Answer:
Substitute –3 for x and 5 for h in the difference quotient.
Step-by-step explanation:
The difference quotient for the function f(x) is 21x² + 21xh + 7h² + 2. Now, we know that the difference quotient equal f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. The change in x is h = x₂ - x₁. So, if x changes from x = -3 to x = 2, where x₁ = -3 and x₂ = 2, h = x₂ - x₁ = 2 - (-3) = 2 + 3 = 5.
So to find the average rate of change of f(x) from x = -3 to x = 2, we substitute x = -3 and h = 5 into the difference equation f(x + h) - f(x) = 21x² + 21xh + 7h² + 2. Since, x starts at x = -3 and increases by 5 units to x = 2.
When the given exponential expression (g³6³p⁷) / (6g²p²p) is simplified, it is equal to 6gp⁴.
<h3>What is an Expression?</h3>
In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
The given exponential expression can be simplified as shown below.
(g³ × 6³ × p⁷) / (6 × g² × p² × p)
Using the exponential property, xⁿ × xᵇ = x⁽ⁿ⁺ᵇ⁾,
= (6³ × g³ × p⁷) / (6 × g² × p³)
= (6³/6) × (g³/g²) × (p⁷/p³)
Using the exponential property, xⁿ/xᵇ = x⁽ⁿ⁻ᵇ⁾
= 6⁽³⁻¹⁾ × g⁽³⁻²⁾ × p⁽⁷⁻³⁾
= 6¹ × g¹ × p⁴
= 6gp⁴
Hence, when the given exponential expression (g³6³p⁷) / (6g²p²p) is simplified, it is equal to 6gp⁴.
Learn more about Expression here:
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Answer:
<h2>BC = 11.9</h2>
Step-by-step explanation:
To solve for BC we use sine
sin ∅ = opposite / hypotenuse
From the question
AC is the hypotenuse
BC is the opposite
So we have
sin 58 = BC / AC
sin 58 = BC / 14
BC = 14 sin 58
BC = 11.87
BC = 11.9 to one decimal place
Hope this helps you
Answer:
He must work 34 hours
Step-by-step explanation:
187×20= 3740
3740÷110= 34
