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Phoenix [80]
3 years ago
9

9. Given a circle with a radius of 6, determine its sector area with an angle measure of 120°.

Mathematics
1 answer:
Sergio039 [100]3 years ago
4 0

Answer:

2160 square units

Step-by-step explanation:

Given data

Radius= 6 units

Angle= 120°

Area of the sector is given as

Area of sector= r^2* ∅/2

Area of sector= 6^2*120/2

Area of sector= 36*60

Area of sector= 2160 square units

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If f(x)=2x+sinx and the function g is the inverse of f then g'(2)=
Alexxx [7]
\bf f(x)=y=2x+sin(x)
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inverse\implies x=2y+sin(y)\leftarrow f^{-1}(x)\leftarrow g(x)
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\textit{now, the "y" in the inverse, is really just g(x)}
\\\\\\
\textit{so, we can write it as }x=2g(x)+sin[g(x)]\\\\
-----------------------------\\\\

\bf \textit{let's use implicit differentiation}\\\\
1=2\cfrac{dg(x)}{dx}+cos[g(x)]\cdot \cfrac{dg(x)}{dx}\impliedby \textit{common factor}
\\\\\\
1=\cfrac{dg(x)}{dx}[2+cos[g(x)]]\implies \cfrac{1}{[2+cos[g(x)]]}=\cfrac{dg(x)}{dx}=g'(x)\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}

now, if we just knew what g(2)  is, we'd be golden, however, we dunno

BUT, recall, g(x) is the inverse of f(x), meaning, all domain for f(x) is really the range of g(x) and, the range for f(x), is the domain for g(x)

for inverse expressions, the domain and range is the same as the original, just switched over

so, g(2) = some range value
that  means if we use that value in f(x),   f( some range value) = 2

so... in short, instead of getting the range from g(2), let's get the domain of f(x) IF the range is 2

thus    2 = 2x+sin(x)

\bf 2=2x+sin(x)\implies 0=2x+sin(x)-2
\\\\\\
-----------------------------\\\\
g'(2)=\cfrac{1}{2+cos[g(2)]}\implies g'(2)=\cfrac{1}{2+cos[2x+sin(x)-2]}

hmmm I was looking for some constant value... but hmm, not sure there is one, so I think that'd be it
5 0
3 years ago
Write an equivalent expression for (x - 11)(x + 9).
vodka [1.7K]

Answer:

x²-2x-99

Step-by-step explanation:

(x-11)(x+9) - foil method

x times x = x squared

x times 9 = 9x

-11 times x = -11x

-11 times 9 = -99

x squared + 9x + 11x + -99

x squared-2x-99

7 0
3 years ago
Which shows the correct substitution of the values a, b, and c from the equation 1 = –2x + 3x2 + 1 into the quadratic formula?
Alchen [17]
1=-2x+3x^2+1\\\\3x^2-2x+1-1=0\\\\3x^2-2x=0\\\\\boxed{a=3;\ b=-2;\ c=0}
6 0
3 years ago
Read 2 more answers
Can someone help me with this problem
user100 [1]

Answer:

About 110.6

Step-by-step explanation:

The sine of an angle is the length of the opposite side divided by the length of the hypotenuse.

\sin 19= \dfrac{36}{x} \\\\x=\dfrac{36}{\sin 19}\approx 110.6

Hope this helps!

5 0
3 years ago
Which of the following plans include a savings plan as a part of the insurance? Whole Life Universal Life Variable Universal Lif
worty [1.4K]

Answer:

Which of the following plans include a savings plan as a part of the insurance?

Whole Life

Universal Life

<u>Variable Universal Life</u>

All of the above

Step-by-step explanation:

6 0
3 years ago
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