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SSSSS [86.1K]
3 years ago
9

The top of a ladder slides down a vertical wall at a rate of 0.675 m/s . At the moment when the bottom of the ladder is 3 m from

the wall, it slides away from the wall at a rate of 0.9 m/s . How long is the ladder
Mathematics
1 answer:
Svetllana [295]3 years ago
4 0

Answer:

L = 5 m

Step-by-step explanation:

The ladder, the vertical wall and the ground form a right triangle. We call A and B the ends points of the ladder ( at the wall, and the ground)

If we call L the lenght of the leadder, we get

L² = y² + x²

Taking derivatives on both sides of the equation

0 = 2y Dy/dt  +  2x Dx/dt

We know that Dy/dt = - 0,675 m/s (is sliding down , is decreasing)

And when x = 3 m  Dx/dt = 0,9 m/s

So we  can get y

0 = 2y*( -0,675) + 2*3*0,9

1,35y  =  5,4

y =   5.4 /1,35    ⇒   y = 4

And  L²  = y² + x²    ⇒  L  = √ (4)² + (3)²   ⇒  L √16 + 9

L = 5 m

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In the diagram below of parallelogram ABCD with diagonals AC and BD, m∠1=45° and m∠DCB=120°.Whatisthemeasureof∠2?
bixtya [17]

Answer:

15degrees

Step-by-step explanation:

From the given diagram

<1+<2 + <DCB = 180

<1+<2+120 = 180

<1+<2 = 180 - 120

<1+<2 = 60

<2 = 60 - <1

<2 = 60 - 45

<2 = 15degrees

Hence the measure <2 is 15degree

5 0
2 years ago
How many factors of 3 does the number 135 have?
Anestetic [448]

Answer:Prime factorization:  

135 = 3 x 3 x 3 x 5, which can also be written 135 = 3³ x 5. 1 + 3 + 5 = 9. Nine is a multiple of both 3 and 9, so this quick divisibility trick lets us know that both 3 and 9 are factors of 135. 135 = 1⁵ x 3³ x 5¹.

6 0
3 years ago
Read 2 more answers
daniiel is currently 26 years older than his son. in 6 years he will be three times older than his son. how old are both of them
Molodets [167]

Answer:

Daniiel is 33 years old.

The son is 7 years old.

Step-by-step explanation:

x+26=3x

The x represents the son.

To solve for x:

-26=x-3x

-26=-2x

x=13

Since the father will be 3 times his son's age in six years we subtract 6.

x=7

This means the son is 7 years old as of right now. To find the father's age you do 7+26=33

7 0
2 years ago
A giant tortoise can travel 0.11 miles in 1 hour. At this rate, how long would it take the tortoise to travel 3 miles?
lakkis [162]

Answer:

about 27.27 hours.

Step-by-step explanation:

If it can travel 0.11 miles in 1 hour, we need to divide 3 miles by 0.11 miles to get the number of hours it would take to travel 3 miles. 3/0.11 is 27.27 repeating.

Hope this helps!

4 0
2 years ago
Read 2 more answers
Hippalectryon
horrorfan [7]
Since the stadium is 6 mi from the practice field which is itself 1 mi from the house, it can either be (1+6)=7 mi North or (1-6)=-5 -> 5 mi South depending on the North/South direction.

the answer is thus A
7 0
2 years ago
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