The value of y is 18.46 when x=10 and z = 26
Step-by-step explanation:
The direct proportion is denoted as:
y∝x
And the inverse proportion will be denoted as:
y∝1/z
combining both
y∝ x/z
When the symbol of proportionality is removed, the proportionality constant is introduced
Given
y = 32 when x=4 and z = 6
Putting the values
So the equation will become:
Putting x=10 and z= 26
Hence,
The value of y is 18.46 when x=10 and z = 26
Keywords: Proportion, variation
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It would be 6 and 3/10 because 4.5 plus 2.3 equals 6.3 so then you just make it into a mixed number and get 6 and 3/10
Answer:
x = 1 ±
Step-by-step explanation:
Given
2x² - 4x = 10 ( divide through by 2 )
x² - 2x = 5
Using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(- 1)x + 1 = 5 + 1
(x - 1)² = 6 ( take the square root of both sides )
x - 1 = ± ( add 1 to both sides )
x = 1 ± ← exact solutions
I assume that it’s an equation so:
2x^3-4=0
x=(2)^(1/3)
Answer:
t-shirts: 2790
profit: $12209
Step-by-step explanation:
Given the function:
p(x) = -x³ + 4x² + x
we want to maximize it.
The following criteria must be satisfied at the maximum:
dp/dx = 0
d²p/dx² < 0
dp/dx = -3x² + 8x + 1 = 0
Using quadratic formula:
d²p/dx² = -6x + 8
d²p/dx² at x = -0.12: -6(-0.12) + 8 = 8.72 > 0
d²p/dx² at x = 2.79: -6(2.79) + 8 = -8.74 < 0
Then, he should prints 2.79 thousands, that is, 2790 t-shirts to make maximum profits.
Replacing into profit equation:
p(x) = -(2.79)³ + 4(2.79)² + 2.79 = 12.209
that is, $12209