There are 23 square green blocks in the figure, and the note up in the corner
shows us that each square has (1 inch x 1 inch) = 1 square inch of area.
You ought to be able to handle it from here.
1/4a + 1/3a +8 =22
1st step add like terms:
1/4a +1/3a = 3/12a +4/12a = 7/12a
7/12a +8 =22
2nd step subtract 8 from each side:
7/12a = 14
3rd step divide both sides by 7/12 to get a:
a = 14 / 7/12
a = 24
Compute the derivative dy/dx using the power, product, and chain rules. Given
x³ + y³ = 11xy
differentiate both sides with respect to x to get
3x² + 3y² dy/dx = 11y + 11x dy/dx
Solve for dy/dx :
(3y² - 11x) dy/dx = 11y - 3x²
dy/dx = (11y - 3x²)/(3y² - 11x)
The tangent line to the curve is horizontal when the slope dy/dx = 0; this happens when
11y - 3x² = 0
or
y = 3/11 x²
(provided that 3y² - 11x ≠ 0)
Substitute y into into the original equation:
x³ + (3/11 x²)³ = 11x (3/11 x²)
x³ + (3/11)³ x⁶ = 3x³
(3/11)³ x⁶ - 2x³ = 0
x³ ((3/11)³ x³ - 2) = 0
One (actually three) of the solutions is x = 0, which corresponds to the origin (0,0). This leaves us with
(3/11)³ x³ - 2 = 0
(3/11 x)³ - 2 = 0
(3/11 x)³ = 2
3/11 x = ³√2
x = (11•³√2)/3
Solving for y gives
y = 3/11 x²
y = 3/11 ((11•³√2)/3)²
y = (11•³√4)/3
So the only other point where the tangent line is horizontal is ((11•³√2)/3, (11•³√4)/3).
Answer:
11/12 = 3/4
Step-by-step explanation:
sorry that's the only one I know :(
Answer:
<em>6 days</em>
<em></em>
Step-by-step explanation:
Let the time taken by Carpenter working alone = 
days
Then time taken by apprentice alone = Twice as that of taken by Carpenter = 2 days
Time taken working together = 2 days
Work done in one day working together = 
Work done in one day by Carpenter working alone = 
Work done in one day by apprentice working alone = 
Work done in one day by Carpenter working alone + Work done in one day by Carpenter working alone = + = Work done in one day working together =
Time taken by Carpenter alone to complete the work = 3 days
Time taken by Apprentice alone to complete the work = 3 
2= <em>6 days</em>
