Answer:
10.75
-5/4
2 7/24
Step-by-step explanation:
1.)
__+-3.5=7.25
Let missing number = x
x - 3.5 = 7.25
x = 7.25 +3.5
x = 10.75
2.)
-3/4-__=1/2
Let missing number = x
-3/4 - x = 1/2
-3/4 - 1/2 = x
(-3 - 2) / 4 = x
-5/4 = x
3.)
-2 3/8-(-4 2/3) = x
-2 3/8 + 4 2/3 = x
-19/8 + 14/3 = x
(-57 + 112) / 24 = x
55 / 24 = x
2 7/24
Answer:
The value is ![u = < \frac{2\sqrt{2}}{10} , \frac{3\sqrt{2}}{10} , - \frac{\sqrt{2}}{2}>](https://tex.z-dn.net/?f=u%20%3D%20%20%3C%20%5Cfrac%7B2%5Csqrt%7B2%7D%7D%7B10%7D%20%2C%20%5Cfrac%7B3%5Csqrt%7B2%7D%7D%7B10%7D%20%2C%20-%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3E)
Step-by-step explanation:
From the question we are told that
The vector is a=<-4,-3,5>
Generally the unit vector is
Here y represent the y-coordinate
So
=>
Generally the resultant of a unit vector is 1
So
![|u| = \sqrt{ (-4y)^2 + (-3y)^2 + (5y)^2} = 1](https://tex.z-dn.net/?f=%7Cu%7C%20%3D%20%5Csqrt%7B%20%28-4y%29%5E2%20%2B%20%28-3y%29%5E2%20%2B%20%285y%29%5E2%7D%20%3D%201%20)
Hence
![|u| = \sqrt{ 16y^2 + 9y^2 + 25y^2} = 1](https://tex.z-dn.net/?f=%7Cu%7C%20%3D%20%5Csqrt%7B%2016y%5E2%20%2B%209y%5E2%20%2B%2025y%5E2%7D%20%3D%20%201%20)
Taking the square of both sides
![16y^2 + 9y^2 + 25y^2 = 1](https://tex.z-dn.net/?f=%2016y%5E2%20%2B%209y%5E2%20%2B%2025y%5E2%20%3D%20%201%20)
=> ![50y^2 = 1](https://tex.z-dn.net/?f=%2050y%5E2%20%3D%20%201%20)
=>
=>
Rationalizing
=>
Given that the first coordinate is positive
Hence the unit vector is
=> ![u = < \frac{2\sqrt{2}}{10} , \frac{3\sqrt{2}}{10} , - \frac{\sqrt{2}}{2}>](https://tex.z-dn.net/?f=u%20%3D%20%20%3C%20%5Cfrac%7B2%5Csqrt%7B2%7D%7D%7B10%7D%20%2C%20%5Cfrac%7B3%5Csqrt%7B2%7D%7D%7B10%7D%20%2C%20-%20%5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%3E)
Answer:
x + y +z= 10
Step-by-step explanation:
4x - y = 5 ---------(I)
4y - z = 7 ---------(II)
4z - x = 18 ---------(III)
Add all the three equations,
4x - y + 4y - z + 4z - x = 5 + 7 + 18
4x - x -y + 4y -z + 4z = 30
3x + 3y + 3z = 30
Divide the entire equation by 3
![\sf \dfrac{3x}{3}+\dfrac{3y}{3}+\dfrac{3z}{3} = \dfrac{30}{3}](https://tex.z-dn.net/?f=%5Csf%20%5Cdfrac%7B3x%7D%7B3%7D%2B%5Cdfrac%7B3y%7D%7B3%7D%2B%5Cdfrac%7B3z%7D%7B3%7D%20%3D%20%5Cdfrac%7B30%7D%7B3%7D)
x + y + z = 10
It would be 5.4 knowing that 9.6 is not the diameter you would need a larger radius so that when it is doubled you get a good number :)
You can expect to roll an odd number 18 times.