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"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from t

Svet_ta [14]

Answer:

Step-by-step explanation:

The question has typographical errors. The correct question is:

"A 12-foot ladder is leaning against a building. If the bottom of the ladder is sliding along the pavement directly away from the building at 3 feet/second, how fast is the top of the ladder moving down when the foot of the ladder is 5 feet from the wall?

Solution:

The ladder forms a right angle triangle with the ground. The length of the ladder represents the hypotenuse.

Let x represent the distance from the top of the ladder to the ground(opposite side)

Let y represent the distance from the foot of the ladder to the base of the wall(adjacent side)

The bottom of the ladder is sliding along the pavement directly away from the building at 3ft/sec. This means that y is increasing at the rate of 3ft/sec. Therefore,

dy/dt = 3 ft/s

The rate at which x is reducing would be

dx/dt

Applying Pythagoras theorem which is expressed as

Hypotenuse² = opposite side² + adjacent side², it becomes

x² + y² = 12²- - - - - - - -1

Differentiating with respect to time, it becomes

2xdx/dt + 2ydy/dt = 0

2xdx/dt = - 2ydy/dt

Dividing through by 2x, it becomes

dx/dt = - y/x ×dy/dt- - - - - - - - - - 2

Substituting y = 5 into equation 1, it becomes

x² + 5 = 144

x² = 144 - 25 = 119

x = √119 = 10.91

Substituting x = 10.91, dy/dt = 3 and y = 5 into equation 2, it becomes

dx/dt = - 5/10.91 × 3

dx/dt = - 1.37 ft/s

7 0

4 years ago

Solve each absolute value equation or inquality and choose the correct answer from the choices provided.

lawyer [7]

1- 13 or -13 (B)

2- -5 < y < -3 (A)

3- t = 6 or -6 (B)

Hope this helps you =)

7 0

3 years ago

Drive to work in 45 min., bus to work takes 1 hr 15 min. If the average rate on the bus is 16 mph slower than his driving rate,

stich3 [128]

Answer:

30 miles

Step-by-step explanation:

Given: Drive to work in 45 min.

Bus would take to travel= 1 hr 15 min

Average rate on the bus is 16 mph slower than his driving rate.

Lets assume the average driving rate be "x" mph.

∴ Average rate of bus= $(x-16)\ mph$

Now converting unit of time taken to travel to work.

Remember; 1 hours= 60 minutes.

Time taken for drive to work= $\frac{45\ minutes}{60\ minutes} = 0.75\ hour$

Time taken in bus to work= 1 hour and 15 minutes= $60\ minutes+ 15\ minutes= 75\ minutes$

∴ Time taken in bus to work in hours= $\frac{75\ minutes}{60\ minutes}= 1.25\ hours$

Considering the distance remain constant to travel for work.

Next, forming an equation to find the value of x.

As we know, $distance= speed\times time$

⇒ $x\times 0.75= (x-16)\times 1.25$

Using distributive property of multiplication.

⇒ $0.75x= 1.25x-20$

Adding both side by 20

⇒ $0.75x+20= 1.25x$

Subtracting both side by 0.75x

⇒ $20= 0.5x$

Dividing both side by 0.5

⇒ $x= \frac{20}{0.5}$

∴ $x= 40\ mph$

Hence the average rate for drive to work is 40mph.

Now, subtitiuting the value of x to find the distance travelled to work.

Distance travelled= $40\times 0.75= 30\ miles$

Hence, distance travelled to work is 30 miles.

6 0

4 years ago

A builder has to fix 3 Walls that have fallen down.He needs 2kg of cement for each wall.How much will he need altogether in kilo

klio [65]

Answer: 6 kilograms

Step-by-step explanation:

3 walls * 2 kilograms each = 6 kilograms in total

8 0

4 years ago

2x+1 = x-2<br> /3<br> show step by step pls

Serggg [28]

Answer:

here is the step

Step-by-step explanation:

2x-x= -2-1

X= -3

4 0

3 years ago

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