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Musya8 [376]
3 years ago
14

Becca Buy 1.5 pounds of grapes and paid $3.72 what was the cost per pound of grapes

Mathematics
1 answer:
Trava [24]3 years ago
4 0
3.72÷1.5=2.48
$2.48 per pound

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Find the minimum value of the function f(x)=x^2+5x-6
mash [69]
<h3><u>Explanation</u></h3>
  • Method 1 (Formula)

\begin{cases}h =  -  \frac{b}{2a}  \\ k =  \frac{4ac -  {b}^{2} }{2a}  \end{cases}

The vertex of Parabola is the maximum/minimum point depending on the value of a.

  • Find Vertex

<u>h-value</u>

h =  -  \frac{5}{2(1)}  \\ h =  -  \frac{5}{2}

<u>k-value</u>

k =  \frac{4(1)( - 6) -  {(5)}^{2} }{4(1)}  \\ k =  \frac{ - 24 - 25}{4}  \\ k =  \frac{ - 49}{4}  \\ k =  -  \frac{49}{4}

The minimum value is the value of k. Therefore the minimum value is - 49/4 at x = -5/2.

  • Method 2 (Derivative)

This is Calculus method. We simply differentiate the function then substitute y' = 0.

  • Differentiate Function

f'(x) = 2 {x}^{2 - 1}  +  {5x}^{1 - 1}  - 0 \\ f'(x) = 2x + 5

Substitute f'(x) = 0

0 = 2x + 5 \\  - 5 = 2x \\   -  \frac{5}{2}  = x

Substitute x = -5/2 in the original equation.

f(x) =  {( -  \frac{5}{2} )}^{2}  + 5( -   \frac{5}{2} ) - 6 \\ f(x) =  \frac{25}{4}  -  \frac{25}{2}  - 6 \\ f(x) =  \frac{25}{4}  -  \frac{50}{4}  -  \frac{24}{4}  \\ f(x) =  \frac{25}{4}  -  \frac{74}{4}  \\ f(x) = -   \frac{49}{4}

<h3><u>Answer</u><u /></h3>

<u>\sf{the  \:  \: minimum  \:  \: value \:  \:  is   \:  \: -  \frac{49}{4}  \:  \: at \:  \:  x =  -  \frac{5}{2} }</u>

4 0
3 years ago
Under his cell phone plan, Henry pays a flat cost of $63.50 per month and $5 per gigabyte. He wants to keep his bill at $77.50 p
Murrr4er [49]

Answer:

2

Step-by-step explanation:

77.50 - 63.50 = 14

per gigabyte $5 + 5 =10

so answer is 2

3 0
2 years ago
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