Answer:
11 1/9 ft^3
Step-by-step explanation:
find the complete question in the attached image
volume of the tank = length x width x height
2 x 5 x 1 2/3
2 x 5 x 5/3 = 50/3 = 16 2/3 ft^3
If the tank is 1/3 filled with water, the volume that needs to be filled with water is 1 - 1/3 = 2/3
volume that needs to be filled with water = 2/3 x volume of the tank
2/3 x 50/3 = 11 1/9 ft^3
Answer:
see explanation
Step-by-step explanation:
A
Given
(x² + 3)² + 21 = 10x² + 30 ← factor out 10 from each term on the right side
(x² + 3)² + 21 = 10(x² + 3) ← subtract 10(x² + 3) from both sides
(x² + 3)² - 10(x² + 3) + 21 = 0
Substituting u = x² + 3 into the equation gives
u² - 10u + 21 = 0 → D
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B
Using u² - 10u + 21 = 0 to solve the equation
Consider the factors of the constant term (+ 21) which sum to give the coefficient of the u- term (- 10)
The factors are - 3 and - 7, since
- 3 × - 7 = 21 and - 3 - 7 = - 10, thus
(u - 3)(u - 7) = 0
Equate each factor to zero and solve for u
u - 3 = 0 ⇒ u = 3
u - 7 = 0 ⇒ u = 7
We now have to use the substitution to convert the solutions into terms of x, that is
x² + 3 = 3 ( subtract 3 from both sides )
x² = 0 ⇒ x = 0 → D
x² + 3 = 7 ( subtract 3 from both sides )
x² = 4 ( take the square root of both sides )
x = ± = ± 2
Thus x = - 2 → C
x = 2 → E