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KIM [24]
3 years ago
6

I'm stuck, could someone help me?

Mathematics
1 answer:
disa [49]3 years ago
6 0
H = -0.5x² + 0.5x + 15 <em>where</em> x = distance from stump and h = height
We want to find the value of x when h = 10.92.
10.92 = -0.5x² + 0.5x + 15
There are many ways to solve a quadratic like this, let's start by subtracting 10.92.
0 = -0.5x² + 0.5x + 4.08
Now we have everything on one side. Let's solve for x.
Since these numbers aren't whole, I wouldn't try to factor/split the middle.
You could either complete the square or use the quadratic formula.
<u>
</u><u>Completing the square</u>
-0.5x² + 0.5x + 4.08 = 0
We need our x² coefficeint to be 1, so let's multiply by -2.
x² - x - 8.16 = 0
Move the constant to the other side.
x² - x = 8.16
Halve the x coefficient -1 to get -0.5, then square it to get 0.25.
Add this to each side.
x² - x + 0.25 = 8.41
Now we have a perfect square trinomial on the left we can factor...
(x-0.5)² = 8.41
Take the square root of each side...
x-0.5 = <span>±2.9
</span>Add that 0.5 to each side...
x = 0.5<span>±2.9
</span>Of course, the frog can't be a negative distance x from the stump, so we have to take the positive value x = 3.4.
<u>
</u><u>Using the quadratic formula
</u>-0.5x² + 0.5x + 4.08 = 0
I'm going to multiply everything by 100 just to get rid of any decimal points.
-50x² + 50x + 408 = 0
To use the quadratic formula:
The solution to any quadratic ax² + bx + c is x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}.
In this case, a = -50, b = 50, and c = 408. Let's input these into our formula.

x=\frac{-50\pm\sqrt{50^2-4(-50)(408)}}{2(-50)}=\frac{-50\pm\sqrt{2500+81600}}{-100}=\frac{-50\pm{84100}}{-100}

=\frac{-50\pm290}{-100}=\frac{240}{-100}\ or\ \frac{-340}{-100}=-0.24\ or\ 0.34

Of course, the frog can't be a negative distance x from the stump, so we have to take the positive value x = 0.34.
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The correct answers are B and C.

Since the mixture requires 5 mL of black wax and 6 mL of white wax, we want multiples of these numbers; specifically, we need multiples that are the same number of times away.

A does not work; 10 is 5*2 and 24 is 6*4.  These won't be in the same ratio.

B works; 15 is 5*3 and 18 is 6*3.  These have the same ratio.

C works; 35 is 5*7 and 42 is 6*7.  These have the same ratio.

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3 years ago
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An arena receives $1,700 per event for 12 concerts. If the costs for this sponsorship total $14,000, what is the profit margin f
miss Akunina [59]

Answer:

total profit margin for all 12 concert is $6,400.

profit margin for all one concert is  $533.33

Step-by-step explanation:

Amount of money received for one event = $1700

Total no of concert = 12

Total money received for 12 event = Amount of money received for one event * Total no of concert

Total money received for 12 event  = $1700 *12 = $20,400

Total cost of sponsorship = $14,000

Profit margin is the difference money invested and money earned.

here total investment is $14,000

Total money earned is  $20,400

Therefore profit margin = money earned - total investment

= $20,400 -  $14,000 = $6,400

Therefore total profit margin for all 12 concert is $6,400.

However to calculate profit margin for one concert we can simply divide the total profit margin for all 12 concert by no of concert (i.e 12)

profit margin for one concert = total profit margin for all 12 concert/total no of concert  = $6,400/12 = $533.33

profit margin for all one concert is  $533.33

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Nata [24]

Answer:

  x ≈ {0.653059729092, 3.75570086464}

Step-by-step explanation:

A graphing calculator can tell you the roots of ...

  f(x) = ln(x) -1/(x -3)

are near 0.653 and 3.756. These values are sufficiently close that Newton's method iteration can find solutions to full calculator precision in a few iterations.

In the attachment, we use g(x) as the iteration function. Since its value is shown even as its argument is being typed, we can start typing with the graphical solution value, then simply copy the digits of the iterated value as they appear. After about 6 or 8 input digits, the output stops changing, so that is our solution.

Rounded to 6 decimal places, the solutions are {0.653060, 3.755701}.

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A similar method can be used on a calculator such as the TI-84. One function can be defined a.s f(x) is above. Another can be defined as g(x) is in the attachment, by making use of the calculator's derivative function. After the first g(0.653) value is found, for example, remaining iterations can be g(Ans) until the result stops changing,

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