Answer: Hence Pair( x, y) = [ 105/2, 105/2]
Step-by-step explanation:
Given that;
Among all pairs of numbers with a sum of 105;
the pair whose product is maximum = ?
so let pairs of numbers with a sum of 105 be x and y respectively
x + y = 105
let y = 105 - x
now
product = xy = x( 105 - x ) = 105x - x²
now
p(x) = 105x - x²
for maximum value of p
dp/dx =0
⇒ dp/dx = 105 - 2x = 0
2x = 105
x = 105/2
y + x = 105
y = 105 - x
y = 105 - 105/2 = 105/2
Hence Pair( x, y) = [ 105/2, 105/2]
Answer: 12+n
Step-by-step explanation:
2.77 × 10 ^ ( -3 ) is the answer
Answer:
x = ±6
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
- Equality Properties
<u>Algebra II</u>
- Extraneous solutions and multiple answers/roots
Step-by-step explanation:
<u>Step 1: Define</u>
-x² = -36
<u>Step 2: Solve for </u><em><u>x</u></em>
- Divide -1 on both sides: x² = 36
- Square root both sides: x = ±6
<u>Step 3: Check</u>
<em>Plug in x to verify it's a solution.</em>
- Substitute in -6: -(-6)² = -36
- Exponents: -(36) = -36
- Multiply: -36 = -36
- Substitute in 6: -(6)² = -36
- Exponents: -(36) = -36
- Multiply: -36 = -36
Here we see that both -6 and 6 do indeed work as solutions.
∴ x = ±6 are both solutions to the equation.
Step-by-step explanation:
Overtime rate= r+50%= 1.5r
Regular hours= 800/r
Overtime hours= 240/1.5r
Total hours worked
