Mathematics, 16.01.2021 16:50 simeragrundy14

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.

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Answer from: lalalooowt

Complete question

A 29-meter ladder is sliding down a vertical wall so the distance between the top of the ladder and the ground is decreasing at 7 meters per minute. At a certain instant, the bottom of the ladder is 21 meters from the wall.

What is the rate of change of the distance between the bottom of the ladder and the wall at that instant(in meters per minute)

$\frac{dx}{dt}=11.94m/min$

Step-by-step explanation:

From the question we are told that

Slant height z=29m

Change in Vertical height $\triangle y=7m/s$

Horizontal length x=21

Generally in finding the distance form the top to the bottom of the wall it is mathematically given by

x^2+y^2=z^2

21^2+y^2=29^2

y^2=29^2+21^2

y=35.81

Generally solving for the differential equation is mathematically represented as

x^2+y^2=29^2

$2x*\frac{dx}{dt} +2y*\frac{dy}{dt} =0$

$x*\frac{dx}{dt} +y*\frac{dy}{dt} =0$

$(21)*\frac{dx}{dt} +(35.81)*(-7) =0$

$(21)*\frac{dx}{dt} -250.64 =0$

$\frac{dx}{dt}=\frac{250.64}{21}$

$\frac{dx}{dt}=11.94m/min$

Answer from: Quest

Iwould like to think so. what’s the question you need with?

Answer from: Quest

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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