Answer: 32.14 after round off it will be 32
Step-by-step explanation:
This is how to round 32.14 to the nearest whole number. In other words, this is how to round 32.14 to the nearest integer.
32.14 has two parts. The integer part to the left of the decimal point and the fractional part to the right of the decimal point:
Integer Part: 32
Fractional Part: 14
Our goal is to round it so we only have an integer part using the following rules:
If the first digit in the fractional part of 32.14 is less than 5 then we simply remove the fractional part to get the answer.
If the first digit in the fractional part of 32.14 is 5 or above, then we add 1 to the integer part and remove the fractional part to get the answer.
The first digit in the fractional part is 1 and 1 is less than 5. Therefore, we simply remove the fractional part to get 32.14 rounded to the nearest whole number as:
32
<u>Annotation</u>General formula for distance-time-velocity relationship is as following
d = v × t
The velocity of the first car will be v₁, the time is 2 hours, the distance will be d₁.
The velocity of the second car will be v₂, the time is 2 hours, the distance will be d₂.
One of them traveling 5 miles per hour faster than the others. That means the velocity of the first car is 5 miles per hour more than the velocity of the second car.
v₁ = v₂ + 5 (first equation)
The distance of the two cars after two hours will be 262 miles apart. Because they go to opposite direction, we could write it as below.
d₁ + d₂ = 262 (second equation)
Plug the d-v-t relationship to the second equationd₁ + d₂ = 262
v₁ × t + v₂ × t = 262
v₁ × 2 + v₂ × 2 = 262
2v₁ + 2v₂ = 262
Plug the v₁ as (v₂+5) from the first equation2v₁ + 2v₂ = 262
2(v₂ + 5) + 2v₂ = 262
2v₂ + 10 + 2v₂ = 262
4v₂ + 10 = 262
4v₂ = 252
v₂ = 252/4
v₂ = 63
The second car is 63 mph fast.Find the velocity of the first car, use the first equationv₁ = v₂ + 5
v₁ = 63 + 5
v₁ = 68
The first car is 68 mph fast.
Answer


Answer:
What is the constant variation of Y =- 2 3x?
The constant of variation, k , is 23 .
What is the constant variation of Y 1 2x?
The constant of variation, k , is 12 .
Step-by-step explanation:
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Answer:
Slope of the Curve: 
Equation of Tangent Line: y + 3 = -3/2(x + 2)
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
Point-Slope Form: y - y₁ = m(x - x₁)
- x₁ - x coordinate
- y₁ - y coordinate
- m - slope
<u>Calculus</u>
The definition of a derivative is the slope of the tangent line.
Basic Power Rule:
- f(x) = cxⁿ
- f’(x) = c·nxⁿ⁻¹
Quotient Rule: ![\frac{d}{dx} [\frac{f(x)}{g(x)} ]=\frac{g(x)f'(x)-g'(x)f(x)}{g^2(x)}](https://tex.z-dn.net/?f=%5Cfrac%7Bd%7D%7Bdx%7D%20%5B%5Cfrac%7Bf%28x%29%7D%7Bg%28x%29%7D%20%5D%3D%5Cfrac%7Bg%28x%29f%27%28x%29-g%27%28x%29f%28x%29%7D%7Bg%5E2%28x%29%7D)
Step-by-step explanation:
<u>Step 1: Define</u>
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<u>Step 2: Take Derivative</u>
- Quotient Rule:

- Multiply:

- Subtract:

<u>Step 3: Find Instantaneous Derivative</u>
- Substitute in <em>x</em>:

- Exponents:

- Simplify:

This value shows the slope of the tangent line at the exact value of x = 2.
- Substitute: y + 3 = -3/2(x + 2)