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2 years ago

7

The fire department needs to rescue a man from a house. There is a large, unstable puddle below the house. The ladder needs to b

e placed 60 feet from the house and reach up to a 40 foot window. How long must the ladder be?

2 answers:

nevsk [136]2 years ago

5 0

Answer: 100 feet

Step-by-step explanation:

60+40=100

s2008m [1.1K]2 years ago

4 0

Answer:

at least 73 feet

Step-by-step explanation:

40^2+60^2=5200

square root 5200=72

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An equation is shown below: 6(2x - 11) 15 = 21 Write the steps you will use to solve the equation and explain each step.

kolbaska11 [484]

Answer:

x=6

Step-by-step explanation:

6(2x -11) 15 =21

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12x -66 + 15 = 21

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12x -51 = 21

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3 years ago

How many yards equal 27 feet

hram777 [196]

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3 years ago

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SOLUTION We observe that f '(x) = -1 / (1 + x2) and find the required series by integrating the power series for -1 / (1 + x2).

Ann [662]

Answer:

Required series is:

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

Step-by-step explanation:

Given that

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

We know that:

$\frac{d}{dx}(tan^{-1}x)=\frac{1}{1+x^{2}}$ ---(2)

Comparing (1) and (2)

$f'(x)=-(tan^{-1}x)$ ---- (3)

Using power series expansion for $tan^{-1}x$

$f'(x)=-tan^{-1}x=-\int {\frac{1}{1+x^{2}} \, dx$

$= -\int{ \sum\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$= -\sum{ \int\limits^{ \infty}_{n=0} (-1)^{n}x^{2n}} \, dx$

$=-[c+\sum\limits^{ \infty}_{n=0} (-1)^{n}\frac{x^{2n+1}}{2n+1}]$

$=C+\sum\limits^{ \infty}_{n=0} (-1)^{n+1}\frac{x^{2n+1}}{2n+1}$

$=C-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

as

$tan^{-1}(0)=0 \implies C=0$

Hence,

$\int{\frac{-1}{1+x^{2}} \, dx =-x+\frac{x^{3}}{3}-\frac{x^{5}}{5}+\frac{x^{7}}{7}+.....$

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3 years ago

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Eva8 [605]

Answer:

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3 years ago

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