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3 years ago

Please help!!!!!!!!!!!

Mathematics

1 answer:

boyakko [2]3 years ago

4 0

Answer:

(7√6)/2

Step-by-step explanation:

The side ratios in these special triangles are ...

30°-60°-90° triangle: 1 : √3 : 2

45°-45°-90° triangle: 1 : 1 : √2

This tells you the length of the horizontal line is 7√3, and the value of x is ...

(7√3)/√2 = (7√6)/2

_____

<em>Additional comment</em>

Call the length of the horizontal line "y". Then the given ratios tell you ...

7 : y = 1 : √3 ⇒ y/7 = √3/1 ⇒ y = 7√3

and

x : y = 1 : √2 ⇒ x/y = 1/√2 ⇒ x = y/√2

When we rationalize the denominator, we get ...

x = (y√2)/2 = ((7√3)√2)/2 = (7√6)/2

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27.1% of city employees ride the bus to work. This is up 47% from last year. What percent of employees rode the bus to work last

dolphi86 [110]

Answer:

18.44%

Step-by-step explanation:

Let :

Percentage who rode bus to work last year = x

Percentage who ride bus to work this year = 27.1%

Percentage who ride bus to work this year = [percentage who rode bus to work last year + 47% of percentage who rode bus to work last year]

Mathematically ;

27.1% = x + 47% of x

0.271 = x + (0.47x)

0.271 = x + 0.47x

0.271 = 1.47x

x = 0.271 / 1.47

x = 0.1843537

x = 0.1843537 * 100%

x = 18.435%

x = 18.44%

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3 years ago

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RUDIKE [14]

Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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mixer [17]

I believe you are correct

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F(x)=(x-6)e^-3x find the interval in which f(x) is increasing, the intervals on which f(x) is decreasing, and the local extrema

Over [174]

$\bf f(x)=(x-6)e^{-3x}\\\\
-----------------------------\\\\
\cfrac{dy}{dx}=1\cdot e^{-3x}+(x-6)-3e^{-3x}\implies \cfrac{dy}{dx}=e^{-3x}[1-3(x-6)]
\\\\\\
\cfrac{dy}{dx}=e^{-3x}(19-3x)\implies \cfrac{dy}{dx}=\cfrac{19-3x}{e^{3x}}$

set the derivative to 0, solve for "x" to get any critical points
keep in mind, setting the denominator to 0, also gives us critical points, however, in this case, the denominator will never be 0, so... no critical points from there

there's only 1 critical point anyway, and do a first-derivative test on it, check a number before it and after it, to see what sign the derivative has, and thus, whether the graph is going up or down, to check for any extrema

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3 years ago