x)}\implies -\cfrac{1}{2}=sin(x)\implies \measuredangle x =
\begin{cases}
\frac{7\pi }{6}\\\\
\frac{11\pi }{6}
\end{cases}
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ICE Princess25 [194]

Answer:

30.4 feet.

Step-by-step explanation:

We have been given the length of the ramp on the blueprint is 7.6 inches.  The scale on the blueprint is 1 inch to 4 feet. We are asked to find the actual length of the ramp.

We will use proportions to solve our given problem as:

\frac{\text{Actual length}}{\text{Scale length}}=\frac{4\text{ ft}}{1\text{ inch}}

Now, we will substitute the scale length of ramp in our proportion as:

\frac{\text{Actual length}}{7.6 \text{ Inches}}=\frac{4\text{ ft}}{1\text{ inch}}

\frac{\text{Actual length}}{7.6 \text{ Inches}}\cdot 7.6 \text{ Inches}=\frac{4\text{ ft}}{1\text{ inch}}\cdot 7.6 \text{ Inches}

\text{Actual length}=4\text{ ft}\cdot 7.6

\text{Actual length}=30.4\text{ ft}

Therefore, the actual length of the ramp would be 30.4 feet.

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Slope -2/3 .x-intercept at 3 written in y=mx+b
siniylev [52]
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Use these values and plug into the slope-intercept form to solve for the y-intercept, b:

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Add 2 to both sides to isolate b:

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Now that we have our slope, m = -2/3, and the y-intercept, 2

The linear equation in slope-intercept form is:

y = -2/3x + 2


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Answer:

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3+(-h)+(-4)

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