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statuscvo [17]
3 years ago
12

A 15-ft ladder rests against a vertical wall. If the top of the ladder slides down the wall at a rate of 0.33 ft/sec, how fast,

in ft/sec, is the bottom of the ladder sliding away from the wall, at the instant when the bottom of the ladder is 9 ft from the wall? Answer with 2 decimal places. Type your answer in the space below. If your answer is a number less than 1, place a leading "0" before the decimal point (ex: 0.35)
Mathematics
1 answer:
3241004551 [841]3 years ago
3 0

Answer:

0.44 ft/sec.

Step-by-step explanation:

Let A is the bottom of the ladder and AB is the distance from the bottom of the wall i.e. B is the bottom of the wall. If C is the top of the ladder and BC is the height of the wall.

Now, Δ ABC is a right triangle and AC is the length of the ladder i.e. hypotenuse.

Now, AC² = AB² + BC² {From Pythagoras Theorem}

Now, differentiating both sides with respect to time t, we get

0 = 2 \times (AB) \times \frac{d(AB)}{dt} +  2 \times (BC) \times \frac{d(BC)}{dt}

⇒  \frac{d(AB)}{dt} = - \frac{BC}{AB} \times  \frac{d(BC)}{dt}

Now, given that \frac{d(BC)}{dt} = - 0.33 feet/sec.

Hence, \frac{d(AB)}{dt} = - \frac{BC}{AB} \times  (- 0.33) ......... (1)

Now, given that AB = 9 ft. and AC = 15 ft.

So, 15² = 9² + BC²  

⇒ BC² = 144

⇒ BC = 12 feet.

Now, from equation (1), we get

\frac{d(AB)}{dt} = - \frac{12}{9} \times  (- 0.33) = 0.44

Therefore, the bottom of the ladder is sliding away from the wall at the rate of 0.44 ft/sec. (Answer)

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The graph represents the normal distribution of recorded weights, in pounds, of cats at a veterinary clinic.
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Answer:

The weights within this range are:

8.9

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9.8

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Step-by-step explanation:

The graph represents the normal distribution with a mean of 9.5 and a standard deviation of 0.5. Therefore, the range of the values within 2 standard deviations is:

9.5 - 2(0.5) ≤ x ≤ 9.5 + 2(0.5)

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3 years ago
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8 0
2 years ago
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The mean length of 4 childrens' big finger is 14cm. The mean length of 9 adults' big finger is 16.1cm. What is the mean length (
Mamont248 [21]

Answer:

The mean length of the 13 people's big finger is 15.45 cm

Step-by-step explanation:

Given;

mean length of 4 childrens' big finger, x' = 14cm

mean length of 9 adults' big finger is 16.1cm, x'' = 16.1cm

Let the total length of the 4 childrens' big finger = t

x' = \frac{t}{n} \\\\x' = \frac{t}{4}\\\\t = 4x'\\\\t = 4 *14\\\\t = 56 \ cm

Let the total length of the 9 adults' big finger = T

x'' = \frac{T}{N} \\\\x'' = \frac{T}{9}\\\\T = 9x''\\\\T = 9*16.1\\\\T = 144.9 \ cm

The total length of the 13 people's big finger = t + T

                                                                           = 56 + 144.9

                                                                            =200.9 cm

The mean length of these 13 people's big finger;

x''' = (200.9) / 13

x''' = 15.4539 cm

x''' = 15.45 cm (2 DP)

Therefore, the mean length of the 13 people's big finger is 15.45 cm

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Divide 110 by 50 to get your answer, which would be 2.2. It would take 2.2 hours to get to your brother's house.
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