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slavikrds [6]
3 years ago
15

Scott made 3 identical necklaces, each having beads and a pendant. The total cost of the beads and pendants for all 3 necklaces

was $14.40.If the beads cost a total of $5.70, how much did each pendant cost?
Mathematics
1 answer:
pantera1 [17]3 years ago
6 0

Answer:

$2.90

Step-by-step explanation:

<u>Lets look at the information given:</u>

Scott made 3 necklaces

$14.40 is the cost for both the beads and pendants for all 3 necklaces

$5.70 was the cost of just beads for all 3 necklaces

Each necklace has 1 pendant

The first step to solving this equation is subtracting the cost of the beads from the total cost for the necklaces:

$14.40 - $5.70= $8.70

Now we know that cost for the 3 pendants for all 3 necklaces was $8.70, but we need to find how much EACH pendant costs. To find out, we simply divide the total cost for all 3 pendants by 3:

$8.70 ÷ 3 = $2.90

So each pendent costs $2.90

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Using the asymptote concept, we have that:

  • The vertical asymptote is x = 9.
  • The horizontal asymptote is y = 3.
  • The end behavior is that as x \rightarrow \infty, y \rightarrow 3.

<h3>What are the asymptotes of a function f(x)?</h3>

  • The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
  • The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.

In this problem, the function is:

f(x) = \frac{3x}{x - 9}

For the vertical asymptote, we have that:

x - 9 = 0 -> x = 9.

For the horizontal asymptote:

y = \lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} \frac{3x}{x - 9} = \lim_{x \rightarrow \infty} \frac{3x}{x} = \lim_{x \rightarrow \infty} 3 = 3

Hence, the end behavior is that as x \rightarrow \infty, y \rightarrow 3.

More can be learned about asymptotes at brainly.com/question/16948935

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8 0
2 years ago
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Step-by-step explanation:

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A rancher plans to make 4 identical and adjacent rectangular pens against a barn (see figure below), each with an area of 100 m^
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Answer:

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Step-by-step explanation:

In calculus terms, you can use the formula for the perimeter which is 2l + 2w, and the area l × w.

Then since the area is 100

l × w = 100. So w = 100/l

Then substitute this into the perimeter formula.

w = 100/l → 2l + 2(w) = 2l + 2(100/l) = 2l + 200/l.

Then take the derivative d/dx [take the derivative of a quantity with respect to x], by using a simpler method known as the power rule:

d/dx[x^n] = nx^n-1

so p = 2l + 200/l becomes p' = 2 - 200/l^2

Since the derivative of a constant is 0, to solve for l, set p' to 0

0 = 2 - 200/l^2 → -200/l^2 = -2 → 200/l^2 = 2 → 2l^2 = 200 → l^2 = 100 → l = √100, l = 10.

Now that we know the length is 10, We can substitute the length in the original equation to find the width.

l = 10 → w = 100/l → w = 100/10, w = 10.

Therefore the perimeter of each rectangular pen is 40, with a length of 10 and width of 10.

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