<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>
Total tickets sold = 800
Total revenue = $3775
Ticket costs:
$3 per child,
$8 per adult,
$5 per senior citizen.
Of those who bought tickets, let
x = number of children
y = number of adults
z = senior citizens
Therefore
x + y + z = 800 (1)
3x + 8y + 5z = 3775 (2)
Twice as many children's tickets were sold as adults. Therefore
x = 2y (3)
Substitute (3) into (1) and (2).
2y + y + z = 800, or
3y + z = 800, or
z = 800 - 3y (4)
3(2y) + 8y + 5z = 3775, or
14y + 5z = 3775 (5)
Substtute (4) nto (5).
14y + 5(800 - 3y) = 3775
-y = -225
y = 225
From (4), obtain
z = 800 - 3y = 125
From (3), obtain
x = 2y = 450
Answer:
The number of tickets sold was:
450 children,
225 adults,
125 senior citizens.
Answer:
Step-by-step explanation:
In order to find the value of n that satisfies this equation, we can perform a series of algebraic steps on it to solve for n.
- <em>Distribute in the 8 on the left side:</em>
- <em />
<em> </em> - <em>Add 4n to both sides</em>
- <em>Add 16 to both sides</em>
- <em>Divide both sides by 20</em>
Therefore, n=1 is the value of n that satisfies this equation.
Hope this helped!
Answer:
B. 1 1/3
Step-by-step explanation:
three can go into 4 once, so we have a whole number of 1 and a leftover 1/3.
= 
hope this helps :)
4 x 3/5
4/1 x 3/5
4x3/5x1
12/5kg of corn a week
(12/5)/7
12/5(1/7)
12/5x7
12/35kg per day
