Answer:
33 1/3% decrease
Step-by-step explanation:
The original area is (6in)(10in) = 60 in². The reduced area is (5in)(8in) = 40 in². Then the change in area is ...
((new value)/(old value) -1) × 100%
(40/60 -1)×100% = -1/3×100% = -33 1/3%
The area decreased by 33 1/3%.
Answer:
y=1/6x-7/6
Step-by-step explanation:
-6y = -x + 7
y = x/6 - 7/6
This is assuming you mean in standard form.
Also, you may have to write it as 'y=1/6x-7/6'
Answer:
1. y' = 3x² / 4y²
2. y'' = 3x/8y⁵[(4y³ – 3x³)]
Step-by-step explanation:
From the question given above, the following data were obtained:
3x³ – 4y³ = 4
y' =?
y'' =?
1. Determination of y'
To obtain y', we simply defferentiate the expression ones. This can be obtained as follow:
3x³ – 4y³ = 4
Differentiate
9x² – 12y²dy/dx = 0
Rearrange
12y²dy/dx = 9x²
Divide both side by 12y²
dy/dx = 9x² / 12y²
dy/dx = 3x² / 4y²
y' = 3x² / 4y²
2. Determination of y''
To obtain y'', we simply defferentiate above expression i.e y' = 3x² / 4y². This can be obtained as follow:
3x² / 4y²
Let:
u = 3x²
v = 4y²
Find u' and v'
u' = 6x
v' = 8ydy/dx
Applying quotient rule
y'' = [vu' – uv'] / v²
y'' = [4y²(6x) – 3x²(8ydy/dx)] / (4y²)²
y'' = [24xy² – 24x²ydy/dx] / 16y⁴
Recall:
dy/dx = 3x² / 4y²
y'' = [24xy² – 24x²y (3x² / 4y² )] / 16y⁴
y'' = [24xy² – 18x⁴/y] / 16y⁴
y'' = 1/16y⁴[24xy² – 18x⁴/y]
y'' = 1/16y⁴[(24xy³ – 18x⁴)/y]
y'' = 1/16y⁵[(24xy³ – 18x⁴)]
y'' = 6x/16y⁵[(4y³ – 3x³)]
y'' = 3x/8y⁵[(4y³ – 3x³)]
Answer:
Already simplified.
Step-by-step explanation:
The only way to simplify an expression is to combine like terms. Like terms is where the variables are exactly the same. t^2 is not the same as t. Thus, cannot combine them, so the expression is already simplified,
9514 1404 393
Answer:
a. 7
b. 7
Step-by-step explanation:
The "work" is to realize that the value of G(x) does not depend on x. It is always 7.
a. G(7) = 7
b. G(-3) = 7
