Answer:
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Step-by-step explanation:
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Answer:
DA/dt = 75.27 cm²
Step-by-step explanation:
Cube Volume = V(c) = 683 cm³
DV(c) /dt = 824 cm³
V(c,x) = x³
Then
DV(c,x)/ dt = 3x² Dx/dt
( DV(c,x)/ dt )/ 3x² = Dx/dt (1)
Now as V(c,x) = x³ when V(c,x) = 683 cm³ x = ∛683
x = 8.806 ( from excel)
And by subtitution of this value in equation (1)
Dx/dt = ( DV(c,x)/ dt )/ 3x² ⇒ Dx/dt = 824 / 3*x²
Dx/dt = 824 /3*77.55
Dx/dt = 824/232,64
Dx/dt = 3,542
Then we got Dx/dt where x is cube edge. The area of the face is x² then
the rate of change of the suface area is
DA/dt = ( Dx/dt )²*6 ( 6 faces of a cube)
DA/dt = (3.542)²*6
DA/dt = 75.27 cm²
Let's convert this fraction to an equal fraction which holds a denominator of 100, since it is a power of 10.
Since the denominator can be multiplied by 5 to achieve 100, we can multiply the entire fraction by 5 to create an equivalent fraction that has a denominator of 100:
17/20 = (17*5)/(20*5) = 85/100
To obtain a decimal from this fraction, take the numerator and move its decimal one place to the left for every 0 in the denominator. Since our denominator has two zeros, we will need to move the decimal place on the 85 two places to the left.
This gives us an answer of .85, which can also be expressed as 0.85.
2.25t+ 5= 13.5t+ 14
⇒ 5- 14= 13.5t- 2.25t
⇒ -9= 11.25t
⇒ -9/11.25= t
⇒ -0.8= t
Final answer: t= -0.8~
