<span>For the plane, we have z = 5x + 9y
For the region, we first find its boundary curves' points of intersection.
x = x^4 ==> x = 0, 1.
Since x > x^4 for y in [0, 1],
The volume of the solid equals
![\int\limits^1_0 { \int\limits_{x^4}^x {(5x+9y)} \, dy } \, dx = \int\limits^1_0 {\left[5xy+ \frac{9}{2} y^2\right]_{x^4}^{x}} \, dx \\ \\ =\int\limits^1_0 {\left[\left(5x(x)+ \frac{9}{2} (x)^2\right)-\left(5x(x^4)+ \frac{9}{2} (x^4)^2\right)\right]} \, dx \\ \\ =\int\limits^1_0 {\left(5x^2+ \frac{9}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx =\int\limits^1_0 {\left( \frac{19}{2} x^2-5x^5- \frac{9}{2} x^8\right)} \, dx \\ \\ =\left[ \frac{19}{6} x^3- \frac{5}{6} x^6- \frac{1}{2} x^9\right]^1_0](https://tex.z-dn.net/?f=%20%5Cint%5Climits%5E1_0%20%7B%20%5Cint%5Climits_%7Bx%5E4%7D%5Ex%20%7B%285x%2B9y%29%7D%20%5C%2C%20dy%20%7D%20%5C%2C%20dx%20%3D%20%5Cint%5Climits%5E1_0%20%7B%5Cleft%5B5xy%2B%20%5Cfrac%7B9%7D%7B2%7D%20y%5E2%5Cright%5D_%7Bx%5E4%7D%5E%7Bx%7D%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D%5Cint%5Climits%5E1_0%20%7B%5Cleft%5B%5Cleft%285x%28x%29%2B%20%5Cfrac%7B9%7D%7B2%7D%20%28x%29%5E2%5Cright%29-%5Cleft%285x%28x%5E4%29%2B%20%5Cfrac%7B9%7D%7B2%7D%20%28x%5E4%29%5E2%5Cright%29%5Cright%5D%7D%20%5C%2C%20dx%20%20%5C%5C%20%20%5C%5C%20%3D%5Cint%5Climits%5E1_0%20%7B%5Cleft%285x%5E2%2B%20%5Cfrac%7B9%7D%7B2%7D%20x%5E2-5x%5E5-%20%5Cfrac%7B9%7D%7B2%7D%20x%5E8%5Cright%29%7D%20%5C%2C%20dx%20%3D%5Cint%5Climits%5E1_0%20%7B%5Cleft%28%20%5Cfrac%7B19%7D%7B2%7D%20x%5E2-5x%5E5-%20%5Cfrac%7B9%7D%7B2%7D%20x%5E8%5Cright%29%7D%20%5C%2C%20dx%20%5C%5C%20%20%5C%5C%20%3D%5Cleft%5B%20%5Cfrac%7B19%7D%7B6%7D%20x%5E3-%20%5Cfrac%7B5%7D%7B6%7D%20x%5E6-%20%5Cfrac%7B1%7D%7B2%7D%20x%5E9%5Cright%5D%5E1_0)
</span>
The answer is C. y=1/4 x + 9
Hope this helps
Answer:
x = 12, x = 7
Step-by-step explanation:
The 2 legs of the triangle are congruent, both 2x + 7, then
2x + 7 + 2x + 7 + x + 11 = 85 ← equation for perimeter
5x + 25 = 85 ( subtract 25 from both sides )
5x = 60 ( divide both sides by 5 )
x = 12
-----------------------------------------------------------
Opposite sides are congruent, then
2(2x) + 2(5x + 3) = 104 ← distribute and simplify both sides
4x + 10x + 6 = 104
14x + 6 = 104 ( subtract 6 from both sides )
14x = 98 ( divide both sides by 14 )
x = 7
Top:
x / (x + 1) - 1 / x
= [x^2 - (x +1)] / x(x+1)
= (x^2 - x - 1 ) / x (x+1)
Bottom:
x / (x + 1) + 1 / x
= [x^2 + (x +1)] / x(x+1)
= (x^2 + x + 1 ) / x (x+1)
Now you have:
(x^2 - x - 1 ) / x (x+1)
----------------------------
(x^2 + x + 1 ) / x (x+1)
= (x^2 - x - 1 ) / x (x+1) * x (x+1) / (x^2 + x + 1 )
= (x^2 - x - 1 ) /(x^2 + x + 1 )
Answer:
x^2 - x - 1
---------------------
x^2 + x + 1
6, because 3/4=6/8 so 6 kids ate it if each has 1/8
