Answer:
The rate at which both of them are moving apart is 4.9761 ft/sec.
Step-by-step explanation:
Given:
Rate at which the woman is walking,
= 3 ft/sec
Rate at which the man is walking,
= 2 ft/sec
Collective rate of both,
= 5 ft/sec
Woman starts walking after 5 mins so we have to consider total time traveled by man as (5+15) min = 20 min
Now,
Distance traveled by man and woman are
and
ft respectively.
⇒ ![m=2\ ft/sec=2\times \frac{60}{min} \times 20\ min =2400\ ft](https://tex.z-dn.net/?f=m%3D2%5C%20ft%2Fsec%3D2%5Ctimes%20%5Cfrac%7B60%7D%7Bmin%7D%20%5Ctimes%2020%5C%20min%20%3D2400%5C%20ft)
⇒ ![w=3\ ft/sec = 3\times \frac{60}{min} \times 15\ min =2700\ ft](https://tex.z-dn.net/?f=w%3D3%5C%20ft%2Fsec%20%3D%203%5Ctimes%20%5Cfrac%7B60%7D%7Bmin%7D%20%5Ctimes%2015%5C%20min%20%3D2700%5C%20%20ft)
As we see in the diagram (attachment) that it forms a right angled triangle and we have to calculate
.
Lets calculate h.
Applying Pythagoras formula.
⇒
⇒ ![h=\sqrt{(2400+2700)^2+500^2} = 5124.45](https://tex.z-dn.net/?f=h%3D%5Csqrt%7B%282400%2B2700%29%5E2%2B500%5E2%7D%20%3D%205124.45)
Now differentiating the Pythagoras formula we can calculate the rate at which both of them are moving apart.
Differentiating with respect to time.
⇒ ![h^2=(m+w)^2+500^2](https://tex.z-dn.net/?f=h%5E2%3D%28m%2Bw%29%5E2%2B500%5E2)
⇒ ![2h\frac{d(h)}{dt}=2(m+w)\frac{d(m+w)}{dt} + \frac{d(500)}{dt}](https://tex.z-dn.net/?f=2h%5Cfrac%7Bd%28h%29%7D%7Bdt%7D%3D2%28m%2Bw%29%5Cfrac%7Bd%28m%2Bw%29%7D%7Bdt%7D%20%20%2B%20%5Cfrac%7Bd%28500%29%7D%7Bdt%7D)
⇒
...as ![\frac{d(500)}{dt}= 0](https://tex.z-dn.net/?f=%5Cfrac%7Bd%28500%29%7D%7Bdt%7D%3D%200)
⇒ Plugging the values.
⇒
...as
ft/sec
⇒
ft/sec
So the rate from which man and woman moving apart is 4.9761 ft/sec.
X>17
add 7 to 10 and you get 17 :)
Answer:
x = -2
Step-by-step explanation:
![17 + 4x = - (5x + 1)](https://tex.z-dn.net/?f=17%20%2B%204x%20%3D%20%20-%20%285x%20%2B%201%29)
Distribute - 1 to (5x + 1) .
![17 + 4x = - 5x - 1](https://tex.z-dn.net/?f=17%20%2B%204x%20%3D%20%20-%205x%20-%201)
Add 1 to both sides.
![18 + 4x = - 5x](https://tex.z-dn.net/?f=18%20%2B%204x%20%3D%20%20-%205x)
Subtract 4x from both sides.
![18 = - 9x](https://tex.z-dn.net/?f=18%20%3D%20%20-%209x)
Divide by - 9 from both sides.
![- 2 = x](https://tex.z-dn.net/?f=%20-%202%20%3D%20x)
Step-by-step explanation:
cos 20° cos 40° cos 60° cos 80°
<em>Simplify cos 60° to ½.</em>
½ cos 20° cos 40° cos 80°
<em>We can use double angle formula, sin(2θ) = 2 sin θ cos θ. Multiply and divide by 2 sin 20°.</em>
½ (2 sin 20° cos 20° cos 40° cos 80°) / (2 sin 20°)
½ (sin 40° cos 40° cos 80°) / (2 sin 20°)
<em>Multiply and divide by 2 and use double angle formula again.</em>
½ (2 sin 40° cos 40° cos 80°) / (4 sin 20°)
½ (sin 80° cos 80°) / (4 sin 20°)
<em>Multiply and divide by 2 and use double angle formula again.</em>
½ (2 sin 80° cos 80°) / (8 sin 20°)
½ (sin 160°) / (8 sin 20°)
<em>Use phase shift identity sin θ = sin(180−θ).</em>
½ (sin 20°) / (8 sin 20°)
1/16