Answer:
y"(2, 1) = -5
Step-by-step explanation:
Step 1: Define implicit differentiation
5 - y² = x²
Step 2: Find dy/dx
- Take implicit differentiation: -2yy' = 2x
- Isolate y': y' = 2x/-2y
- Isolate y': y' = -x/y
Step 3: Find d²y/dx²
- Quotient Rule: y'' = [y(-1) - y'(-x)] / y²
- Substitute y': y" = [-y - (-x/y)(-x)] / y²
- Simplify: y" = [-y - x²/y] / y²
- Multiply top/bottom by y: y" = (-y² - x²) / y³
- Factor negative: y" = -(y² + x²) / y³
Step 4: Substitute and Evaluate
y"(2, 1) = -(1² + 2²) / 1³
y"(2, 1) = -(1 + 4) / 1
y"(2, 1) = -5/1
y"(2, 1) = -5
2 hours because 65 miles is = to one hour
130=65x2
130 miles is =to 2 hours
Answer:
40 nickels
Step-by-step explanation:
1 2/5 to 2 1/3 = 7/5 : 7/3
= 21/15 : 35/15
21/15 = 24
35/15 = x
(35/15 * 24) / 21/15
∴ 56 ÷ 21/15
= 40 nickels
Answer: 7/16
Step-by-step explanation:
Distance of the relay race = 1 3/4 miles
Number of runners for the relay team = 4 runners
Distance to be run by each runner will be:
= Distance of the relay race / Number of runners
= 1 3/4 ÷ 4
= 7/4 ÷ 4
= 7/4 × 1/4
= 7/16
Each runner will run 7/16 miles
Answer:
A
Step-by-step explanation:
<h3><u>Commutative Property</u></h3>
- (a + b) + c = c + (a + b)
<u>(40.50 + 56.95) + 25.75</u> ; <u>25.75 + (40.50 + 56.95)</u> correctly represent the situation using the commutative property.
