Answer:
work is pictured and shown
Answer:
1/8 miles
Step-by-step explanation:
You have to subtract
for the answer.
First, you gotta make 3/4 have a common denominator.
To do this multiply 3/4 by 2/2 (2/2 equals one, so value isn't changed.)
and you get 6/8.
Then you can subtract 6/8 - 5/8 to get 1/8 miles.
And there's no need to simplify 1/8.
Answer:
The value is ![v_b = 9.89 \ miles /hour](https://tex.z-dn.net/?f=v_b%20%20%3D%20%209.89%20%5C%20%20miles%20%2Fhour)
Step-by-step explanation:
From the question we are told that
The velocity of the wind southward is ![v = 5 j \ miles / hour](https://tex.z-dn.net/?f=v%20%20%3D%20%205%20j%20%5C%20%20miles%20%2F%20hour)
The resultant velocity of the bird with the with wind is
Generally for an object moving in the northwest direction the angle with the horizontal is 45°
Generally the velocity of the bird in the along the x -axis is
![V_x= v_b cos 45^o i](https://tex.z-dn.net/?f=V_x%3D%20v_b%20cos%2045%5Eo%20i)
Generally the velocity of the bird in the along the y -axis is
![V_y=(v_b sin 45^o - 5)j](https://tex.z-dn.net/?f=%20V_y%3D%28v_b%20sin%2045%5Eo%20-%205%29j)
Here
is the velocity of the bird without the wind
Generally the resultant velocity of the bird with the with wind is mathematically represented as
![V = \sqrt{V_x^2 + V_y^2 }](https://tex.z-dn.net/?f=V%20%20%3D%20%20%5Csqrt%7BV_x%5E2%20%2B%20V_y%5E2%20%7D)
=> ![\sqrt{53} = \sqrt{(v_b cos 45^o)^2 + (v_b sin 45^o - 5)^2 }](https://tex.z-dn.net/?f=%20%20%5Csqrt%7B53%7D%20%20%3D%20%20%5Csqrt%7B%28v_b%20cos%2045%5Eo%29%5E2%20%2B%20%28v_b%20sin%2045%5Eo%20-%205%29%5E2%20%7D)
Generally
![sin 45^o = \frac{1}{\sqrt{2} }](https://tex.z-dn.net/?f=sin%2045%5Eo%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D)
and
![cos 45^o = \frac{1}{\sqrt{2} }](https://tex.z-dn.net/?f=cos%2045%5Eo%20%3D%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D)
So
![\sqrt{53} = \sqrt{(v_b* (\frac{1}{\sqrt{2} ))^2 + ([v_b * (\frac{1}{\sqrt{2} ) ]- 5)^2 }](https://tex.z-dn.net/?f=%20%20%5Csqrt%7B53%7D%20%20%3D%20%20%5Csqrt%7B%28v_b%2A%20%28%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%29%29%5E2%20%2B%20%28%5Bv_b%20%2A%20%28%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%29%20%5D-%205%29%5E2%20%7D)
=> ![53 = \frac{1}{2} v_b^2 + \frac{1}{2} v_b^2 + 5^2 -2*5 * \frac{1}{\sqrt{2} } v_b](https://tex.z-dn.net/?f=53%20%3D%20%20%5Cfrac%7B1%7D%7B2%7D%20v_b%5E2%20%20%2B%20%20%5Cfrac%7B1%7D%7B2%7D%20v_b%5E2%20%2B%205%5E2%20-2%2A5%20%2A%20%5Cfrac%7B1%7D%7B%5Csqrt%7B2%7D%20%7D%20v_b)
=>
=>
Solving the above quadratic equation using quadratic formula we obtain that
![v_b = 9.89 \ miles /hour](https://tex.z-dn.net/?f=v_b%20%20%3D%20%209.89%20%5C%20%20miles%20%2Fhour)
The other value is negative so we do not make use of it because we know that the bird is moving in the positive x and y axis
<span>x in (-oo:+oo)</span><span>
(1/3)*((6/5)*x-3) = 0</span><span>
1/3*(6/5*x-3) = 0</span><span>
( 1/3 )</span><span>
1/3 = 0</span><span>
x belongs to the empty set</span><span>
( 6/5*x-3 )</span><span>
6/5*x-3 = 0 // + 3</span><span>
6/5*x = 3 // : 6/5</span><span>
x = 3/6/5</span><span>
x = 5/2</span><span>
x = 5/2</span>
Answer:
80 %
Step-by-step explanation:
Total number of cards = 5
Number of green cards=1
Number of non green cards= 4
Percantage of non green cards= 4 /5 x 100 = 80 %
I think this is right!