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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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kumpel [21]
1/7 gallon  = 1 batch 

<em>[multiply by 7 through]</em>
1 gallon = 7 batches

<em>[multiply by 8/9 through]</em>
8/9 gallon = 7 x 8/9
8/9 gallon = 6 2/9 

<em>[Good enough to make 6 batches, not enough to make 7 batches]</em>

So he can make 6 batches of collard green


5 0
2 years ago
The arc of the parabola y = x^2 from (3,9) to (4,16) is rotated about the y-axis. Find the area of the resulting surface. Please
Hitman42 [59]

Answer:

156.5

Step-by-step explanation:

Thinking process:

The area can be calculated using the formula:

S = \int\limits^4_3 {2\pi x\sqrt{1+}(2x)^{2} } \, dx

We let the substitution take place.

Therefore, we let u = 1 + 4x^{2}

Thus, du = 8dx.

So,

xdx = \frac{1}{8}du

Also, the interval of the integration changes to [ 37, 65]

Thus,

S = \int\limits^4_3 {2\pi \sqrt{1+4x^{2} } } \, dx \\= \int\limits^65_35 {2\pi \sqrt{\frac{1}{8}u } } \, dx

= \frac{1}{6} [ 65^{\frac{3}{2}-37^{\frac{3}{2} }  }

= 156.5 units²

8 0
3 years ago
Among all pairs of numbers whose difference is 6, find a pair whose product is as small as possible. What is the minimum product
kkurt [141]
Ummm if its multiply then its 1 and 6. is its addition then its 1 and 5 or 6 and 0. if its divide it would be 6 and 1. is its subtraction then it would be 7 and 1 or 6 and 0

3 0
3 years ago
Is this how you set up my equation?
muminat
Looks correct. :)...........
8 0
3 years ago
Read 2 more answers
Figure ABCD is a kite. The area of ABCD is 48 square units. The length of line segment BD is 8 units. What is the length of AC?
astra-53 [7]
The area of a kite:
A = d1 * d2 / 2
d1 = BD = 8 units
48 = 8 * AC / 2
48 * 2 = 8 AC
96 = 8 AC
AC = 96 : 8 = 12
Answer: D ) 12 units
7 0
3 years ago
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