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3 years ago

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Abbi invested $1,300 in a certificate of deposit with a simple interest rate of 3%. Find the interest earned in 6 years. Then fi

nd the total of principal plus interest.
A.)$234.00; $1,534.00
B.)$23,400.00; $24,700.00
C.)$39.00; $1,339.00
D.)$252.27; $1,552.27

1 answer:

drek231 [11]3 years ago

5 0

Your answer is A..................................

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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.

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

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

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3 years ago

In which step did Viet make an error? 2 ( x − 3 ) 2 + 4 = 102 2 ( x − 3 ) 2 = 106 Step 1 ( x − 3 ) 2 = 53 Step 2 x − 3 = ± 53 St

vitfil [10]

Answer:

Step 2

Step-by-step explanation:

Given

Step 1: $2(x - 3)^2 + 4 = 102$

Step 2: $2(x - 3)^2 = 106$

Step 3: $x - 3 = \±\sqrt{53$

Step 4: $x = \±\sqrt{53} + 3$

Required

Where did Viet made an error?

The step 1 indicates the original question.

$2(x - 3)^2 + 4 = 102$

To get to step 2, we have to subtract 4 from both sides of the equation.

$2(x - 3)^2 + 4 -4= 102 - 4$

$2(x - 3)^2 = 98$

However, the above expression is different from Viet's evaluation.

<em>Hence, we can conclude that Viet made an error in step 2</em>

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