Answer:
the volume of the solid is 
Step-by-step explanation:
Given the data in the question;
y = x and y = x²
so
x = x²
x - x² = 0
Radius will be; r = ( x - x² )/2
Area of the circular disk πr² = π[ ( x - x² )/2 ]²
A = 
( x - x² )²
So, our volume will be;
V = ₀∫¹ A(x) dx
we substitute
= ₀∫¹ ( x - x² )² dx
{ lets expand; ( x - x² )² = x(x-x²) -x²(x-x²) = x² - x³ - x³ + x⁴ = x² + x⁴ - 2x³ }
so we have;
= ₀∫¹ ( x² + x⁴ - 2x³ ) dx
= 
+ 
- 
![]^1_0](https://tex.z-dn.net/?f=%5D%5E1_0)
= [ 
+ 
- 
]
= [ 
]
V =
Therefore, the volume of the solid is
Answer:
Dimension of room = 18 foot x 18 foot
Step-by-step explanation:
Let the square room is of side a foot,
The cost of re-finishing the hardwood floors is $2.25 per square foot and the cost of purchasing and installing the new baseboards $14.5 per linear foot
Total cost is $1773.
Cost for re-finishing the hardwood floors = Area x 2.25
Area = a²
Cost for re-finishing the hardwood floors = 2.25 a²
Cost of purchasing and installing the new baseboards = Perimeter x 14.5
Perimeter = 4a
Cost of purchasing and installing the new baseboards = 4a x 14.5 = 58 a
Total cost = Cost for re-finishing the hardwood floors + Cost of purchasing and installing the new baseboards
1773 = 2.25 a² + 58a
2.25 a² + 58a - 1773 = 0
a = 18 or a = -43.77(not possible)
Dimension of room = 18 foot x 18 foot
Y = -2x + 5 y =3x - 2
Since both equations are equal to 'y' you can set them equal to each other to solve.
-2x + 5 = 3x - 2 Subtract 3x from both sides
-5x + 5 = -2 Subtract 5 from both sides
-5x = -7 Divide -5 on both sides
x = 7/5
Plug 7/5 back in for x and solve for y.
y = -2(7/5) + 5
y = (-14/5) + (25/5)
y = 11/5
(7/5, 11/5) OR (1.4, 2.2)
Answer:
Step-by-step explanation:
%change=100(final-initial)/(initial)
%change=100(26-20)/20
%change=30%
Since this is positive the number of dogs increased by 30%
