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6 months ago

Determine the exact value of sin 240

Mathematics

1 answer:

iren2701 [21]6 months ago

7 0

simplify : the exact value of sin 240

Explanation: sin(240)=sin(60+180)=-sin60

$\begin{gathered} -sin60=-\frac{\sqrt{3}}{2} \\ =-0.87 \end{gathered}$

Final answer: the required vaalue of the sin 240 is -0.87

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Answer:

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Step-by-step explanation:

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2 years ago

Find the linear approximation of the function g(x) = 3 root 1 + x at a = 0. g(x). Use it to approximate the numbers 3 root 0.95

Virty [35]

Answer:

$L(x)=1+\dfrac{1}{3}x$

$\sqrt[3]{0.95} \approx 0.9833$

$\sqrt[3]{1.1} \approx 1.0333$

Step-by-step explanation:

Given the function: $g(x)=\sqrt[3]{1+x}$

We are to determine the linear approximation of the function g(x) at a = 0.

Linear Approximating Polynomial, $L(x)=f(a)+f'(a)(x-a)$

a=0

$g(0)=\sqrt[3]{1+0}=1$

$g'(x)=\frac{1}{3}(1+x)^{-2/3} \\g'(0)=\frac{1}{3}(1+0)^{-2/3}=\frac{1}{3}$

Therefore:

$L(x)=1+\frac{1}{3}(x-0)\\\\$The linear approximating polynomial of g(x) is:$\\\\L(x)=1+\dfrac{1}{3}x$

(b) $\sqrt[3]{0.95}= \sqrt[3]{1-0.05}$

When x = - 0.05

$L(-0.05)=1+\dfrac{1}{3}(-0.05)=0.9833$

$\sqrt[3]{0.95} \approx 0.9833$

(c)

(b) $\sqrt[3]{1.1}= \sqrt[3]{1+0.1}$

When x = 0.1

$L(1.1)=1+\dfrac{1}{3}(0.1)=1.0333$

$\sqrt[3]{1.1} \approx 1.0333$

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Step-by-step explanation:

$\frac{1}{4} \boxed{?} \frac{3}{8} \\ \\ \frac{1}{4} = \frac{2}{8} \\ \\ \because \: 2 < 3 \\ \therefore \: \frac{1}{4} \boxed{ < } \frac{3}{8}$

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3 years ago

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Answer:

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Step-by-step explanation:

We are given g(x)=3x-4 and are asked to find (gog) (x)

gog(x)=g(g(x))

g(x)=3x-4

Hence

g(g(x))=g(3x-4)

=3(3x-4)-4

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Hence

gog(x)=9x-16

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