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pantera1 [17]
2 years ago
6

Out triangle-shaped pennants on the first day of school. If each pennant has a base of 5 inches and a height of 12 inches, what

is the area of each pennant in square inches?
Mathematics
1 answer:
brilliants [131]2 years ago
3 0

Answer:

Area of the penny = 30 square inches

Step-by-step explanation:

Out triangle-shaped pennants on the first day of school. If each pennant has a base of 5 inches and a height of 12 inches, what is the area of each pennant in square inches?

The pennant is triangular in shape. Hence:

Area of a Triangle = 1/2× Base × Height

Base of the pennant = 5 inches

Height = 12 inches

Area of the pennant = 1/2 × 5 inches × 12 inches

= 30 square inches

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Answer:

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[-1.113826815, 1.113826815]

Step-by-step explanation:

According to Taylor's theorem

\bf f(x)=f(0)+f'(0)x+f''(0)\displaystyle\frac{x^2}{2}+f^{(3)}(0)\displaystyle\frac{x^3}{3!}+f^{(4)}(0)\displaystyle\frac{x^4}{4!}+f^{(5)}(0)\displaystyle\frac{x^5}{5!}+R_6(x)

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<em> </em>

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\bf f'(x)=-sin(x)\\f''(x)=-cos(x)\\f^{(3)}(x)=sin(x)\\f^{(4)}(x)=cos(x)\\f^{(5)}(x)=-sin(x)\\f^{(6)}(x)=-cos(x)

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\bf cos(x)\approx1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{4!}=\\\\=1-\displaystyle\frac{x^2}{2}+\displaystyle\frac{x^4}{24}

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\bf R_6(x)=-cos(c)\displaystyle\frac{x^6}{6!}

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\bf |R_6(x)|\leq|\displaystyle\frac{x^6}{6!}|=\displaystyle\frac{|x|^6}{6!}

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Working this inequality out, we find

\bf \displaystyle\frac{|x|^6}{6!}\leq0.002652\Rightarrow |x|^6\leq1.90944\Rightarrow\\\\\Rightarrow |x|\leq\sqrt[6]{1.90944}\Rightarrow |x|\leq1.113826815

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