Hey there!
Answer:
B. 3x + 4 ft.
Step-by-step explanation:
Remember that:
Perimeter of a rectangle: P = 2l + 2w
Given:
P = 8x + 8
w = x.
Plug the given information into the equation:
8x + 8 = 2l + 2x
Subtract 2x from both sides:
6x + 8 = 2l
Divide both sides by 2:
(6x + 8)/2 = 2l/2
3x + 4 = l.
Therefore, the length of the garden is:
l = 3x + 4 ft.

If
, then we can immediately cancel the factors of
:

Factorize the numerator and denominator:


Next, if
, then

Answer: 0.33 , 1/4 , 1/8 , 0
Step-by-step explanation:
1/4 is 0.25
1/8 is 0.125
After converting to decimal it’s all easy
Answer:
The magnetic field is
Direction is inward
Step-by-step explanation:
The diagram for this question is shown on the first uploaded image
From the question we are told that
The radius of BC is 
The radius of DA is 
The length of CD is 
The length of AB is 
The current is 
The magnetic field is mathematically represented as

![B = \frac{\mu_o I}{4 \pi } [ \frac{\theta_{DA}}{r_{DA}} + \frac{\theta_{BC}}{r_{BC}}+ \frac{\theta_{CD}}{r_{CD}}+\frac{\theta_{AB}}{r_{AB}}]](https://tex.z-dn.net/?f=B%20%3D%20%20%5Cfrac%7B%5Cmu_o%20I%7D%7B4%20%5Cpi%20%7D%20%5B%20%5Cfrac%7B%5Ctheta_%7BDA%7D%7D%7Br_%7BDA%7D%7D%20%2B%20%5Cfrac%7B%5Ctheta_%7BBC%7D%7D%7Br_%7BBC%7D%7D%2B%20%5Cfrac%7B%5Ctheta_%7BCD%7D%7D%7Br_%7BCD%7D%7D%2B%5Cfrac%7B%5Ctheta_%7BAB%7D%7D%7Br_%7BAB%7D%7D%5D)
Where

Where 

so
![B = \frac{\mu_o I}{4 \pi } [ \frac{\frac{2\pi}{3} }{0.20} - \frac{\frac{2\pi}{3}}{0.30}}+ \frac{0}{0.10}+\frac{0}{0.10}]](https://tex.z-dn.net/?f=B%20%3D%20%20%5Cfrac%7B%5Cmu_o%20I%7D%7B4%20%5Cpi%20%7D%20%5B%20%5Cfrac%7B%5Cfrac%7B2%5Cpi%7D%7B3%7D%20%7D%7B0.20%7D%20-%20%5Cfrac%7B%5Cfrac%7B2%5Cpi%7D%7B3%7D%7D%7B0.30%7D%7D%2B%20%5Cfrac%7B0%7D%7B0.10%7D%2B%5Cfrac%7B0%7D%7B0.10%7D%5D)

The direction is into the page
This because the magnitude of the magnetic field due to arc BC whose direction is outward is less than that of DA whose direction is inward
This is because according to Fleming's Left Hand Rule the direction of current is perpendicular to the direction of magnetic field so since current in arc BC and DA are moving in opposite direction their magnetic field will also be moving in opposite direction
Answer:
There are (63) combinations. The notation means "six choose three". Out of six items (flavors) choose three.
(nk)=n!k!(n−k)!.
(63)=6!3!3!.
Think of it this way. There are 6 ways to choose a flavor. Once you choose, there are 5 ways to choose the next. After that, there are 4 flavors left. which is 6!/3!=6⋅5⋅4⋅3⋅2⋅13⋅2⋅1=6⋅5⋅4=120.
But, you could have chosen {chocolate,vanilla,strawberry} and you get the same combination as {vanilla, strawberry, chocolate} so we have to divide by 3!=3⋅2⋅1=6 to account for the order of choosing.
So the number of combinations of flavors is (63)=1206=20.
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