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zhenek [66]
3 years ago
14

A painter places an 8.5 ft ladder against a wall. the bottom of the ladder is 4 ft from the base of the wall. how high up the wa

ll does the ladder reach?
Mathematics
1 answer:
Oduvanchick [21]3 years ago
6 0
Use the Pythagorean Theorem:
a² + b² = c²
4² + b² = 8.5²
16 + b² = 72.25
        b² = 56.25
        b = 7.5

 The ladder reaches a height of 7.5 ft on the wall
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Answer:

t_3(x)=\frac{7\pi}{4}+\frac{7}{2}(x-1)-\frac{7}{4}(x-1)^2+\frac{7}{12}(x-1)^3

Step-by-step explanation:

We are given that

f(x)=7tan^{-1}(x)

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T_n(x)=\sum_{r=0}^{n}\frac{f^r(a)(x-a)^r}{r!}

Substitute n=3 and a=1

t_3(x)=f(1)+f'(1)(x-1)+\frac{f''(1)(x-1)^2}{2!}+\frac{f'''(1)(x-1)^3}{3!}

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Using the formula

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f'(1)=\frac{7}{2}

f''(x)=\frac{-14x}{(1+x^2)^2}

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By using the formula

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f'''(1)=-14(\frac{-3(1)+1}{2^3})=\frac{7}{2}

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