5.
1 answer:
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Answer:
Solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
Step-by-step explanation:
Given, equation is \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} →→→ (1)
Now, by cubing the equation on both sides, we get
( \sqrt[3]{15x-1} + \sqrt[3]{13x+1} )³ = (4\sqrt[3]{x})³
⇒ (15x-1) + (13x+1) + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64 x.
(since (a+b)³ = a³ + b³ + 3ab(a+b) ).
⇒ 28x + 3×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1} + \sqrt[3]{13x+1}) = 64x.
(since from (1), \sqrt[3]{15x-1} + \sqrt[3]{13x+1} = 4\sqrt[3]{x} )
⇒ 12×\sqrt[3]{15x-1}× \sqrt[3]{13x+1} (\sqrt[3]{15x-1}×\sqrt[3]{x}= 36x.
⇒ 3x = .
Now, once again cubing on both sides, we get
(3x)³ = ()³.
⇒ 27x³ = (15x-1)(13x+1)(x).
⇒ 27x³ = 195x³ + 2x² - x
⇒ 168x³ + 2x² - x = 0
⇒ x(168x² + 2x -1) = 0
⇒ by, solving the equation we get ,
x = 0 ; x = \frac{1}{14} ; x = \frac{-1}{12}
therefore, solution is x= 0 , x = \frac{1}{14} , x = \frac{-1}{12}
Answer:
The volume of water in the fish tank is 4.5 cubic feet
see the explanation
Step-by-step explanation:
<u><em>The complete question is</em></u>
Explain how you found the volume of water in the fish tank if it was only 1/2 full with water. Show your work and solution. Don't forget your UNITS!
You have a fish tank with the following dimensions:
Height: 3 feet
Width: 1.5 feet
Length: 2 feet
step 1
Find the volume of the fish tank
The volume of a rectangular prism ( fish tank) is equal to
substitute the given values
step 2
Find the volume of water in the fish tank
Remember that
The fish tank it was only one and a half full with water
so
Multiply the volume of the fish tank by one and a half to obtain the volume of water