![\dfrac{\sqrt[3]{x+h}-\sqrt[3]x}h\times\dfrac{\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}}{\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}}=\dfrac{(\sqrt[3]{x+h})^3-(\sqrt[3]x)^3}\cdots](https://tex.z-dn.net/?f=%5Cdfrac%7B%5Csqrt%5B3%5D%7Bx%2Bh%7D-%5Csqrt%5B3%5Dx%7Dh%5Ctimes%5Cdfrac%7B%5Csqrt%5B3%5D%7B%28x%2Bh%29%5E2%7D%2B%5Csqrt%5B3%5D%7Bx%28x%2Bh%29%7D%2B%5Csqrt%5B3%5D%7Bx%5E2%7D%7D%7B%5Csqrt%5B3%5D%7B%28x%2Bh%29%5E2%7D%2B%5Csqrt%5B3%5D%7Bx%28x%2Bh%29%7D%2B%5Csqrt%5B3%5D%7Bx%5E2%7D%7D%3D%5Cdfrac%7B%28%5Csqrt%5B3%5D%7Bx%2Bh%7D%29%5E3-%28%5Csqrt%5B3%5Dx%29%5E3%7D%5Ccdots)
The
s then cancel, leaving you with the
![\cdots=\sqrt[3]{(x+h)^2}+\sqrt[3]{x(x+h)}+\sqrt[3]{x^2}](https://tex.z-dn.net/?f=%5Ccdots%3D%5Csqrt%5B3%5D%7B%28x%2Bh%29%5E2%7D%2B%5Csqrt%5B3%5D%7Bx%28x%2Bh%29%7D%2B%5Csqrt%5B3%5D%7Bx%5E2%7D)
term.
If it's not clear what I did above, consider the substitution
![a=\sqrt[3]{x+h}](https://tex.z-dn.net/?f=a%3D%5Csqrt%5B3%5D%7Bx%2Bh%7D)
and
![b=\sqrt[3]x](https://tex.z-dn.net/?f=b%3D%5Csqrt%5B3%5Dx)
. Then
Solve for x:
5 - sqrt(x) + sqrt(3 x - 11) = 6
Subtract 5 from both sides:
sqrt(3 x - 11) - sqrt(x) = 1
(sqrt(3 x - 11) - sqrt(x))^2 = -11 + 4 x - 2 sqrt(x) sqrt(3 x - 11) = -11 + 4 x - 2 sqrt(x (3 x - 11)) = 1:
-11 + 4 x - 2 sqrt(x (3 x - 11)) = 1
Subtract 4 x - 11 from both sides:
-2 sqrt(x (3 x - 11)) = 12 - 4 x
Raise both sides to the power of two:
4 x (3 x - 11) = (12 - 4 x)^2
Expand out terms of the left hand side:
12 x^2 - 44 x = (12 - 4 x)^2
Expand out terms of the right hand side:
12 x^2 - 44 x = 16 x^2 - 96 x + 144
Subtract 16 x^2 - 96 x + 144 from both sides:
-4 x^2 + 52 x - 144 = 0
The left hand side factors into a product with three terms:
-4 (x - 9) (x - 4) = 0
Divide both sides by -4:
(x - 9) (x - 4) = 0
Split into two equations:
x - 9 = 0 or x - 4 = 0
Add 9 to both sides:
x = 9 or x - 4 = 0
Add 4 to both sides:
x = 9 or x = 4
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(4) + sqrt(3×4 - 11) = 4:
So this solution is incorrect
5 - sqrt(x) + sqrt(3 x - 11) ⇒ 5 - sqrt(9) + sqrt(3×9 - 11) = 6:
So this solution is correct
The solution is:
Answer: x = 9
Answer:
3.6669
Step-by-step explanation:
Given is a frequency distribution and we are expected to find the mean of the distribution.
Let X be the no of total pets owned and f be the number of adults owning those pets.
Total
x 1 2 3 4 5 6 7
F 248 567 1402 728 419 456 203 4023
x*f 248 1134 4206 2912 2095 2736 1421 14752
Mean 3.666915237
Thus we find the total of all frequencies and then sum of product of x*f.
Mean = sum of f*x/sum of x
Here mean= 3.6669
There is 15 sentence in 3 paragraph
Answer: $ 45,444.44
Step-by-step explanation:
Given: Jill budgets 18% of her yearly salary for clothing.
His total clothing bill for the year is $8,180.
Let x= her yearly salary
Then according to the question , we have
18% of x = 8180
Convert 18% into decimal by dividing it by 100 , we get
0.18 x= 8180
Multiply both sides by 100
⇒ 18x = 818000
Divide both sides by 18 , we get
x= 45444.44
Hence, her yearly salary = $ 45,444.44
