To simplify
![\sqrt[4]{\dfrac{24x^6y}{128x^4y^5}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B24x%5E6y%7D%7B128x%5E4y%5E5%7D%7D)
we need to use the fact that
![\sqrt[4]{x^4}=|x|](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7Bx%5E4%7D%3D%7Cx%7C)
Why the absolute value? It's because 
.
We start by rewriting as
![\sqrt[4]{\dfrac{2^23x^6y}{2^6x^4y^5}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%5E23x%5E6y%7D%7B2%5E6x%5E4y%5E5%7D%7D)
![\sqrt[4]{\dfrac{2^23x^4x^2y}{2^42^2x^4y^4y}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B2%5E23x%5E4x%5E2y%7D%7B2%5E42%5E2x%5E4y%5E4y%7D%7D)
Since 
, we have 
, and the above reduces to
![\sqrt[4]{\dfrac{3x^2y}{2^4y^4y}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%5Cdfrac%7B3x%5E2y%7D%7B2%5E4y%5E4y%7D%7D)
Then we pull out any 4th powers under the radical, and simplify everything we can:
![\dfrac1{\sqrt[4]{2^4y^4}}\sqrt[4]{\dfrac{3x^2y}{y}}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%5Csqrt%5B4%5D%7B2%5E4y%5E4%7D%7D%5Csqrt%5B4%5D%7B%5Cdfrac%7B3x%5E2y%7D%7By%7D%7D)
![\dfrac1{|2y|}\sqrt[4]{3x^2}](https://tex.z-dn.net/?f=%5Cdfrac1%7B%7C2y%7C%7D%5Csqrt%5B4%5D%7B3x%5E2%7D)
where 
allows us to write 
, and this also means that 
. So we end up with
![\dfrac{\sqrt[4]{3x^2}}{2y}](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B4%5D%7B3x%5E2%7D%7D%7B2y%7D)
making the last option the correct answer.
Answer:
the y intercept is 4
Step-by-step explanation:
the 4 is where the line starts so it would be (0,4)
Question: How do you solve [3.2 x (6.1 x 6.3)] - 2.8 with PEMDAS?
PEMDAS is the order of operations with which you solve an equation. So first parentheses, then exponents, then multiplication, then division, then addition, and last subtraction.
Answer: First, you solve the parentheses in the parentheses:
>6.1 x 6.3 = 38.43
Now ur equation is: (3.2 x 38.43) - 2.8
Now you solve what's inside this parentheses:
>3.2 x 38.43 = 122.976
Now you do the subtraction, because you have already solved all of what's in the parentheses:
>122.976 - 2.8 = 120. 176
And so, your answer is 120.176
This is what your equation should look like when you're solving:
>[3.2 x (6.1 x 6.3)] - 2.8 = y
>[3.2 x (38.43)] - 2.8 = y
>(3.2 x 38.43) - 2.8 = y
>122.976 - 2.8 = y
>122.976 - 2.8 = 120. 176
We know that 1 gallon= 4 quarts
therefore, 14 gallons=56 quarts
so
14gallons/s=56 qt/s
if we would need to find just gallons/second in quarts /second the answer will be simple, but we need to find the answer in qt/min
is there are 56 qt per second, it means that it will be
56*60 in 1 minute
56*60=3360
final answer
14 gallons/s=3360 qt/min
Answer:
y = 1/e
y = 0.37
Step-by-step explanation:
y = (ln x)/x; (e, 1/e)
Step 1
Find the point of tangency.
It's given as (e,1/e) or (2.72,0.37)
Step 2
Find the first derivative, and evaluate it at x=e
Using product rule.
d(uv) = udv + vdu
Where u = lnx and v = 1/x
du = 1/x , dv = -1/x^2
f'(x) = -lnx/x^2 +1/x^2
f'(x) = (1-lnx)/x^2
At x = e
f'(e) = (1-lne)/e^2
f'(e) = 0
The slope of the tangent line at this point is m= 0
Step 3
Find the equation of the tangent line at (e,1/e) with a slope of m=0
y−y1 = m(x - x1)
y-(1/e) = 0(x-1)
y = 1/e
y = 0.37
